text: 460,113,1273128407392571394,2566842619,Michal Šustr,"Search has played a fundamental role in computer game research since the very beginning. But what is sound search in imperfect information games?  Our new theoretical paper <LINK> ! <LINK> Unlike in perfect info games, players may need to randomize their strategies in order to play optimally. Think of Poker - if you always bet with strong cards or fold with weak ones, your opponent will figure this out during repeated play and learn to exploit you. <LINK> In two-player zero-sum games we typically look for strong strategies with guarantees against worst-case adversaries: Nash equilibria (or rather their epsilon-approximation). In ""Sound Search in Imperfect Information Games"" we argue that the fixed-strategy definitions of exploitability and epsilon-Nash equilibria are however ill suited to measure the worst-case performance of an **online** (search) algorithm. In fact, the issues with evaluating the worst-case performance are quite subtle and they are very easy to overlook! This has led to a number of discussions with co-authors :) One of the basic problems is that the play strategy may be only locally consistent: it corresponds to some epsilon-equilibrium for a state, but ""stitching"" different strategies together across all states may not yield epsilon-equilibrium anymore! We thus formalize epsilon-soundness, a concept that connects the worst-case performance of an online algorithm to the performance of an (offline) epsilon-Nash equilibrium. We introduce also a consistency framework -- a hierarchy that connects the behavior of an online algorithm to a Nash equilibrium. Our multiple levels of consistency describe in what sense an online algorithm plays ""just like a fixed Nash equilibrium''. Our definition of soundness and the consistency hierarchy finally provide appropriate tools to analyze online algorithms in imp. info. games. We inspect some of the previous online algorithms in a new light, bringing new insights into their worst case performance guarantees. Finally, I'd like to express my gratitude to @Lifrordi, M. Moravcik, N. Burch, @sharky6000 and @MichaelHBowling for the collaboration! Thank you all for your input, comments and discussions, it is very much appreciated.",https://arxiv.org/abs/2006.08740,"Search has played a fundamental role in computer game research since the very beginning. And while online search has been commonly used in perfect information games such as Chess and Go, online search methods for imperfect information games have only been introduced relatively recently. This paper addresses the question of what is a sound online algorithm in an imperfect information setting of two-player zero-sum games. We argue that the~fixed-strategy~definitions of exploitability and $\epsilon$-Nash equilibria are ill-suited to measure an online algorithm's worst-case performance. We thus formalize $\epsilon$-soundness, a concept that connects the worst-case performance of an online algorithm to the performance of an $\epsilon$-Nash equilibrium. As $\epsilon$-soundness can be difficult to compute in general, we introduce a consistency framework -- a hierarchy that connects an online algorithm's behavior to a Nash equilibrium. These multiple levels of consistency describe in what sense an online algorithm plays ""just like a fixed Nash equilibrium"". These notions further illustrate the difference between perfect and imperfect information settings, as the same consistency guarantees have different worst-case online performance in perfect and imperfect information games. The definitions of soundness and the consistency hierarchy finally provide appropriate tools to analyze online algorithms in repeated imperfect information games. We thus inspect some of the previous online algorithms in a new light, bringing new insights into their worst-case performance guarantees. ",Sound Algorithms in Imperfect Information Games,10,"['Search has played a fundamental role in computer game research since the very beginning. But what is sound search in imperfect information games? \n\nOur new theoretical paper <LINK> ! <LINK>', 'Unlike in perfect info games, players may need to randomize their strategies in order to play optimally. Think of Poker - if you always bet with strong cards or fold with weak ones, your opponent will figure this out during repeated play and learn to exploit you. https://t.co/VnpBNhZmg7', 'In two-player zero-sum games we typically look for strong strategies with guarantees against worst-case adversaries: Nash equilibria (or rather their epsilon-approximation).', 'In ""Sound Search in Imperfect Information Games"" we argue that the fixed-strategy definitions of exploitability and epsilon-Nash equilibria are however ill suited to measure the worst-case performance of an **online** (search) algorithm.', 'In fact, the issues with evaluating the worst-case performance are quite subtle and they are very easy to overlook! This has led to a number of discussions with co-authors :)', 'One of the basic problems is that the play strategy may be only locally consistent: it corresponds to some epsilon-equilibrium for a state, but ""stitching"" different strategies together across all states may not yield epsilon-equilibrium anymore!', 'We thus formalize epsilon-soundness, a concept that connects the worst-case performance of an online algorithm to the performance of an (offline) epsilon-Nash equilibrium.', 'We introduce also a consistency framework -- a hierarchy that connects the behavior of an online algorithm to a Nash equilibrium. Our multiple levels of consistency describe in what sense an online algorithm plays ""just like a fixed Nash equilibrium\'\'.', 'Our definition of soundness and the consistency hierarchy finally provide appropriate tools to analyze online algorithms in imp. info. games. We inspect some of the previous online algorithms in a new light, bringing new insights into their worst case performance guarantees.', ""Finally, I'd like to express my gratitude to @Lifrordi, M. Moravcik, N. Burch, @sharky6000 and @MichaelHBowling for the collaboration! Thank you all for your input, comments and discussions, it is very much appreciated.""]",20,06,2214