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Optimal Estimation of High Dimensional Smooth Additive Function Based on Noisy Observations | null | Given $\bx_j = \btheta + \bepsilon_j$, $j=1,...,n$ where $\btheta \in \RR^d$ is an unknown parameter and $\bepsilon_j$ are i.i.d. Gaussian noise vectors, we study the estimation of $f(\btheta)$ for a given smooth function $f:\RR^d \rightarrow \RR$ equipped with an additive structure. We inherit the idea from a recent work which introduced an effective bias reduction technique through iterative bootstrap and derive a bias-reducing estimator. By establishing its normal approximation results, we show that the proposed estimator can achieve asymptotic normality with a looser constraint on smoothness compared with general smooth function due to the additive structure. Such results further imply that the proposed estimator is asymptotically efficient. Both upper and lower bounds on mean squared error are proved which shows the proposed estimator is minimax optimal for the smooth class considered. Numerical simulation results are presented to validate our analysis and show its superior performance of the proposed estimator over the plug-in approach in terms of bias reduction and building confidence intervals. | Fan Zhou, Ping Li | null | null | 2,021 | icml |
Provably Efficient Reinforcement Learning for Discounted MDPs with Feature Mapping | null | Modern tasks in reinforcement learning have large state and action spaces. To deal with them efficiently, one often uses predefined feature mapping to represent states and actions in a low dimensional space. In this paper, we study reinforcement learning for discounted Markov Decision Processes (MDPs), where the transition kernel can be parameterized as a linear function of certain feature mapping. We propose a novel algorithm which makes use of the feature mapping and obtains a $\tilde O(d\sqrt{T}/(1-\gamma)^2)$ regret, where $d$ is the dimension of the feature space, $T$ is the time horizon and $\gamma$ is the discount factor of the MDP. To the best of our knowledge, this is the first polynomial regret bound without accessing a generative model or making strong assumptions such as ergodicity of the MDP. By constructing a special class of MDPs, we also show that for any algorithms, the regret is lower bounded by $\Omega(d\sqrt{T}/(1-\gamma)^{1.5})$. Our upper and lower bound results together suggest that the proposed reinforcement learning algorithm is near-optimal up to a $(1-\gamma)^{-0.5}$ factor. | Dongruo Zhou, Jiafan He, Quanquan Gu | null | null | 2,021 | icml |
Probabilistic Sequential Shrinking: A Best Arm Identification Algorithm for Stochastic Bandits with Corruptions | null | We consider a best arm identification (BAI) problem for stochastic bandits with adversarial corruptions in the fixed-budget setting of T steps. We design a novel randomized algorithm, Probabilistic Sequential Shrinking(u) (PSS(u)), which is agnostic to the amount of corruptions. When the amount of corruptions per step (CPS) is below a threshold, PSS(u) identifies the best arm or item with probability tending to 1 as T{\rightarrow}$\infty$. Otherwise, the optimality gap of the identified item degrades gracefully with the CPS.We argue that such a bifurcation is necessary. In PSS(u), the parameter u serves to balance between the optimality gap and success probability. The injection of randomization is shown to be essential to mitigate the impact of corruptions. To demonstrate this, we design two attack strategies that are applicable to any algorithm. We apply one of them to a deterministic analogue of PSS(u) known as Successive Halving (SH) by Karnin et al. (2013). The attack strategy results in a high failure probability for SH, but PSS(u) remains robust. In the absence of corruptions, PSS(2)’s performance guarantee matches SH’s. We show that when the CPS is sufficiently large, no algorithm can achieve a BAI probability tending to 1 as T{\rightarrow}$\infty$. Numerical experiments corroborate our theoretical findings. | Zixin Zhong, Wang Chi Cheung, Vincent Tan | null | null | 2,021 | icml |
Fused Acoustic and Text Encoding for Multimodal Bilingual Pretraining and Speech Translation | null | Recently, representation learning for text and speech has successfully improved many language related tasks. However, all existing methods suffer from two limitations: (a) they only learn from one input modality, while a unified representation for both speech and text is needed by tasks such as end-to-end speech translation, and as a result, (b) they can not exploit various large-scale text and speech data and their performance is limited by the scarcity of parallel speech translation data. To address these problems, we propose a Fused Acoustic and Text Masked Language Model (FAT-MLM) which jointly learns a unified representation for both acoustic and text input from various types of corpora including parallel data for speech recognition and machine translation, and even pure speech and text data. Within this cross-modal representation learning framework, we further present an end-to-end model for Fused Acoustic and Text Speech Translation (FAT-ST). Experiments on three translation directions show that by fine-tuning from FAT-MLM, our proposed speech translation models substantially improve translation quality by up to +5.9 BLEU. | Renjie Zheng, Junkun Chen, Mingbo Ma, Liang Huang | null | null | 2,021 | icml |
Amortized Conditional Normalized Maximum Likelihood: Reliable Out of Distribution Uncertainty Estimation | null | While deep neural networks provide good performance for a range of challenging tasks, calibration and uncertainty estimation remain major challenges, especially under distribution shift. In this paper, we propose the amortized conditional normalized maximum likelihood (ACNML) method as a scalable general-purpose approach for uncertainty estimation, calibration, and out-of-distribution robustness with deep networks. Our algorithm builds on the conditional normalized maximum likelihood (CNML) coding scheme, which has minimax optimal properties according to the minimum description length principle, but is computationally intractable to evaluate exactly for all but the simplest of model classes. We propose to use approximate Bayesian inference technqiues to produce a tractable approximation to the CNML distribution. Our approach can be combined with any approximate inference algorithm that provides tractable posterior densities over model parameters. We demonstrate that ACNML compares favorably to a number of prior techniques for uncertainty estimation in terms of calibration when faced with distribution shift. | Aurick Zhou, Sergey Levine | null | null | 2,021 | icml |
Few-shot Language Coordination by Modeling Theory of Mind | null | No man is an island. Humans develop the ability to communicate with a large community by coordinating with different interlocutors within short conversations. This ability is largely understudied by the research on building neural language communicative agents. We study the task of few-shot language coordination: agents quickly adapting to their conversational partners’ language abilities. Different from current communicative agents trained with self-play, we in- investigate this more general paradigm by requiring the lead agent to coordinate with a population of agents each of whom has different linguistic abilities. This leads to a general agent able to quickly adapt to communicating with unseen agents in the population. Unlike prior work, success here requires the ability to model the partner’s beliefs, a vital component of human communication. Drawing inspiration from the study of theory-of-mind (ToM; Premack & Woodruff (1978)), we study the effect of the speaker explicitly modeling the listener’s mental state. Learning by communicating with a population, the speakers, as shown in our experiments, acquire the ability to learn to predict the reactions of their partner upon various messages on-the-fly. The speaker’s predictions for the future actions help it generate the best instructions in order to maximize communicative goal with message costs. To examine our hypothesis that the instructions generated with ToM modeling yield better communication per- performance, we employ our agents in both a referential game and a language navigation task. Positive results from our experiments also hint at the importance of explicitly modeling language acquisition as a socio-pragmatic progress. | Hao Zhu, Graham Neubig, Yonatan Bisk | null | null | 2,021 | icml |
Clusterability as an Alternative to Anchor Points When Learning with Noisy Labels | null | The label noise transition matrix, characterizing the probabilities of a training instance being wrongly annotated, is crucial to designing popular solutions to learning with noisy labels. Existing works heavily rely on finding “anchor points” or their approximates, defined as instances belonging to a particular class almost surely. Nonetheless, finding anchor points remains a non-trivial task, and the estimation accuracy is also often throttled by the number of available anchor points. In this paper, we propose an alternative option to the above task. Our main contribution is the discovery of an efficient estimation procedure based on a clusterability condition. We prove that with clusterable representations of features, using up to third-order consensuses of noisy labels among neighbor representations is sufficient to estimate a unique transition matrix. Compared with methods using anchor points, our approach uses substantially more instances and benefits from a much better sample complexity. We demonstrate the estimation accuracy and advantages of our estimates using both synthetic noisy labels (on CIFAR-10/100) and real human-level noisy labels (on Clothing1M and our self-collected human-annotated CIFAR-10). Our code and human-level noisy CIFAR-10 labels are available at https://github.com/UCSC-REAL/HOC. | Zhaowei Zhu, Yiwen Song, Yang Liu | null | null | 2,021 | icml |
Towards Defending against Adversarial Examples via Attack-Invariant Features | null | Deep neural networks (DNNs) are vulnerable to adversarial noise. Their adversarial robustness can be improved by exploiting adversarial examples. However, given the continuously evolving attacks, models trained on seen types of adversarial examples generally cannot generalize well to unseen types of adversarial examples. To solve this problem, in this paper, we propose to remove adversarial noise by learning generalizable invariant features across attacks which maintain semantic classification information. Specifically, we introduce an adversarial feature learning mechanism to disentangle invariant features from adversarial noise. A normalization term has been proposed in the encoded space of the attack-invariant features to address the bias issue between the seen and unseen types of attacks. Empirical evaluations demonstrate that our method could provide better protection in comparison to previous state-of-the-art approaches, especially against unseen types of attacks and adaptive attacks. | Dawei Zhou, Tongliang Liu, Bo Han, Nannan Wang, Chunlei Peng, Xinbo Gao | null | null | 2,021 | icml |
Expressive 1-Lipschitz Neural Networks for Robust Multiple Graph Learning against Adversarial Attacks | null | Recent findings have shown multiple graph learning models, such as graph classification and graph matching, are highly vulnerable to adversarial attacks, i.e. small input perturbations in graph structures and node attributes can cause the model failures. Existing defense techniques often defend specific attacks on particular multiple graph learning tasks. This paper proposes an attack-agnostic graph-adaptive 1-Lipschitz neural network, ERNN, for improving the robustness of deep multiple graph learning while achieving remarkable expressive power. A K_l-Lipschitz Weibull activation function is designed to enforce the gradient norm as K_l at layer l. The nearest matrix orthogonalization and polar decomposition techniques are utilized to constraint the weight norm as 1/K_l and make the norm-constrained weight close to the original weight. The theoretical analysis is conducted to derive lower and upper bounds of feasible K_l under the 1-Lipschitz constraint. The combination of norm-constrained weight and activation function leads to the 1-Lipschitz neural network for expressive and robust multiple graph learning. | Xin Zhao, Zeru Zhang, Zijie Zhang, Lingfei Wu, Jiayin Jin, Yang Zhou, Ruoming Jin, Dejing Dou, Da Yan | null | null | 2,021 | icml |
Spectral vertex sparsifiers and pair-wise spanners over distributed graphs | null | Graph sparsification is a powerful tool to approximate an arbitrary graph and has been used in machine learning over graphs. As real-world networks are becoming very large and naturally distributed, distributed graph sparsification has drawn considerable attention. In this work, we design communication-efficient distributed algorithms for constructing spectral vertex sparsifiers, which closely preserve effective resistance distances on a subset of vertices of interest in the original graphs, under the well-established message passing communication model. We prove that the communication cost approximates the lower bound with only a small gap. We further provide algorithms for constructing pair-wise spanners which approximate the shortest distances between each pair of vertices in a target set, instead of all pairs, and incur communication costs that are much smaller than those of existing algorithms in the message passing model. Experiments are performed to validate the communication efficiency of the proposed algorithms under the guarantee that the constructed sparsifiers have a good approximation quality. | Chunjiang Zhu, Qinqing Liu, Jinbo Bi | null | null | 2,021 | icml |
Demystifying Inductive Biases for (Beta-)VAE Based Architectures | null | The performance of Beta-Variational-Autoencoders and their variants on learning semantically meaningful, disentangled representations is unparalleled. On the other hand, there are theoretical arguments suggesting the impossibility of unsupervised disentanglement. In this work, we shed light on the inductive bias responsible for the success of VAE-based architectures. We show that in classical datasets the structure of variance, induced by the generating factors, is conveniently aligned with the latent directions fostered by the VAE objective. This builds the pivotal bias on which the disentangling abilities of VAEs rely. By small, elaborate perturbations of existing datasets, we hide the convenient correlation structure that is easily exploited by a variety of architectures. To demonstrate this, we construct modified versions of standard datasets in which (i) the generative factors are perfectly preserved; (ii) each image undergoes a mild transformation causing a small change of variance; (iii) the leading VAE-based disentanglement architectures fail to produce disentangled representations whilst the performance of a non-variational method remains unchanged. | Dominik Zietlow, Michal Rolinek, Georg Martius | null | null | 2,021 | icml |
Accumulated Decoupled Learning with Gradient Staleness Mitigation for Convolutional Neural Networks | null | Gradient staleness is a major side effect in decoupled learning when training convolutional neural networks asynchronously. Existing methods that ignore this effect might result in reduced generalization and even divergence. In this paper, we propose an accumulated decoupled learning (ADL), which includes a module-wise gradient accumulation in order to mitigate the gradient staleness. Unlike prior arts ignoring the gradient staleness, we quantify the staleness in such a way that its mitigation can be quantitatively visualized. As a new learning scheme, the proposed ADL is theoretically shown to converge to critical points in spite of its asynchronism. Extensive experiments on CIFAR-10 and ImageNet datasets are conducted, demonstrating that ADL gives promising generalization results while the state-of-the-art methods experience reduced generalization and divergence. In addition, our ADL is shown to have the fastest training speed among the compared methods. | Huiping Zhuang, Zhenyu Weng, Fulin Luo, Toh Kar-Ann, Haizhou Li, Zhiping Lin | null | null | 2,021 | icml |
On the Convergence of Hamiltonian Monte Carlo with Stochastic Gradients | null | Hamiltonian Monte Carlo (HMC), built based on the Hamilton’s equation, has been witnessed great success in sampling from high-dimensional posterior distributions. However, it also suffers from computational inefficiency, especially for large training datasets. One common idea to overcome this computational bottleneck is using stochastic gradients, which only queries a mini-batch of training data in each iteration. However, unlike the extensive studies on the convergence analysis of HMC using full gradients, few works focus on establishing the convergence guarantees of stochastic gradient HMC algorithms. In this paper, we propose a general framework for proving the convergence rate of HMC with stochastic gradient estimators, for sampling from strongly log-concave and log-smooth target distributions. We show that the convergence to the target distribution in $2$-Wasserstein distance can be guaranteed as long as the stochastic gradient estimator is unbiased and its variance is upper bounded along the algorithm trajectory. We further apply the proposed framework to analyze the convergence rates of HMC with four standard stochastic gradient estimators: mini-batch stochastic gradient (SG), stochastic variance reduced gradient (SVRG), stochastic average gradient (SAGA), and control variate gradient (CVG). Theoretical results explain the inefficiency of mini-batch SG, and suggest that SVRG and SAGA perform better in the tasks with high-precision requirements, while CVG performs better for large dataset. Experiment results verify our theoretical findings. | Difan Zou, Quanquan Gu | null | null | 2,021 | icml |
Exploration in Approximate Hyper-State Space for Meta Reinforcement Learning | null | To rapidly learn a new task, it is often essential for agents to explore efficiently - especially when performance matters from the first timestep. One way to learn such behaviour is via meta-learning. Many existing methods however rely on dense rewards for meta-training, and can fail catastrophically if the rewards are sparse. Without a suitable reward signal, the need for exploration during meta-training is exacerbated. To address this, we propose HyperX, which uses novel reward bonuses for meta-training to explore in approximate hyper-state space (where hyper-states represent the environment state and the agent’s task belief). We show empirically that HyperX meta-learns better task-exploration and adapts more successfully to new tasks than existing methods. | Luisa M Zintgraf, Leo Feng, Cong Lu, Maximilian Igl, Kristian Hartikainen, Katja Hofmann, Shimon Whiteson | null | null | 2,021 | icml |
Batched Dueling Bandits | null | The K-armed dueling bandit problem, where the feedback is in the form of noisy pairwise comparisons, has been widely studied. Previous works have only focused on the sequential setting where the policy adapts after every comparison. However, in many applications such as search ranking and recommendation systems, it is preferable to perform comparisons in a limited number of parallel batches. We study the batched K-armed dueling bandit problem under two standard settings: (i) existence of a Condorcet winner, and (ii) strong stochastic transitivity and stochastic triangle inequality. For both settings, we obtain algorithms with a smooth trade-off between the number of batches and regret. Our regret bounds match the best known sequential regret bounds (up to poly-logarithmic factors), using only a logarithmic number of batches. We complement our regret analysis with a nearly-matching lower bound. Finally, we also validate our theoretical results via experiments on synthetic and real data. | Arpit Agarwal, Rohan Ghuge, Viswanath Nagarajan | null | null | 2,022 | icml |
Learning Fair Policies in Decentralized Cooperative Multi-Agent Reinforcement Learning | null | We consider the problem of learning fair policies in (deep) cooperative multi-agent reinforcement learning (MARL). We formalize it in a principled way as the problem of optimizing a welfare function that explicitly encodes two important aspects of fairness: efficiency and equity. We provide a theoretical analysis of the convergence of policy gradient for this problem. As a solution method, we propose a novel neural network architecture, which is composed of two sub-networks specifically designed for taking into account these two aspects of fairness. In experiments, we demonstrate the importance of the two sub-networks for fair optimization. Our overall approach is general as it can accommodate any (sub)differentiable welfare function. Therefore, it is compatible with various notions of fairness that have been proposed in the literature (e.g., lexicographic maximin, generalized Gini social welfare function, proportional fairness). Our method is generic and can be implemented in various MARL settings: centralized training and decentralized execution, or fully decentralized. Finally, we experimentally validate our approach in various domains and show that it can perform much better than previous methods, both in terms of efficiency and equity. | Matthieu Zimmer, Claire Glanois, Umer Siddique, Paul Weng | null | null | 2,021 | icml |
Provable Robustness of Adversarial Training for Learning Halfspaces with Noise | null | We analyze the properties of adversarial training for learning adversarially robust halfspaces in the presence of agnostic label noise. Denoting $\mathsf{OPT}_{p,r}$ as the best classification error achieved by a halfspace that is robust to perturbations of $\ell^{p}$ balls of radius $r$, we show that adversarial training on the standard binary cross-entropy loss yields adversarially robust halfspaces up to classification error $\tilde O(\sqrt{\mathsf{OPT}_{2,r}})$ for $p=2$, and $\tilde O(d^{1/4} \sqrt{\mathsf{OPT}_{\infty, r}})$ when $p=\infty$. Our results hold for distributions satisfying anti-concentration properties enjoyed by log-concave isotropic distributions among others. We additionally show that if one instead uses a non-convex sigmoidal loss, adversarial training yields halfspaces with an improved robust classification error of $O(\mathsf{OPT}_{2,r})$ for $p=2$, and $O(d^{1/4} \mathsf{OPT}_{\infty, r})$ when $p=\infty$. To the best of our knowledge, this is the first work showing that adversarial training provably yields robust classifiers in the presence of noise. | Difan Zou, Spencer Frei, Quanquan Gu | null | null | 2,021 | icml |
Hierarchical Shrinkage: Improving the accuracy and interpretability of tree-based models. | null | Decision trees and random forests (RF) are a cornerstone of modern machine learning practice. Due to their tendency to overfit, trees are typically regularized by a variety of techniques that modify their structure (e.g. pruning). We introduce Hierarchical Shrinkage (HS), a post-hoc algorithm which regularizes the tree not by altering its structure, but by shrinking the prediction over each leaf toward the sample means over each of its ancestors, with weights depending on a single regularization parameter and the number of samples in each ancestor. Since HS is a post-hoc method, it is extremely fast, compatible with any tree-growing algorithm and can be used synergistically with other regularization techniques. Extensive experiments over a wide variety of real-world datasets show that HS substantially increases the predictive performance of decision trees even when used in conjunction with other regularization techniques. Moreover, we find that applying HS to individual trees in a RF often improves its accuracy and interpretability by simplifying and stabilizing decision boundaries and SHAP values. We further explain HS by showing that it to be equivalent to ridge regression on a basis that is constructed of decision stumps associated to the internal nodes of a tree. All code and models are released in a full-fledged package available on Github | Abhineet Agarwal, Yan Shuo Tan, Omer Ronen, Chandan Singh, Bin Yu | null | null | 2,022 | icml |
Deep equilibrium networks are sensitive to initialization statistics | null | Deep equilibrium networks (DEQs) are a promising way to construct models which trade off memory for compute. However, theoretical understanding of these models is still lacking compared to traditional networks, in part because of the repeated application of a single set of weights. We show that DEQs are sensitive to the higher order statistics of the matrix families from which they are initialized. In particular, initializing with orthogonal or symmetric matrices allows for greater stability in training. This gives us a practical prescription for initializations which allow for training with a broader range of initial weight scales. | Atish Agarwala, Samuel S Schoenholz | null | null | 2,022 | icml |
A Functional Perspective on Learning Symmetric Functions with Neural Networks | null | Symmetric functions, which take as input an unordered, fixed-size set, are known to be universally representable by neural networks that enforce permutation invariance. These architectures only give guarantees for fixed input sizes, yet in many practical applications, including point clouds and particle physics, a relevant notion of generalization should include varying the input size. In this work we treat symmetric functions (of any size) as functions over probability measures, and study the learning and representation of neural networks defined on measures. By focusing on shallow architectures, we establish approximation and generalization bounds under different choices of regularization (such as RKHS and variation norms), that capture a hierarchy of functional spaces with increasing degree of non-linear learning. The resulting models can be learned efficiently and enjoy generalization guarantees that extend across input sizes, as we verify empirically. | Aaron Zweig, Joan Bruna | null | null | 2,021 | icml |
Learning of Cluster-based Feature Importance for Electronic Health Record Time-series | null | The recent availability of Electronic Health Records (EHR) has allowed for the development of algorithms predicting inpatient risk of deterioration and trajectory evolution. However, prediction of disease progression with EHR is challenging since these data are sparse, heterogeneous, multi-dimensional, and multi-modal time-series. As such, clustering is regularly used to identify similar groups within the patient cohort to improve prediction. Current models have shown some success in obtaining cluster representations of patient trajectories. However, they i) fail to obtain clinical interpretability for each cluster, and ii) struggle to learn meaningful cluster numbers in the context of imbalanced distribution of disease outcomes. We propose a supervised deep learning model to cluster EHR data based on the identification of clinically understandable phenotypes with regard to both outcome prediction and patient trajectory. We introduce novel loss functions to address the problems of class imbalance and cluster collapse, and furthermore propose a feature-time attention mechanism to identify cluster-based phenotype importance across time and feature dimensions. We tested our model in two datasets corresponding to distinct medical settings. Our model yielded added interpretability to cluster formation and outperformed benchmarks by at least 4% in relevant metrics. | Henrique Aguiar, Mauro Santos, Peter Watkinson, Tingting Zhu | null | null | 2,022 | icml |
PAC-Bayesian Bounds on Rate-Efficient Classifiers | null | We derive analytic bounds on the noise invariance of majority vote classifiers operating on compressed inputs. Specifically, starting from recent bounds on the true risk of majority vote classifiers, we extend the applicability of PAC-Bayesian theory to quantify the resilience of majority votes to input noise stemming from compression. The derived bounds are intuitive in binary classification settings, where they can be measured as expressions of voter differentials and voter pair agreement. By combining measures of input distortion with analytic guarantees on noise invariance, we prescribe rate-efficient machines to compress inputs without affecting subsequent classification. Our validation shows how bounding noise invariance can inform the compression stage for any majority vote classifier such that worst-case implications of bad input reconstructions are known, and inputs can be compressed to the minimum amount of information needed prior to inference. | Alhabib Abbas, Yiannis Andreopoulos | null | null | 2,022 | icml |
Sharp-MAML: Sharpness-Aware Model-Agnostic Meta Learning | null | Model-agnostic meta learning (MAML) is currently one of the dominating approaches for few-shot meta-learning. Albeit its effectiveness, the optimization of MAML can be challenging due to the innate bilevel problem structure. Specifically, the loss landscape of MAML is much more complex with possibly more saddle points and local minimizers than its empirical risk minimization counterpart. To address this challenge, we leverage the recently invented sharpness-aware minimization and develop a sharpness-aware MAML approach that we term Sharp-MAML. We empirically demonstrate that Sharp-MAML and its computation-efficient variant can outperform the plain-vanilla MAML baseline (e.g., +3% accuracy on Mini-Imagenet). We complement the empirical study with the convergence rate analysis and the generalization bound of Sharp-MAML. To the best of our knowledge, this is the first empirical and theoretical study on sharpness-aware minimization in the context of bilevel learning. | Momin Abbas, Quan Xiao, Lisha Chen, Pin-Yu Chen, Tianyi Chen | null | null | 2,022 | icml |
Minimum Cost Intervention Design for Causal Effect Identification | null | Pearl’s do calculus is a complete axiomatic approach to learn the identifiable causal effects from observational data. When such an effect is not identifiable, it is necessary to perform a collection of often costly interventions in the system to learn the causal effect. In this work, we consider the problem of designing the collection of interventions with the minimum cost to identify the desired effect. First, we prove that this prob-em is NP-complete, and subsequently propose an algorithm that can either find the optimal solution or a logarithmic-factor approximation of it. This is done by establishing a connection between our problem and the minimum hitting set problem. Additionally, we propose several polynomial time heuristic algorithms to tackle the computational complexity of the problem. Although these algorithms could potentially stumble on sub-optimal solutions, our simulations show that they achieve small regrets on random graphs. | Sina Akbari, Jalal Etesami, Negar Kiyavash | null | null | 2,022 | icml |
XAI for Transformers: Better Explanations through Conservative Propagation | null | Transformers have become an important workhorse of machine learning, with numerous applications. This necessitates the development of reliable methods for increasing their transparency. Multiple interpretability methods, often based on gradient information, have been proposed. We show that the gradient in a Transformer reflects the function only locally, and thus fails to reliably identify the contribution of input features to the prediction. We identify Attention Heads and LayerNorm as main reasons for such unreliable explanations and propose a more stable way for propagation through these layers. Our proposal, which can be seen as a proper extension of the well-established LRP method to Transformers, is shown both theoretically and empirically to overcome the deficiency of a simple gradient-based approach, and achieves state-of-the-art explanation performance on a broad range of Transformer models and datasets. | Ameen Ali, Thomas Schnake, Oliver Eberle, Grégoire Montavon, Klaus-Robert Müller, Lior Wolf | null | null | 2,022 | icml |
Meaningfully debugging model mistakes using conceptual counterfactual explanations | null | Understanding and explaining the mistakes made by trained models is critical to many machine learning objectives, such as improving robustness, addressing concept drift, and mitigating biases. However, this is often an ad hoc process that involves manually looking at the model’s mistakes on many test samples and guessing at the underlying reasons for those incorrect predictions. In this paper, we propose a systematic approach, conceptual counterfactual explanations (CCE), that explains why a classifier makes a mistake on a particular test sample(s) in terms of human-understandable concepts (e.g. this zebra is misclassified as a dog because of faint stripes). We base CCE on two prior ideas: counterfactual explanations and concept activation vectors, and validate our approach on well-known pretrained models, showing that it explains the models’ mistakes meaningfully. In addition, for new models trained on data with spurious correlations, CCE accurately identifies the spurious correlation as the cause of model mistakes from a single misclassified test sample. On two challenging medical applications, CCE generated useful insights, confirmed by clinicians, into biases and mistakes the model makes in real-world settings. The code for CCE is publicly available and can easily be applied to explain mistakes in new models. | Abubakar Abid, Mert Yuksekgonul, James Zou | null | null | 2,022 | icml |
On the Convergence of the Shapley Value in Parametric Bayesian Learning Games | null | Measuring contributions is a classical problem in cooperative game theory where the Shapley value is the most well-known solution concept. In this paper, we establish the convergence property of the Shapley value in parametric Bayesian learning games where players perform a Bayesian inference using their combined data, and the posterior-prior KL divergence is used as the characteristic function. We show that for any two players, under some regularity conditions, their difference in Shapley value converges in probability to the difference in Shapley value of a limiting game whose characteristic function is proportional to the log-determinant of the joint Fisher information. As an application, we present an online collaborative learning framework that is asymptotically Shapley-fair. Our result enables this to be achieved without any costly computations of posterior-prior KL divergences. Only a consistent estimator of the Fisher information is needed. The effectiveness of our framework is demonstrated with experiments using real-world data. | Lucas Agussurja, Xinyi Xu, Bryan Kian Hsiang Low | null | null | 2,022 | icml |
Individual Preference Stability for Clustering | null | In this paper, we propose a natural notion of individual preference (IP) stability for clustering, which asks that every data point, on average, is closer to the points in its own cluster than to the points in any other cluster. Our notion can be motivated from several perspectives, including game theory and algorithmic fairness. We study several questions related to our proposed notion. We first show that deciding whether a given data set allows for an IP-stable clustering in general is NP-hard. As a result, we explore the design of efficient algorithms for finding IP-stable clusterings in some restricted metric spaces. We present a polytime algorithm to find a clustering satisfying exact IP-stability on the real line, and an efficient algorithm to find an IP-stable 2-clustering for a tree metric. We also consider relaxing the stability constraint, i.e., every data point should not be too far from its own cluster compared to any other cluster. For this case, we provide polytime algorithms with different guarantees. We evaluate some of our algorithms and several standard clustering approaches on real data sets. | Saba Ahmadi, Pranjal Awasthi, Samir Khuller, Matthäus Kleindessner, Jamie Morgenstern, Pattara Sukprasert, Ali Vakilian | null | null | 2,022 | icml |
Optimistic Linear Support and Successor Features as a Basis for Optimal Policy Transfer | null | In many real-world applications, reinforcement learning (RL) agents might have to solve multiple tasks, each one typically modeled via a reward function. If reward functions are expressed linearly, and the agent has previously learned a set of policies for different tasks, successor features (SFs) can be exploited to combine such policies and identify reasonable solutions for new problems. However, the identified solutions are not guaranteed to be optimal. We introduce a novel algorithm that addresses this limitation. It allows RL agents to combine existing policies and directly identify optimal policies for arbitrary new problems, without requiring any further interactions with the environment. We first show (under mild assumptions) that the transfer learning problem tackled by SFs is equivalent to the problem of learning to optimize multiple objectives in RL. We then introduce an SF-based extension of the Optimistic Linear Support algorithm to learn a set of policies whose SFs form a convex coverage set. We prove that policies in this set can be combined via generalized policy improvement to construct optimal behaviors for any new linearly-expressible tasks, without requiring any additional training samples. We empirically show that our method outperforms state-of-the-art competing algorithms both in discrete and continuous domains under value function approximation. | Lucas Nunes Alegre, Ana Bazzan, Bruno C. Da Silva | null | null | 2,022 | icml |
How Faithful is your Synthetic Data? Sample-level Metrics for Evaluating and Auditing Generative Models | null | Devising domain- and model-agnostic evaluation metrics for generative models is an important and as yet unresolved problem. Most existing metrics, which were tailored solely to the image synthesis setup, exhibit a limited capacity for diagnosing the different modes of failure of generative models across broader application domains. In this paper, we introduce a 3-dimensional evaluation metric, ($\alpha$-Precision, $\beta$-Recall, Authenticity), that characterizes the fidelity, diversity and generalization performance of any generative model in a domain-agnostic fashion. Our metric unifies statistical divergence measures with precision-recall analysis, enabling sample- and distribution-level diagnoses of model fidelity and diversity. We introduce generalization as an additional, independent dimension (to the fidelity-diversity trade-off) that quantifies the extent to which a model copies training data{—}a crucial performance indicator when modeling sensitive data with requirements on privacy. The three metric components correspond to (interpretable) probabilistic quantities, and are estimated via sample-level binary classification. The sample-level nature of our metric inspires a novel use case which we call model auditing, wherein we judge the quality of individual samples generated by a (black-box) model, discarding low-quality samples and hence improving the overall model performance in a post-hoc manner. | Ahmed Alaa, Boris Van Breugel, Evgeny S. Saveliev, Mihaela van der Schaar | null | null | 2,022 | icml |
An Initial Alignment between Neural Network and Target is Needed for Gradient Descent to Learn | null | This paper introduces the notion of “Initial Alignment” (INAL) between a neural network at initialization and a target function. It is proved that if a network and a Boolean target function do not have a noticeable INAL, then noisy gradient descent with normalized i.i.d. initialization will not learn in polynomial time. Thus a certain amount of knowledge about the target (measured by the INAL) is needed in the architecture design. This also provides an answer to an open problem posed in (AS-NeurIPS’20). The results are based on deriving lower-bounds for descent algorithms on symmetric neural networks without explicit knowledge of the target function beyond its INAL. | Emmanuel Abbe, Elisabetta Cornacchia, Jan Hazla, Christopher Marquis | null | null | 2,022 | icml |
RUMs from Head-to-Head Contests | null | Random utility models (RUMs) encode the likelihood that a particular item will be selected from a slate of competing items. RUMs are well-studied objects in both discrete choice theory and, more recently, in the machine learning community, as they encode a fairly broad notion of rational user behavior. In this paper, we focus on slates of size two representing head-to-head contests. Given a tournament matrix $M$ such that $M_{i,j}$ is the probability that item $j$ will be selected from $\{i, j\}$, we consider the problem of finding the RUM that most closely reproduces $M$. For this problem we obtain a polynomial-time algorithm returning a RUM that approximately minimizes the average error over the pairs. Our experiments show that RUMs can perfectly represent many of the tournament matrices that have been considered in the literature; in fact, the maximum average error induced by RUMs on the matrices we considered is negligible ($\approx 0.001$). We also show that RUMs are competitive, on prediction tasks, with previous approaches. | Matteo Almanza, Flavio Chierichetti, Ravi Kumar, Alessandro Panconesi, Andrew Tomkins | null | null | 2,022 | icml |
Understanding the unstable convergence of gradient descent | null | Most existing analyses of (stochastic) gradient descent rely on the condition that for $L$-smooth costs, the step size is less than $2/L$. However, many works have observed that in machine learning applications step sizes often do not fulfill this condition, yet (stochastic) gradient descent still converges, albeit in an unstable manner. We investigate this unstable convergence phenomenon from first principles, and discuss key causes behind it. We also identify its main characteristics, and how they interrelate based on both theory and experiments, offering a principled view toward understanding the phenomenon. | Kwangjun Ahn, Jingzhao Zhang, Suvrit Sra | null | null | 2,022 | icml |
Scalable First-Order Bayesian Optimization via Structured Automatic Differentiation | null | Bayesian Optimization (BO) has shown great promise for the global optimization of functions that are expensive to evaluate, but despite many successes, standard approaches can struggle in high dimensions. To improve the performance of BO, prior work suggested incorporating gradient information into a Gaussian process surrogate of the objective, giving rise to kernel matrices of size $nd$ {\texttimes} $nd$ for $n$ observations in $d$ dimensions. Naı̈vely multiplying with (resp. inverting) these matrices requires $O(n^2d^2)$ (resp. $O(n^3d^3)$) operations, which becomes infeasible for moderate dimensions and sample sizes. Here, we observe that a wide range of kernels gives rise to structured matrices, enabling an exact $O(n^2d)$ matrix-vector multiply for gradient observations and $O(n^2d^2)$ for Hessian observations. Beyond canonical kernel classes, we derive a programmatic approach to leveraging this type of structure for transformations and combinations of the discussed kernel classes, which constitutes a structure-aware automatic differentiation algorithm. Our methods apply to virtually all canonical kernels and automatically extend to complex kernels, like the neural network, radial basis function network, and spectral mixture kernels without any additional derivations, enabling flexible, problem-dependent modeling while scaling first-order BO to high $d$. | Sebastian E Ament, Carla P Gomes | null | null | 2,022 | icml |
Online Algorithms with Multiple Predictions | null | This paper studies online algorithms augmented with multiple machine-learned predictions. We give a generic algorithmic framework for online covering problems with multiple predictions that obtains an online solution that is competitive against the performance of the best solution obtained from the predictions. Our algorithm incorporates the use of predictions in the classic potential-based analysis of online algorithms. We apply our algorithmic framework to solve classical problems such as online set cover, (weighted) caching, and online facility location in the multiple predictions setting. | Keerti Anand, Rong Ge, Amit Kumar, Debmalya Panigrahi | null | null | 2,022 | icml |
Neuro-Symbolic Language Modeling with Automaton-augmented Retrieval | null | Retrieval-based language models (R-LM) model the probability of natural language text by combining a standard language model (LM) with examples retrieved from an external datastore at test time. While effective, a major bottleneck of using these models in practice is the computationally costly datastore search, which can be performed as frequently as every time step. In this paper, we present RetoMaton - retrieval automaton - which approximates the datastore search, based on (1) saving pointers between consecutive datastore entries, and (2) clustering of entries into "states". This effectively results in a weighted finite automaton built on top of the datastore, instead of representing the datastore as a flat list. The creation of the automaton is unsupervised, and a RetoMaton can be constructed from any text collection: either the original training corpus or from another domain. Traversing this automaton at inference time, in parallel to the LM inference, reduces its perplexity by up to 1.85, or alternatively saves up to 83% of the nearest neighbor searches over $k$NN-LM (Khandelwal et al., 2020) without hurting perplexity. Our code and trained models are available at https://github.com/neulab/retomaton . | Uri Alon, Frank Xu, Junxian He, Sudipta Sengupta, Dan Roth, Graham Neubig | null | null | 2,022 | icml |
Deploying Convolutional Networks on Untrusted Platforms Using 2D Holographic Reduced Representations | null | Due to the computational cost of running inference for a neural network, the need to deploy the inferential steps on a third party’s compute environment or hardware is common. If the third party is not fully trusted, it is desirable to obfuscate the nature of the inputs and outputs, so that the third party can not easily determine what specific task is being performed. Provably secure protocols for leveraging an untrusted party exist but are too computational demanding to run in practice. We instead explore a different strategy of fast, heuristic security that we call Connectionist Symbolic Pseudo Secrets. By leveraging Holographic Reduced Representations (HRRs), we create a neural network with a pseudo-encryption style defense that empirically shows robustness to attack, even under threat models that unrealistically favor the adversary. | Mohammad Mahmudul Alam, Edward Raff, Tim Oates, James Holt | null | null | 2,022 | icml |
A Natural Actor-Critic Framework for Zero-Sum Markov Games | null | We introduce algorithms based on natural actor-critic and analyze their sample complexity for solving two player zero-sum Markov games in the tabular case. Our results improve the best-known sample complexities of policy gradient/actor-critic methods for convergence to Nash equilibrium in the multi-agent setting. We use the error propagation scheme in approximate dynamic programming, recent advances for global convergence of policy gradient methods, temporal difference learning, and techniques from stochastic primal-dual optimization. Our algorithms feature two stages, requiring agents to agree on an etiquette before starting their interactions, which is feasible for instance in self-play. However, the agents only access to joint reward and joint next state and not to each other’s actions or policies. Our complexity results match the best-known results for global convergence of policy gradient algorithms for single agent RL. We provide numerical verification of our methods for a two player bandit environment and a two player game, Alesia. We observe improved empirical performance as compared to the recently proposed optimistic gradient descent-ascent variant for Markov games. | Ahmet Alacaoglu, Luca Viano, Niao He, Volkan Cevher | null | null | 2,022 | icml |
Towards Understanding Sharpness-Aware Minimization | null | Sharpness-Aware Minimization (SAM) is a recent training method that relies on worst-case weight perturbations which significantly improves generalization in various settings. We argue that the existing justifications for the success of SAM which are based on a PAC-Bayes generalization bound and the idea of convergence to flat minima are incomplete. Moreover, there are no explanations for the success of using m-sharpness in SAM which has been shown as essential for generalization. To better understand this aspect of SAM, we theoretically analyze its implicit bias for diagonal linear networks. We prove that SAM always chooses a solution that enjoys better generalization properties than standard gradient descent for a certain class of problems, and this effect is amplified by using m-sharpness. We further study the properties of the implicit bias on non-linear networks empirically, where we show that fine-tuning a standard model with SAM can lead to significant generalization improvements. Finally, we provide convergence results of SAM for non-convex objectives when used with stochastic gradients. We illustrate these results empirically for deep networks and discuss their relation to the generalization behavior of SAM. The code of our experiments is available at https://github.com/tml-epfl/understanding-sam. | Maksym Andriushchenko, Nicolas Flammarion | null | null | 2,022 | icml |
On Last-Iterate Convergence Beyond Zero-Sum Games | null | Most existing results about last-iterate convergence of learning dynamics are limited to two-player zero-sum games, and only apply under rigid assumptions about what dynamics the players follow. In this paper we provide new results and techniques that apply to broader families of games and learning dynamics. First, we show that in a class of games that includes constant-sum polymatrix and strategically zero-sum games, the trajectories of dynamics such as optimistic mirror descent (OMD) exhibit a boundedness property, which holds even when players employ different algorithms and prediction mechanisms. This property enables us to obtain $O(1/\sqrt{T})$ rates and optimal $O(1)$ regret bounds. Our analysis also reveals a surprising property: OMD either reaches arbitrarily close to a Nash equilibrium or it outperforms the robust price of anarchy in efficiency. Moreover, for potential games we establish convergence to an $\epsilon$-equilibrium after $O(1/\epsilon^2)$ iterations for mirror descent under a broad class of regularizers, as well as optimal $O(1)$ regret bounds for OMD variants. Our framework also extends to near-potential games, and unifies known analyses for distributed learning in Fisher’s market model. Finally, we analyze the convergence, efficiency, and robustness of optimistic gradient descent (OGD) in general-sum continuous games. | Ioannis Anagnostides, Ioannis Panageas, Gabriele Farina, Tuomas Sandholm | null | null | 2,022 | icml |
Fair and Fast k-Center Clustering for Data Summarization | null | We consider two key issues faced by many clustering methods when used for data summarization, namely (a) an unfair representation of "demographic groups” and (b) distorted summarizations, where data points in the summary represent subsets of the original data of vastly different sizes. Previous work made important steps towards handling separately each of these two issues in the context of the fundamental k-Center clustering objective through the study of fast algorithms for natural models that address them. We show that it is possible to effectively address both (a) and (b) simultaneously by presenting a clustering procedure that works for a canonical combined model and (i) is fast, both in theory and practice, (ii) exhibits a worst-case constant-factor guarantee, and (iii) gives promising computational results showing that there can be significant benefits in addressing both issues together instead of sequentially. | Haris Angelidakis, Adam Kurpisz, Leon Sering, Rico Zenklusen | null | null | 2,022 | icml |
Minimax Classification under Concept Drift with Multidimensional Adaptation and Performance Guarantees | null | The statistical characteristics of instance-label pairs often change with time in practical scenarios of supervised classification. Conventional learning techniques adapt to such concept drift accounting for a scalar rate of change by means of a carefully chosen learning rate, forgetting factor, or window size. However, the time changes in common scenarios are multidimensional, i.e., different statistical characteristics often change in a different manner. This paper presents adaptive minimax risk classifiers (AMRCs) that account for multidimensional time changes by means of a multivariate and high-order tracking of the time-varying underlying distribution. In addition, differently from conventional techniques, AMRCs can provide computable tight performance guarantees. Experiments on multiple benchmark datasets show the classification improvement of AMRCs compared to the state-of-the-art and the reliability of the presented performance guarantees. | Verónica Álvarez, Santiago Mazuelas, Jose A Lozano | null | null | 2,022 | icml |
Gradient Based Clustering | null | We propose a general approach for distance based clustering, using the gradient of the cost function that measures clustering quality with respect to cluster assignments and cluster center positions. The approach is an iterative two step procedure (alternating between cluster assignment and cluster center updates) and is applicable to a wide range of functions, satisfying some mild assumptions. The main advantage of the proposed approach is a simple and computationally cheap update rule. Unlike previous methods that specialize to a specific formulation of the clustering problem, our approach is applicable to a wide range of costs, including non-Bregman clustering methods based on the Huber loss. We analyze the convergence of the proposed algorithm, and show that it converges to the set of appropriately defined fixed points, under arbitrary center initialization. In the special case of Bregman cost functions, the algorithm converges to the set of centroidal Voronoi partitions, which is consistent with prior works. Numerical experiments on real data demonstrate the effectiveness of the proposed method. | Aleksandar Armacki, Dragana Bajovic, Dusan Jakovetic, Soummya Kar | null | null | 2,022 | icml |
Interactive Correlation Clustering with Existential Cluster Constraints | null | We consider the problem of clustering with user feedback. Existing methods express constraints about the input data points, most commonly through must-link and cannot-link constraints on data point pairs. In this paper, we introduce existential cluster constraints: a new form of feedback where users indicate the features of desired clusters. Specifically, users make statements about the existence of a cluster having (and not having) particular features. Our approach has multiple advantages: (1) constraints on clusters can express user intent more efficiently than point pairs; (2) in cases where the users’ mental model is of the desired clusters, it is more natural for users to express cluster-wise preferences; (3) it functions even when privacy restrictions prohibit users from seeing raw data. In addition to introducing existential cluster constraints, we provide an inference algorithm for incorporating our constraints into the output clustering. Finally, we demonstrate empirically that our proposed framework facilitates more accurate clustering with dramatically fewer user feedback inputs. | Rico Angell, Nicholas Monath, Nishant Yadav, Andrew Mccallum | null | null | 2,022 | icml |
VariGrow: Variational Architecture Growing for Task-Agnostic Continual Learning based on Bayesian Novelty | null | Continual Learning (CL) is the problem of sequentially learning a set of tasks and preserving all the knowledge acquired. Many existing methods assume that the data stream is explicitly divided into a sequence of known contexts (tasks), and use this information to know when to transfer knowledge from one context to another. Unfortunately, many real-world CL scenarios have no clear task nor context boundaries, motivating the study of task-agnostic CL, where neither the specific tasks nor their switches are known both in training and testing. This paper proposes a variational architecture growing framework dubbed VariGrow. By interpreting dynamically growing neural networks as a Bayesian approximation, and defining flexible implicit variational distributions, VariGrow detects if a new task is arriving through an energy-based novelty score. If the novelty score is high and the sample is “detected" as a new task, VariGrow will grow a new expert module to be responsible for it. Otherwise, the sample will be assigned to one of the existing experts who is most “familiar" with it (i.e., one with the lowest novelty score). We have tested VariGrow on several CIFAR and ImageNet-based benchmarks for the strict task-agnostic CL setting and demonstrate its consistent superior performance. Perhaps surprisingly, its performance can even be competitive compared to task-aware methods. | Randy Ardywibowo, Zepeng Huo, Zhangyang Wang, Bobak J Mortazavi, Shuai Huang, Xiaoning Qian | null | null | 2,022 | icml |
Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imaging | null | Image-to-image regression is an important learning task, used frequently in biological imaging. Current algorithms, however, do not generally offer statistical guarantees that protect against a model’s mistakes and hallucinations. To address this, we develop uncertainty quantification techniques with rigorous statistical guarantees for image-to-image regression problems. In particular, we show how to derive uncertainty intervals around each pixel that are guaranteed to contain the true value with a user-specified confidence probability. Our methods work in conjunction with any base machine learning model, such as a neural network, and endow it with formal mathematical guarantees{—}regardless of the true unknown data distribution or choice of model. Furthermore, they are simple to implement and computationally inexpensive. We evaluate our procedure on three image-to-image regression tasks: quantitative phase microscopy, accelerated magnetic resonance imaging, and super-resolution transmission electron microscopy of a Drosophila melanogaster brain. | Anastasios N Angelopoulos, Amit Pal Kohli, Stephen Bates, Michael Jordan, Jitendra Malik, Thayer Alshaabi, Srigokul Upadhyayula, Yaniv Romano | null | null | 2,022 | icml |
Near-optimal rate of consistency for linear models with missing values | null | Missing values arise in most real-world data sets due to the aggregation of multiple sources and intrinsically missing information (sensor failure, unanswered questions in surveys...). In fact, the very nature of missing values usually prevents us from running standard learning algorithms. In this paper, we focus on the extensively-studied linear models, but in presence of missing values, which turns out to be quite a challenging task. Indeed, the Bayes predictor can be decomposed as a sum of predictors corresponding to each missing pattern. This eventually requires to solve a number of learning tasks, exponential in the number of input features, which makes predictions impossible for current real-world datasets. First, we propose a rigorous setting to analyze a least-square type estimator and establish a bound on the excess risk which increases exponentially in the dimension. Consequently, we leverage the missing data distribution to propose a new algorithm, and derive associated adaptive risk bounds that turn out to be minimax optimal. Numerical experiments highlight the benefits of our method compared to state-of-the-art algorithms used for predictions with missing values. | Alexis Ayme, Claire Boyer, Aymeric Dieuleveut, Erwan Scornet | null | null | 2,022 | icml |
Online Balanced Experimental Design | null | We consider the experimental design problem in an online environment, an important practical task for reducing the variance of estimates in randomized experiments which allows for greater precision, and in turn, improved decision making. In this work, we present algorithms that build on recent advances in online discrepancy minimization which accommodate both arbitrary treatment probabilities and multiple treatments. The proposed algorithms are computational efficient, minimize covariate imbalance, and include randomization which enables robustness to misspecification. We provide worst case bounds on the expected mean squared error of the causal estimate and show that the proposed estimator is no worse than an implicit ridge regression, which are within a logarithmic factor of the best known results for offline experimental design. We conclude with a detailed simulation study showing favorable results relative to complete randomization as well as to offline methods for experimental design with time complexities exceeding our algorithm, which has a linear dependence on the number of observations, by polynomial factors. | David Arbour, Drew Dimmery, Tung Mai, Anup Rao | null | null | 2,022 | icml |
AdaGrad Avoids Saddle Points | null | Adaptive first-order methods in optimization have widespread ML applications due to their ability to adapt to non-convex landscapes. However, their convergence guarantees are typically stated in terms of vanishing gradient norms, which leaves open the issue of converging to undesirable saddle points (or even local maxima). In this paper, we focus on the AdaGrad family of algorithms - from scalar to full-matrix preconditioning - and we examine the question of whether the method’s trajectories avoid saddle points. A major challenge that arises here is that AdaGrad’s step-size (or, more accurately, the method’s preconditioner) evolves over time in a filtration-dependent way, i.e., as a function of all gradients observed in earlier iterations; as a result, avoidance results for methods with a constant or vanishing step-size do not apply. We resolve this challenge by combining a series of step-size stabilization arguments with a recursive representation of the AdaGrad preconditioner that allows us to employ center-stable techniques and ultimately show that the induced trajectories avoid saddle points from almost any initial condition. | Kimon Antonakopoulos, Panayotis Mertikopoulos, Georgios Piliouras, Xiao Wang | null | null | 2,022 | icml |
Optimal Algorithms for Mean Estimation under Local Differential Privacy | null | We study the problem of mean estimation of $\ell_2$-bounded vectors under the constraint of local differential privacy. While the literature has a variety of algorithms that achieve the (asymptotic) optimal rates for this problem, the performance of these algorithms in practice can vary significantly due to varying (and often large) hidden constants. In this work, we investigate the question of designing the randomizer with the smallest variance. We show that PrivUnit (Bhowmick et al. 2018) with optimized parameters achieves the optimal variance among a large family of natural randomizers. To prove this result, we establish some properties of local randomizers, and use symmetrization arguments that allow us to write the optimal randomizer as the optimizer of a certain linear program. These structural results, which should extend to other problems, then allow us to show that the optimal randomizer belongs to the PrivUnit family. We also develop a new variant of PrivUnit based on the Gaussian distribution which is more amenable to mathematical analysis and enjoys the same optimality guarantees. This allows us to establish several useful properties on the exact constants of the optimal error as well as to numerically estimate these constants. | Hilal Asi, Vitaly Feldman, Kunal Talwar | null | null | 2,022 | icml |
Do More Negative Samples Necessarily Hurt In Contrastive Learning? | null | Recent investigations in noise contrastive estimation suggest, both empirically as well as theoretically, that while having more “negative samples” in the contrastive loss improves downstream classification performance initially, beyond a threshold, it hurts downstream performance due to a “collision-coverage” trade-off. But is such a phenomenon inherent in contrastive learning? We show in a simple theoretical setting, where positive pairs are generated by sampling from the underlying latent class (introduced by Saunshi et al. (ICML 2019)), that the downstream performance of the representation optimizing the (population) contrastive loss in fact does not degrade with the number of negative samples. Along the way, we give a structural characterization of the optimal representation in our framework, for noise contrastive estimation. We also provide empirical support for our theoretical results on CIFAR-10 and CIFAR-100 datasets. | Pranjal Awasthi, Nishanth Dikkala, Pritish Kamath | null | null | 2,022 | icml |
UnderGrad: A Universal Black-Box Optimization Method with Almost Dimension-Free Convergence Rate Guarantees | null | Universal methods achieve optimal convergence rate guarantees in convex optimization without any prior knowledge of the problem’s regularity parameters or the attributes of the gradient oracle employed by the method. In this regard, existing state-of-the-art algorithms achieve an $O(1/T^2)$ convergence rate in Lipschitz smooth problems with a perfect gradient oracle, and an $O(1/sqrt{T})$ convergence speed when the underlying problem is non-smooth and/or the gradient oracle is stochastic. On the downside, these methods do not take into account the dependence of these guarantees on the problem’s dimensionality, and this can have a catastrophic impact on a method’s convergence, in both theory and practice. Our paper aims to bridge this gap by providing a scalable universal method - dubbed UnDERGrad - which enjoys an almost dimension-free oracle complexity in problems with a favorable geometry (like the simplex, $\ell_1$-ball or trace-constraints), while retaining the order-optimal dependence on T described above. These "best of both worlds" guarantees are achieved via a primal-dual update scheme inspired by the dual exploration method for variational inequalities. | Kimon Antonakopoulos, Dong Quan Vu, Volkan Cevher, Kfir Levy, Panayotis Mertikopoulos | null | null | 2,022 | icml |
Private optimization in the interpolation regime: faster rates and hardness results | null | In non-private stochastic convex optimization, stochastic gradient methods converge much faster on interpolation problems—namely, problems where there exists a solution that simultaneously minimizes all of the sample losses—than on non-interpolating ones; similar improvements are not known in the private setting. In this paper, we investigate differentially private stochastic optimization in the interpolation regime. First, we show that without additional assumptions, interpolation problems do not exhibit an improved convergence rates with differential privacy. However, when the functions exhibit quadratic growth around the optimum, we show (near) exponential improvements in the private sample complexity. In particular, we propose an adaptive algorithm that improves the sample complexity to achieve expected error $\alpha$ from $\frac{d}{\diffp \sqrt{\alpha}}$ to $\frac{1}{\alpha^\rho} + \frac{d}{\diffp} \log\paren{\frac{1}{\alpha}}$ for any fixed $\rho >0$, while retaining the standard minimax-optimal sample complexity for non-interpolation problems. We prove a lower bound that shows the dimension-dependent term in the expression above is tight. Furthermore, we provide a superefficiency result which demonstrates the necessity of the polynomial term for adaptive algorithms: any algorithm that has a polylogarithmic sample complexity for interpolation problems cannot achieve the minimax-optimal rates for the family of non-interpolation problems. | Hilal Asi, Karan Chadha, Gary Cheng, John Duchi | null | null | 2,022 | icml |
Understanding Gradient Descent on the Edge of Stability in Deep Learning | null | Deep learning experiments by \citet{cohen2021gradient} using deterministic Gradient Descent (GD) revealed an Edge of Stability (EoS) phase when learning rate (LR) and sharpness (i.e., the largest eigenvalue of Hessian) no longer behave as in traditional optimization. Sharpness stabilizes around $2/$LR and loss goes up and down across iterations, yet still with an overall downward trend. The current paper mathematically analyzes a new mechanism of implicit regularization in the EoS phase, whereby GD updates due to non-smooth loss landscape turn out to evolve along some deterministic flow on the manifold of minimum loss. This is in contrast to many previous results about implicit bias either relying on infinitesimal updates or noise in gradient. Formally, for any smooth function $L$ with certain regularity condition, this effect is demonstrated for (1) Normalized GD, i.e., GD with a varying LR $\eta_t =\frac{\eta}{\norm{\nabla L(x(t))}}$ and loss $L$; (2) GD with constant LR and loss $\sqrt{L- \min_x L(x)}$. Both provably enter the Edge of Stability, with the associated flow on the manifold minimizing $\lambda_{1}(\nabla^2 L)$. The above theoretical results have been corroborated by an experimental study. | Sanjeev Arora, Zhiyuan Li, Abhishek Panigrahi | null | null | 2,022 | icml |
Proving Theorems using Incremental Learning and Hindsight Experience Replay | null | Traditional automated theorem proving systems for first-order logic depend on speed-optimized search and many handcrafted heuristics designed to work over a wide range of domains. Machine learning approaches in the literature either depend on these traditional provers to bootstrap themselves, by leveraging these heuristics, or can struggle due to limited existing proof data. The latter issue can be explained by the lack of a smooth difficulty gradient in theorem proving datasets; large gaps in difficulty between different theorems can make training harder or even impossible. In this paper, we adapt the idea of hindsight experience replay from reinforcement learning to the automated theorem proving domain, so as to use the intermediate data generated during unsuccessful proof attempts. We build a first-order logic prover by disabling all the smart clause-scoring heuristics of the state-of-the-art E prover and replacing them with a clause-scoring neural network learned by using hindsight experience replay in an incremental learning setting. Clauses are represented as graphs and presented to transformer networks with spectral features. We show that provers trained in this way can outperform previous machine learning approaches and compete with the state of the art heuristic-based theorem prover E in its best configuration, on the popular benchmarks MPTP2078, M2k and Mizar40. The proofs generated by our algorithm are also almost always significantly shorter than E’s proofs. | Eser Aygün, Ankit Anand, Laurent Orseau, Xavier Glorot, Stephen M Mcaleer, Vlad Firoiu, Lei M Zhang, Doina Precup, Shibl Mourad | null | null | 2,022 | icml |
Adapting the Linearised Laplace Model Evidence for Modern Deep Learning | null | The linearised Laplace method for estimating model uncertainty has received renewed attention in the Bayesian deep learning community. The method provides reliable error bars and admits a closed-form expression for the model evidence, allowing for scalable selection of model hyperparameters. In this work, we examine the assumptions behind this method, particularly in conjunction with model selection. We show that these interact poorly with some now-standard tools of deep learning–stochastic approximation methods and normalisation layers–and make recommendations for how to better adapt this classic method to the modern setting. We provide theoretical support for our recommendations and validate them empirically on MLPs, classic CNNs, residual networks with and without normalisation layers, generative autoencoders and transformers. | Javier Antoran, David Janz, James U Allingham, Erik Daxberger, Riccardo Rb Barbano, Eric Nalisnick, Jose Miguel Hernandez-Lobato | null | null | 2,022 | icml |
EAT-C: Environment-Adversarial sub-Task Curriculum for Efficient Reinforcement Learning | null | Reinforcement learning (RL) is inefficient on long-horizon tasks due to sparse rewards and its policy can be fragile to slightly perturbed environments. We address these challenges via a curriculum of tasks with coupled environments, generated by two policies trained jointly with RL: (1) a co-operative planning policy recursively decomposing a hard task into a coarse-to-fine sub-task tree; and (2) an adversarial policy modifying the environment in each sub-task. They are complementary to acquire more informative feedback for RL: (1) provides dense reward of easier sub-tasks while (2) modifies sub-tasks’ environments to be more challenging and diverse. Conversely, they are trained by RL’s dense feedback on sub-tasks so their generated curriculum keeps adaptive to RL’s progress. The sub-task tree enables an easy-to-hard curriculum for every policy: its top-down construction gradually increases sub-tasks the planner needs to generate, while the adversarial training between the environment and RL follows a bottom-up traversal that starts from a dense sequence of easier sub-tasks allowing more frequent environment changes. We compare EAT-C with RL/planning targeting similar problems and methods with environment generators or adversarial agents. Extensive experiments on diverse tasks demonstrate the advantages of our method on improving RL’s efficiency and generalization. | Shuang Ao, Tianyi Zhou, Jing Jiang, Guodong Long, Xuan Song, Chengqi Zhang | null | null | 2,022 | icml |
Iterative Hard Thresholding with Adaptive Regularization: Sparser Solutions Without Sacrificing Runtime | null | We propose a simple modification to the iterative hard thresholding (IHT) algorithm, which recovers asymptotically sparser solutions as a function of the condition number. When aiming to minimize a convex function f(x) with condition number $\kappa$ subject to x being an s-sparse vector, the standard IHT guarantee is a solution with relaxed sparsity $O(s\kappa^2)$, while our proposed algorithm, regularized IHT, returns a solution with sparsity $O(s\kappa)$. Our algorithm significantly improves over ARHT [Axiotis & Sviridenko, 2021] which also achieves $O(s\kappa)$, as it does not require re-optimization in each iteration (and so is much faster), is deterministic, and does not require knowledge of the optimal solution value f(x*) or the optimal sparsity level s. Our main technical tool is an adaptive regularization framework, in which the algorithm progressively learns the weights of an l_2 regularization term that will allow convergence to sparser solutions. We also apply this framework to low rank optimization, where we achieve a similar improvement of the best known condition number dependence from $\kappa^2$ to $\kappa$. | Kyriakos Axiotis, Maxim Sviridenko | null | null | 2,022 | icml |
Congested Bandits: Optimal Routing via Short-term Resets | null | For traffic routing platforms, the choice of which route to recommend to a user depends on the congestion on these routes – indeed, an individual’s utility depends on the number of people using the recommended route at that instance. Motivated by this, we introduce the problem of Congested Bandits where each arm’s reward is allowed to depend on the number of times it was played in the past $\Delta$ timesteps. This dependence on past history of actions leads to a dynamical system where an algorithm’s present choices also affect its future pay-offs, and requires an algorithm to plan for this. We study the congestion aware formulation in the multi-armed bandit (MAB) setup and in the contextual bandit setup with linear rewards. For the multi-armed setup, we propose a UCB style algorithm and show that its policy regret scales as $\tilde{O}(\sqrt{K \Delta T})$. For the linear contextual bandit setup, our algorithm, based on an iterative least squares planner, achieves policy regret $\tilde{O}(\sqrt{dT} + \Delta)$. From an experimental standpoint, we corroborate the no-regret properties of our algorithms via a simulation study. | Pranjal Awasthi, Kush Bhatia, Sreenivas Gollapudi, Kostas Kollias | null | null | 2,022 | icml |
Stability Based Generalization Bounds for Exponential Family Langevin Dynamics | null | Recent years have seen advances in generalization bounds for noisy stochastic algorithms, especially stochastic gradient Langevin dynamics (SGLD) based on stability (Mou et al., 2018; Li et al., 2020) and information theoretic approaches (Xu & Raginsky, 2017; Negrea et al., 2019; Steinke & Zakynthinou, 2020). In this paper, we unify and substantially generalize stability based generalization bounds and make three technical contributions. First, we bound the generalization error in terms of expected (not uniform) stability which arguably leads to quantitatively sharper bounds. Second, as our main contribution, we introduce Exponential Family Langevin Dynamics (EFLD), a substantial generalization of SGLD, which includes noisy versions of Sign-SGD and quantized SGD as special cases. We establish data dependent expected stability based generalization bounds for any EFLD algorithm with a O(1/n) sample dependence and dependence on gradient discrepancy rather than the norm of gradients, yielding significantly sharper bounds. Third, we establish optimization guarantees for special cases of EFLD. Further, empirical results on benchmarks illustrate that our bounds are non-vacuous, quantitatively sharper than existing bounds, and behave correctly under noisy labels. | Arindam Banerjee, Tiancong Chen, Xinyan Li, Yingxue Zhou | null | null | 2,022 | icml |
H-Consistency Bounds for Surrogate Loss Minimizers | null | We present a detailed study of estimation errors in terms of surrogate loss estimation errors. We refer to such guarantees as H-consistency bounds, since they account for the hypothesis set H adopted. These guarantees are significantly stronger than H-calibration or H-consistency. They are also more informative than similar excess error bounds derived in the literature, when H is the family of all measurable functions. We prove general theorems providing such guarantees, for both the distribution-dependent and distribution-independent settings. We show that our bounds are tight, modulo a convexity assumption. We also show that previous excess error bounds can be recovered as special cases of our general results. We then present a series of explicit bounds in the case of the zero-one loss, with multiple choices of the surrogate loss and for both the family of linear functions and neural networks with one hidden-layer. We further prove more favorable distribution-dependent guarantees in that case. We also present a series of explicit bounds in the case of the adversarial loss, with surrogate losses based on the supremum of the $\rho$-margin, hinge or sigmoid loss and for the same two general hypothesis sets. Here too, we prove several enhancements of these guarantees under natural distributional assumptions. Finally, we report the results of simulations illustrating our bounds and their tightness. | Pranjal Awasthi, Anqi Mao, Mehryar Mohri, Yutao Zhong | null | null | 2,022 | icml |
How Tempering Fixes Data Augmentation in Bayesian Neural Networks | null | While Bayesian neural networks (BNNs) provide a sound and principled alternative to standard neural networks, an artificial sharpening of the posterior usually needs to be applied to reach comparable performance. This is in stark contrast to theory, dictating that given an adequate prior and a well-specified model, the untempered Bayesian posterior should achieve optimal performance. Despite the community’s extensive efforts, the observed gains in performance still remain disputed with several plausible causes pointing at its origin. While data augmentation has been empirically recognized as one of the main drivers of this effect, a theoretical account of its role, on the other hand, is largely missing. In this work we identify two interlaced factors concurrently influencing the strength of the cold posterior effect, namely the correlated nature of augmentations and the degree of invariance of the employed model to such transformations. By theoretically analyzing simplified settings, we prove that tempering implicitly reduces the misspecification arising from modeling augmentations as i.i.d. data. The temperature mimics the role of the effective sample size, reflecting the gain in information provided by the augmentations. We corroborate our theoretical findings with extensive empirical evaluations, scaling to realistic BNNs. By relying on the framework of group convolutions, we experiment with models of varying inherent degree of invariance, confirming its hypothesized relationship with the optimal temperature. | Gregor Bachmann, Lorenzo Noci, Thomas Hofmann | null | null | 2,022 | icml |
A$^3$T: Alignment-Aware Acoustic and Text Pretraining for Speech Synthesis and Editing | null | Recently, speech representation learning has improved many speech-related tasks such as speech recognition, speech classification, and speech-to-text translation. However, all the above tasks are in the direction of speech understanding, but for the inverse direction, speech synthesis, the potential of representation learning is yet to be realized, due to the challenging nature of generating high-quality speech. To address this problem, we propose our framework, Alignment-Aware Acoustic-Text Pretraining (A$^3$T), which reconstructs masked acoustic signals with text input and acoustic-text alignment during training. In this way, the pretrained model can generate high quality reconstructed spectrogram, which can be applied to the speech editing and unseen speaker TTS directly. Experiments show A$^3$T outperforms SOTA models on speech editing, and improves multi-speaker speech synthesis without the external speaker verification model. | He Bai, Renjie Zheng, Junkun Chen, Mingbo Ma, Xintong Li, Liang Huang | null | null | 2,022 | icml |
Near-Optimal Learning of Extensive-Form Games with Imperfect Information | null | This paper resolves the open question of designing near-optimal algorithms for learning imperfect-information extensive-form games from bandit feedback. We present the first line of algorithms that require only $\widetilde{\mathcal{O}}((XA+YB)/\varepsilon^2)$ episodes of play to find an $\varepsilon$-approximate Nash equilibrium in two-player zero-sum games, where $X,Y$ are the number of information sets and $A,B$ are the number of actions for the two players. This improves upon the best known sample complexity of $\widetilde{\mathcal{O}}((X^2A+Y^2B)/\varepsilon^2)$ by a factor of $\widetilde{\mathcal{O}}(\max\{X, Y\})$, and matches the information-theoretic lower bound up to logarithmic factors. We achieve this sample complexity by two new algorithms: Balanced Online Mirror Descent, and Balanced Counterfactual Regret Minimization. Both algorithms rely on novel approaches of integrating balanced exploration policies into their classical counterparts. We also extend our results to learning Coarse Correlated Equilibria in multi-player general-sum games. | Yu Bai, Chi Jin, Song Mei, Tiancheng Yu | null | null | 2,022 | icml |
data2vec: A General Framework for Self-supervised Learning in Speech, Vision and Language | null | While the general idea of self-supervised learning is identical across modalities, the actual algorithms and objectives differ widely because they were developed with a single modality in mind. To get us closer to general self-supervised learning, we present data2vec, a framework that uses the same learning method for either speech, NLP or computer vision. The core idea is to predict latent representations of the full input data based on a masked view of the input in a self-distillation setup using a standard Transformer architecture. Instead of predicting modality-specific targets such as words, visual tokens or units of human speech which are local in nature, data2vec predicts contextualized latent representations that contain information from the entire input. Experiments on the major benchmarks of speech recognition, image classification, and natural language understanding demonstrate a new state of the art or competitive performance to predominant approaches. | Alexei Baevski, Wei-Ning Hsu, Qiantong Xu, Arun Babu, Jiatao Gu, Michael Auli | null | null | 2,022 | icml |
Gaussian Mixture Variational Autoencoder with Contrastive Learning for Multi-Label Classification | null | Multi-label classification (MLC) is a prediction task where each sample can have more than one label. We propose a novel contrastive learning boosted multi-label prediction model based on a Gaussian mixture variational autoencoder (C-GMVAE), which learns a multimodal prior space and employs a contrastive loss. Many existing methods introduce extra complex neural modules like graph neural networks to capture the label correlations, in addition to the prediction modules. We find that by using contrastive learning in the supervised setting, we can exploit label information effectively in a data-driven manner, and learn meaningful feature and label embeddings which capture the label correlations and enhance the predictive power. Our method also adopts the idea of learning and aligning latent spaces for both features and labels. In contrast to previous works based on a unimodal prior, C-GMVAE imposes a Gaussian mixture structure on the latent space, to alleviate the posterior collapse and over-regularization issues. C-GMVAE outperforms existing methods on multiple public datasets and can often match other models’ full performance with only 50% of the training data. Furthermore, we show that the learnt embeddings provide insights into the interpretation of label-label interactions. | Junwen Bai, Shufeng Kong, Carla P Gomes | null | null | 2,022 | icml |
From Noisy Prediction to True Label: Noisy Prediction Calibration via Generative Model | null | Noisy labels are inevitable yet problematic in machine learning society. It ruins the generalization of a classifier by making the classifier over-fitted to noisy labels. Existing methods on noisy label have focused on modifying the classifier during the training procedure. It has two potential problems. First, these methods are not applicable to a pre-trained classifier without further access to training. Second, it is not easy to train a classifier and regularize all negative effects from noisy labels, simultaneously. We suggest a new branch of method, Noisy Prediction Calibration (NPC) in learning with noisy labels. Through the introduction and estimation of a new type of transition matrix via generative model, NPC corrects the noisy prediction from the pre-trained classifier to the true label as a post-processing scheme. We prove that NPC theoretically aligns with the transition matrix based methods. Yet, NPC empirically provides more accurate pathway to estimate true label, even without involvement in classifier learning. Also, NPC is applicable to any classifier trained with noisy label methods, if training instances and its predictions are available. Our method, NPC, boosts the classification performances of all baseline models on both synthetic and real-world datasets. The implemented code is available at https://github.com/BaeHeeSun/NPC. | Heesun Bae, Seungjae Shin, Byeonghu Na, Joonho Jang, Kyungwoo Song, Il-Chul Moon | null | null | 2,022 | icml |
Data Scaling Laws in NMT: The Effect of Noise and Architecture | null | In this work, we study the effect of varying the architecture and training data quality on the data scaling properties of Neural Machine Translation (NMT). First, we establish that the test loss of encoder-decoder transformer models scales as a power law in the number of training samples, with a dependence on the model size. Then, we systematically vary aspects of the training setup to understand how they impact the data scaling laws. In particular, we change the following (1) Architecture and task setup: We compare to a transformer-LSTM hybrid, and a decoder-only transformer with a language modeling loss (2) Noise level in the training distribution: We experiment with filtering, and adding iid synthetic noise. In all the above cases, we find that the data scaling exponents are minimally impacted, suggesting that marginally worse architectures or training data can be compensated for by adding more data. Lastly, we find that using back-translated data instead of parallel data, can significantly degrade the scaling exponent. | Yamini Bansal, Behrooz Ghorbani, Ankush Garg, Biao Zhang, Colin Cherry, Behnam Neyshabur, Orhan Firat | null | null | 2,022 | icml |
Generative Modeling for Multi-task Visual Learning | null | Generative modeling has recently shown great promise in computer vision, but it has mostly focused on synthesizing visually realistic images. In this paper, motivated by multi-task learning of shareable feature representations, we consider a novel problem of learning a shared generative model that is useful across various visual perception tasks. Correspondingly, we propose a general multi-task oriented generative modeling (MGM) framework, by coupling a discriminative multi-task network with a generative network. While it is challenging to synthesize both RGB images and pixel-level annotations in multi-task scenarios, our framework enables us to use synthesized images paired with only weak annotations (i.e., image-level scene labels) to facilitate multiple visual tasks. Experimental evaluation on challenging multi-task benchmarks, including NYUv2 and Taskonomy, demonstrates that our MGM framework improves the performance of all the tasks by large margins, consistently outperforming state-of-the-art multi-task approaches in different sample-size regimes. | Zhipeng Bao, Martial Hebert, Yu-Xiong Wang | null | null | 2,022 | icml |
ASAP.SGD: Instance-based Adaptiveness to Staleness in Asynchronous SGD | null | Concurrent algorithmic implementations of Stochastic Gradient Descent (SGD) give rise to critical questions for compute-intensive Machine Learning (ML). Asynchrony implies speedup in some contexts, and challenges in others, as stale updates may lead to slower, or non-converging executions. While previous works showed asynchrony-adaptiveness can improve stability and speedup by reducing the step size for stale updates according to static rules, there is no one-size-fits-all adaptation rule, since the optimal strategy depends on several factors. We introduce (i) $\mathtt{ASAP.SGD}$, an analytical framework capturing necessary and desired properties of staleness-adaptive step size functions and (ii) \textsc{tail}-$\tau$, a method for utilizing key properties of the execution instance, generating a tailored strategy that not only dampens the impact of stale updates, but also leverages fresh ones. We recover convergence bounds for adaptiveness functions satisfying the $\mathtt{ASAP.SGD}$ conditions for general, convex and non-convex problems, and establish novel bounds for ones satisfying the Polyak-Lojasiewicz property. We evaluate \textsc{tail}-$\tau$ with representative AsyncSGD concurrent algorithms, for Deep Learning problems, showing \textsc{tail}-$\tau$ is a vital complement to AsyncSGD, with (i) persistent speedup in wall-clock convergence time in the parallelism spectrum, (ii) considerably lower risk of non-convergence, as well as (iii) precision levels for which original SGD implementations fail. | Karl Bäckström, Marina Papatriantafilou, Philippas Tsigas | null | null | 2,022 | icml |
Certified Neural Network Watermarks with Randomized Smoothing | null | Watermarking is a commonly used strategy to protect creators’ rights to digital images, videos and audio. Recently, watermarking methods have been extended to deep learning models – in principle, the watermark should be preserved when an adversary tries to copy the model. However, in practice, watermarks can often be removed by an intelligent adversary. Several papers have proposed watermarking methods that claim to be empirically resistant to different types of removal attacks, but these new techniques often fail in the face of new or better-tuned adversaries. In this paper, we propose the first certifiable watermarking method. Using the randomized smoothing technique, we show that our watermark is guaranteed to be unremovable unless the model parameters are changed by more than a certain $\ell_2$ threshold. In addition to being certifiable, our watermark is also empirically more robust compared to previous watermarking methods. | Arpit Bansal, Ping-Yeh Chiang, Michael J Curry, Rajiv Jain, Curtis Wigington, Varun Manjunatha, John P Dickerson, Tom Goldstein | null | null | 2,022 | icml |
Fast Composite Optimization and Statistical Recovery in Federated Learning | null | As a prevalent distributed learning paradigm, Federated Learning (FL) trains a global model on a massive amount of devices with infrequent communication. This paper investigates a class of composite optimization and statistical recovery problems in the FL setting, whose loss function consists of a data-dependent smooth loss and a non-smooth regularizer. Examples include sparse linear regression using Lasso, low-rank matrix recovery using nuclear norm regularization, etc. In the existing literature, federated composite optimization algorithms are designed only from an optimization perspective without any statistical guarantees. In addition, they do not consider commonly used (restricted) strong convexity in statistical recovery problems. We advance the frontiers of this problem from both optimization and statistical perspectives. From optimization upfront, we propose a new algorithm named Fast Federated Dual Averaging for strongly convex and smooth loss and establish state-of-the-art iteration and communication complexity in the composite setting. In particular, we prove that it enjoys a fast rate, linear speedup, and reduced communication rounds. From statistical upfront, for restricted strongly convex and smooth loss, we design another algorithm, namely Multi-stage Federated Dual Averaging, and prove a high probability complexity bound with linear speedup up to optimal statistical precision. Numerical experiments in both synthetic and real data demonstrate that our methods perform better than other baselines. To the best of our knowledge, this is the first work providing fast optimization algorithms and statistical recovery guarantees for composite problems in FL. | Yajie Bao, Michael Crawshaw, Shan Luo, Mingrui Liu | null | null | 2,022 | icml |
Asymptotically-Optimal Gaussian Bandits with Side Observations | null | We study the problem of Gaussian bandits with general side information, as first introduced by Wu, Szepesvári, and György. In this setting, the play of an arm reveals information about other arms, according to an arbitrary a priori known side information matrix: each element of this matrix encodes the fidelity of the information that the “row" arm reveals about the “column" arm. In the case of Gaussian noise, this model subsumes standard bandits, full-feedback, and graph-structured feedback as special cases. In this work, we first construct an LP-based asymptotic instance-dependent lower bound on the regret. The LP optimizes the cost (regret) required to reliably estimate the suboptimality gap of each arm. This LP lower bound motivates our main contribution: the first known asymptotically optimal algorithm for this general setting. | Alexia Atsidakou, Orestis Papadigenopoulos, Constantine Caramanis, Sujay Sanghavi, Sanjay Shakkottai | null | null | 2,022 | icml |
Imitation Learning by Estimating Expertise of Demonstrators | null | Many existing imitation learning datasets are collected from multiple demonstrators, each with different expertise at different parts of the environment. Yet, standard imitation learning algorithms typically treat all demonstrators as homogeneous, regardless of their expertise, absorbing the weaknesses of any suboptimal demonstrators. In this work, we show that unsupervised learning over demonstrator expertise can lead to a consistent boost in the performance of imitation learning algorithms. We develop and optimize a joint model over a learned policy and expertise levels of the demonstrators. This enables our model to learn from the optimal behavior and filter out the suboptimal behavior of each demonstrator. Our model learns a single policy that can outperform even the best demonstrator, and can be used to estimate the expertise of any demonstrator at any state. We illustrate our findings on real-robotic continuous control tasks from Robomimic and discrete environments such as MiniGrid and chess, out-performing competing methods in 21 out of 23 settings, with an average of 7% and up to 60% improvement in terms of the final reward. | Mark Beliaev, Andy Shih, Stefano Ermon, Dorsa Sadigh, Ramtin Pedarsani | null | null | 2,022 | icml |
Neural Fisher Discriminant Analysis: Optimal Neural Network Embeddings in Polynomial Time | null | Fisher’s Linear Discriminant Analysis (FLDA) is a statistical analysis method that linearly embeds data points to a lower dimensional space to maximize a discrimination criterion such that the variance between classes is maximized while the variance within classes is minimized. We introduce a natural extension of FLDA that employs neural networks, called Neural Fisher Discriminant Analysis (NFDA). This method finds the optimal two-layer neural network that embeds data points to optimize the same discrimination criterion. We use tools from convex optimization to transform the optimal neural network embedding problem into a convex problem. The resulting problem is easy to interpret and solve to global optimality. We evaluate the method’s performance on synthetic and real datasets. | Burak Bartan, Mert Pilanci | null | null | 2,022 | icml |
Representation Topology Divergence: A Method for Comparing Neural Network Representations. | null | Comparison of data representations is a complex multi-aspect problem. We propose a method for comparing two data representations. We introduce the Representation Topology Divergence (RTD) score measuring the dissimilarity in multi-scale topology between two point clouds of equal size with a one-to-one correspondence between points. The two data point clouds can lie in different ambient spaces. The RTD score is one of the few topological data analysis based practical methods applicable to real machine learning datasets. Experiments show the agreement of RTD with the intuitive assessment of data representation similarity. The proposed RTD score is sensitive to the data representation’s fine topological structure. We use the RTD score to gain insights on neural networks representations in computer vision and NLP domains for various problems: training dynamics analysis, data distribution shift, transfer learning, ensemble learning, disentanglement assessment. | Serguei Barannikov, Ilya Trofimov, Nikita Balabin, Evgeny Burnaev | null | null | 2,022 | icml |
Sparse Mixed Linear Regression with Guarantees: Taming an Intractable Problem with Invex Relaxation | null | In this paper, we study the problem of sparse mixed linear regression on an unlabeled dataset that is generated from linear measurements from two different regression parameter vectors. Since the data is unlabeled, our task is to not only figure out a good approximation of regression parameter vectors but also label the dataset correctly. In its original form, this problem is NP-hard. The most popular algorithms to solve this problem (such as Expectation-Maximization) have a tendency to stuck at local minima. We provide a novel invex relaxation for this intractable problem which leads to a solution with provable theoretical guarantees. This relaxation enables exact recovery of data labels. Furthermore, we recover close approximation of regression parameter vectors which match the true parameter vectors in support and sign. Our formulation uses a carefully constructed primal dual witnesses framework for the invex problem. Furthermore, we show that the sample complexity of our method is only logarithmic in terms of the dimension of the regression parameter vectors. | Adarsh Barik, Jean Honorio | null | null | 2,022 | icml |
Fictitious Play and Best-Response Dynamics in Identical Interest and Zero-Sum Stochastic Games | null | This paper proposes an extension of a popular decentralized discrete-time learning procedure when repeating a static game called fictitious play (FP) (Brown, 1951; Robinson, 1951) to a dynamic model called discounted stochastic game (Shapley, 1953). Our family of discrete-time FP procedures is proven to converge to the set of stationary Nash equilibria in identical interest discounted stochastic games. This extends similar convergence results for static games (Monderer & Shapley, 1996a). We then analyze the continuous-time counterpart of our FP procedures, which include as a particular case the best-response dynamic introduced and studied by Leslie et al. (2020) in the context of zero-sum stochastic games. We prove the converge of this dynamics to stationary Nash equilibria in identical-interest and zero-sum discounted stochastic games. Thanks to stochastic approximations, we can infer from the continuous-time convergence some discrete time results such as the convergence to stationary equilibria in zero-sum and team stochastic games (Holler, 2020). | Lucas Baudin, Rida Laraki | null | null | 2,022 | icml |
Estimating the Optimal Covariance with Imperfect Mean in Diffusion Probabilistic Models | null | Diffusion probabilistic models (DPMs) are a class of powerful deep generative models (DGMs). Despite their success, the iterative generation process over the full timesteps is much less efficient than other DGMs such as GANs. Thus, the generation performance on a subset of timesteps is crucial, which is greatly influenced by the covariance design in DPMs. In this work, we consider diagonal and full covariances to improve the expressive power of DPMs. We derive the optimal result for such covariances, and then correct it when the mean of DPMs is imperfect. Both the optimal and the corrected ones can be decomposed into terms of conditional expectations over functions of noise. Building upon it, we propose to estimate the optimal covariance and its correction given imperfect mean by learning these conditional expectations. Our method can be applied to DPMs with both discrete and continuous timesteps. We consider the diagonal covariance in our implementation for computational efficiency. For an efficient practical implementation, we adopt a parameter sharing scheme and a two-stage training process. Empirically, our method outperforms a wide variety of covariance design on likelihood results, and improves the sample quality especially on a small number of timesteps. | Fan Bao, Chongxuan Li, Jiacheng Sun, Jun Zhu, Bo Zhang | null | null | 2,022 | icml |
Approximate Bayesian Computation with Domain Expert in the Loop | null | Approximate Bayesian computation (ABC) is a popular likelihood-free inference method for models with intractable likelihood functions. As ABC methods usually rely on comparing summary statistics of observed and simulated data, the choice of the statistics is crucial. This choice involves a trade-off between loss of information and dimensionality reduction, and is often determined based on domain knowledge. However, handcrafting and selecting suitable statistics is a laborious task involving multiple trial-and-error steps. In this work, we introduce an active learning method for ABC statistics selection which reduces the domain expert’s work considerably. By involving the experts, we are able to handle misspecified models, unlike the existing dimension reduction methods. Moreover, empirical results show better posterior estimates than with existing methods, when the simulation budget is limited. | Ayush Bharti, Louis Filstroff, Samuel Kaski | null | null | 2,022 | icml |
Matching Normalizing Flows and Probability Paths on Manifolds | null | Continuous Normalizing Flows (CNFs) are a class of generative models that transform a prior distribution to a model distribution by solving an ordinary differential equation (ODE). We propose to train CNFs on manifolds by minimizing probability path divergence (PPD), a novel family of divergences between the probability density path generated by the CNF and a target probability density path. PPD is formulated using a logarithmic mass conservation formula which is a linear first order partial differential equation relating the log target probabilities and the CNF’s defining vector field. PPD has several key benefits over existing methods: it sidesteps the need to solve an ODE per iteration, readily applies to manifold data, scales to high dimensions, and is compatible with a large family of target paths interpolating pure noise and data in finite time. Theoretically, PPD is shown to bound classical probability divergences. Empirically, we show that CNFs learned by minimizing PPD achieve state-of-the-art results in likelihoods and sample quality on existing low-dimensional manifold benchmarks, and is the first example of a generative model to scale to moderately high dimensional manifolds. | Heli Ben-Hamu, Samuel Cohen, Joey Bose, Brandon Amos, Maximillian Nickel, Aditya Grover, Ricky T. Q. Chen, Yaron Lipman | null | null | 2,022 | icml |
Minimax M-estimation under Adversarial Contamination | null | We present a new finite-sample analysis of Catoni’s M-estimator under adversarial contamination, where an adversary is allowed to corrupt a fraction of the samples arbitrarily. We make minimal assumptions on the distribution of the uncontaminated random variables, namely, we only assume the existence of a known upper bound $\upsilon_{\varepsilon} > 0$ on the $(1+\varepsilon)^{th}$ central moment of the random variables, namely, for $\varepsilon \in (0,1]$ \[ \mathbb{E}_{X_1 \sim \mathcal{D}} \Big| X_1 - \mu \Big|^{1+\varepsilon} \leq \upsilon_{\varepsilon}. \]{We} provide a lower bound on the minimax error rate for the mean estimation problem under adversarial corruption under this weak assumption, and establish that the proposed M-estimator achieves this lower bound (up to multiplicative constants). When the variance is infinite, the tolerance to contamination of any estimator reduces as $\varepsilon \downarrow 0$. We establish a tight upper bound that characterizes this bargain. To illustrate the usefulness of the derived robust M-estimator in an online setting, we present a bandit algorithm for the partially identifiable best arm identification problem that improves upon the sample complexity of the state of the art algorithms. | Sujay Bhatt, Guanhua Fang, Ping Li, Gennady Samorodnitsky | null | null | 2,022 | icml |
Nearly Optimal Catoni’s M-estimator for Infinite Variance | null | In this paper, we extend the remarkable M-estimator of Catoni \citep{Cat12} to situations where the variance is infinite. In particular, given a sequence of i.i.d random variables $\{X_i\}_{i=1}^n$ from distribution $\mathcal{D}$ over $\mathbb{R}$ with mean $\mu$, we only assume the existence of a known upper bound $\upsilon_{\varepsilon} > 0$ on the $(1+\varepsilon)^{th}$ central moment of the random variables, namely, for $\varepsilon \in (0,1]$ \[ \mathbb{E}_{X_1 \sim \mathcal{D}} \Big| X_1 - \mu \Big|^{1+\varepsilon} \leq \upsilon_{\varepsilon}. \]{The} extension is non-trivial owing to the difficulty in characterizing the roots of certain polynomials of degree smaller than $2$. The proposed estimator has the same order of magnitude and the same asymptotic constant as in \citet{Cat12}, but for the case of bounded moments. We further propose a version of the estimator that does not require even the knowledge of $\upsilon_{\varepsilon}$, but adapts the moment bound in a data-driven manner. Finally, to illustrate the usefulness of the derived non-asymptotic confidence bounds, we consider an application in multi-armed bandits and propose best arm identification algorithms, in the fixed confidence setting, that outperform the state of the art. | Sujay Bhatt, Guanhua Fang, Ping Li, Gennady Samorodnitsky | null | null | 2,022 | icml |
Safe Learning in Tree-Form Sequential Decision Making: Handling Hard and Soft Constraints | null | We study decision making problems in which an agent sequentially interacts with a stochastic environment defined by means of a tree structure. The agent repeatedly faces the environment over time, and, after each round, it perceives a utility and a cost, which are both stochastic. The goal of the agent is to learn an optimal strategy in an online fashion, while, at the same time, keeping costs below a given safety threshold. Our model naturally fits many real-world scenarios, such as, e.g., opponent exploitation in games and web link selection. We study the hard-threshold problem of achieving sublinear regret while guaranteeing that the threshold constraint is satisfied at every iteration with high probability. First, we show that, in general, any algorithm with such a guarantee incurs in a linear regret. This motivates the introduction of a relaxed problem, namely the soft-threshold problem, in which we only require that the cumulative violation of the threshold constraint grows sublinearly, and, thus, we can provide an algorithm with sublinear regret. Next, we show how, in the hard-threshold problem, a sublinear regret algorithm can be designed under the additional assumption that there exists a known strategy strictly satisfying the threshold constraint. We also show that our regret bounds are tight. Finally, we cast the opponent exploitation problem to our model, and we experimentally evaluate our algorithms on a standard testbed of games. | Martino Bernasconi, Federico Cacciamani, Matteo Castiglioni, Alberto Marchesi, Nicola Gatti, Francesco Trovò | null | null | 2,022 | icml |
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Neural Inverse Kinematic | null | Inverse kinematic (IK) methods recover the parameters of the joints, given the desired position of selected elements in the kinematic chain. While the problem is well-defined and low-dimensional, it has to be solved rapidly, accounting for multiple possible solutions. In this work, we propose a neural IK method that employs the hierarchical structure of the problem to sequentially sample valid joint angles conditioned on the desired position and on the preceding joints along the chain. In our solution, a hypernetwork $f$ recovers the parameters of multiple primary networks {$g_1,g_2,…,g_N$, where $N$ is the number of joints}, such that each $g_i$ outputs a distribution of possible joint angles, and is conditioned on the sampled values obtained from the previous primary networks $g_j, j
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BibTeX
@InProceedings{pmlr-v162-bensadoun22a,
title = {Neural Inverse Kinematic},
author = {Bensadoun, Raphael and Gur, Shir and Blau, Nitsan and Wolf, Lior},
booktitle = {Proceedings of the 39th International Conference on Machine Learning},
pages = {1787--1797},
year = {2022},
editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan},
volume = {162},
series = {Proceedings of Machine Learning Research},
month = {17--23 Jul},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v162/bensadoun22a/bensadoun22a.pdf},
url = {https://proceedings.mlr.press/v162/bensadoun22a.html},
abstract = {Inverse kinematic (IK) methods recover the parameters of the joints, given the desired position of selected elements in the kinematic chain. While the problem is well-defined and low-dimensional, it has to be solved rapidly, accounting for multiple possible solutions. In this work, we propose a neural IK method that employs the hierarchical structure of the problem to sequentially sample valid joint angles conditioned on the desired position and on the preceding joints along the chain. In our solution, a hypernetwork $f$ recovers the parameters of multiple primary networks {$g_1,g_2,…,g_N$, where $N$ is the number of joints}, such that each $g_i$ outputs a distribution of possible joint angles, and is conditioned on the sampled values obtained from the previous primary networks $g_j, j
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%0 Conference Paper
%T Neural Inverse Kinematic
%A Raphael Bensadoun
%A Shir Gur
%A Nitsan Blau
%A Lior Wolf
%B Proceedings of the 39th International Conference on Machine Learning
%C Proceedings of Machine Learning Research
%D 2022
%E Kamalika Chaudhuri
%E Stefanie Jegelka
%E Le Song
%E Csaba Szepesvari
%E Gang Niu
%E Sivan Sabato
%F pmlr-v162-bensadoun22a
%I PMLR
%P 1787--1797
%U https://proceedings.mlr.press/v162/bensadoun22a.html
%V 162
%X Inverse kinematic (IK) methods recover the parameters of the joints, given the desired position of selected elements in the kinematic chain. While the problem is well-defined and low-dimensional, it has to be solved rapidly, accounting for multiple possible solutions. In this work, we propose a neural IK method that employs the hierarchical structure of the problem to sequentially sample valid joint angles conditioned on the desired position and on the preceding joints along the chain. In our solution, a hypernetwork $f$ recovers the parameters of multiple primary networks {$g_1,g_2,…,g_N$, where $N$ is the number of joints}, such that each $g_i$ outputs a distribution of possible joint angles, and is conditioned on the sampled values obtained from the previous primary networks $g_j, j
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Bensadoun, R., Gur, S., Blau, N. & Wolf, L.. (2022). Neural Inverse Kinematic. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:1787-1797 Available from https://proceedings.mlr.press/v162/bensadoun22a.html.
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