ICML 2022 Papers

We study reinforcement learning for infinite-horizon discounted linear kernel MDPs, where the transition probability function is linear in a predefined feature mapping. Existing UCLK \citep{zhou2020provably} algorithm for this setting only has a regret guarantee, which cannot lead to a tight sample complexity bound. In this paper, we extend the uniform-PAC sample complexity from episodic setting to the infinite-horizon discounted setting, and propose a novel algorithm dubbed UPAC-UCLK that achieves an $\Tilde{O}\big(d^2/((1-\gamma)^4\epsilon^2)+1/((1-\gamma)^6\epsilon^2)\big)$ uniform-PAC sample complexity, where $d$ is the dimension of the feature mapping, $\gamma \in(0,1)$ is the discount factor of the MDP and $\epsilon$ is the accuracy parameter. To the best of our knowledge, this is the first $\tilde{O}(1/\epsilon^2)$ sample complexity bound for learning infinite-horizon discounted MDPs with linear function approximation (without access to the generative model).

Offline reinforcement learning (RL) enables effective learning from previously collected data without exploration, which shows great promise in real-world applications when exploration is expensive or even infeasible. The discount factor, $\gamma$, plays a vital role in improving online RL sample efficiency and estimation accuracy, but the role of the discount factor in offline RL is not well explored. This paper examines two distinct effects of $\gamma$ in offline RL with theoretical analysis, namely the regularization effect and the pessimism effect. On the one hand, $\gamma$ is a regulator to trade-off optimality with sample efficiency upon existing offline techniques. On the other hand, lower guidance $\gamma$ can also be seen as a way of pessimism where we optimize the policy’s performance in the worst possible models. We empirically verify the above theoretical observation with tabular MDPs and standard D4RL tasks. The results show that the discount factor plays an essential role in the performance of offline RL algorithms, both under small data regimes upon existing offline methods and in large data regimes without other conservative methods.

The last decade saw impressive progress towards understanding the performance of algorithms in

A set of novel approaches for estimating epistemic uncertainty in deep neural networks with a single forward pass has recently emerged as a valid alternative to Bayesian Neural Networks. On the premise of informative representations, these deterministic uncertainty methods (DUMs) achieve strong performance on detecting out-of-distribution (OOD) data while adding negligible computational costs at inference time. However, it remains unclear whether DUMs are well calibrated and can seamlessly scale to real-world applications - both prerequisites for their practical deployment. To this end, we first provide a taxonomy of DUMs, and evaluate their calibration under continuous distributional shifts. Then, we extend them to semantic segmentation. We find that, while DUMs scale to realistic vision tasks and perform well on OOD detection, the practicality of current methods is undermined by poor calibration under distributional shifts.

When training deep neural networks for classification tasks, an intriguing empirical phenomenon has been widely observed in the last-layer classifiers and features, where (i) the class means and the last-layer classifiers all collapse to the vertices of a Simplex Equiangular Tight Frame (ETF) up to scaling, and (ii) cross-example within-class variability of last-layer activations collapses to zero. This phenomenon is called Neural Collapse (NC), which seems to take place regardless of the choice of loss functions. In this work, we justify NC under the mean squared error (MSE) loss, where recent empirical evidence shows that it performs comparably or even better than the de-facto cross-entropy loss. Under a simplified unconstrained feature model, we provide the first global landscape analysis for vanilla nonconvex MSE loss and show that the (only!) global minimizers are neural collapse solutions, while all other critical points are strict saddles whose Hessian exhibit negative curvature directions. Furthermore, we justify the usage of rescaled MSE loss by probing the optimization landscape around the NC solutions, showing that the landscape can be improved by tuning the rescaling hyperparameters. Finally, our theoretical findings are experimentally verified on practical network architectures.

Non-autoregressive Transformer (NAT) is a family of text generation models, which aims to reduce the decoding latency by predicting the whole sentences in parallel. However, such latency reduction sacrifices the ability to capture left-to-right dependencies, thereby making NAT learning very challenging. In this paper, we present theoretical and empirical analyses to reveal the challenges of NAT learning and propose a unified perspective to understand existing successes. First, we show that simply training NAT by maximizing the likelihood can lead to an approximation of marginal distributions but drops all dependencies between tokens, where the dropped information can be measured by the dataset’s conditional total correlation. Second, we formalize many previous objectives in a unified framework and show that their success can be concluded as maximizing the likelihood on a proxy distribution, leading to a reduced information loss. Empirical studies show that our perspective can explain the phenomena in NAT learning and guide the design of new training methods.

Learning to cooperate with other agents is challenging when those agents also possess the ability to adapt to our own behavior. Practical and theoretical approaches to learning in cooperative settings typically assume that other agents’ behaviors are stationary, or else make very specific assumptions about other agents’ learning processes. The goal of this work is to understand whether we can reliably learn to cooperate with other agents without such restrictive assumptions, which are unlikely to hold in real-world applications. Our main contribution is a set of impossibility results, which show that no learning algorithm can reliably learn to cooperate with all possible adaptive partners in a repeated matrix game, even if that partner is guaranteed to cooperate with some stationary strategy. Motivated by these results, we then discuss potential alternative assumptions which capture the idea that an adaptive partner will only adapt rationally to our behavior.

We focus on parameterized policy search for reinforcement learning over continuous action spaces. Typically, one assumes the score function associated with a policy is bounded, which {fails to hold even for Gaussian policies. } To properly address this issue, one must introduce an exploration tolerance parameter to quantify the region in which it is bounded. Doing so incurs a persistent bias that appears in the attenuation rate of the expected policy gradient norm, which is inversely proportional to the radius of the action space. To mitigate this hidden bias, heavy-tailed policy parameterizations may be used, which exhibit a bounded score function, but doing so can cause instability in algorithmic updates. To address these issues, in this work, we study the convergence of policy gradient algorithms under heavy-tailed parameterizations, which we propose to stabilize with a combination of mirror ascent-type updates and gradient tracking. Our main theoretical contribution is the establishment that this scheme converges with constant batch sizes, whereas prior works require these parameters to respectively shrink to null or grow to infinity. Experimentally, this scheme under a heavy-tailed policy parameterization yields improved reward accumulation across a variety of settings as compared with standard benchmarks.

Many recent studies have highlighted the susceptibility of virtually all machine-learning models to adversarial attacks. Adversarial attacks are imperceptible changes to an input example of a given prediction model. Such changes are carefully designed to alter the otherwise correct prediction of the model. In this paper, we study the generalization properties of adversarial learning. In particular, we derive high-probability generalization bounds on the adversarial risk in terms of the empirical adversarial risk, the complexity of the function class and the adversarial noise set. Our bounds are generally applicable to many models, losses, and adversaries. We showcase its applicability by deriving adversarial generalization bounds for the multi-class classification setting and various prediction models (including linear models and Deep Neural Networks). We also derive optimistic adversarial generalization bounds for the case of smooth losses. These are the first fast-rate bounds valid for adversarial deep learning to the best of our knowledge.

The knowledge gradient (KG) algorithm is a popular and effective algorithm for the best arm identification (BAI) problem. Due to the complex calculation of KG, theoretical analysis of this algorithm is difficult, and existing results are mostly about the asymptotic performance of it, e.g., consistency, asymptotic sample allocation, etc. In this research, we present new theoretical results about the finite-time performance of the KG algorithm. Under independent and normally distributed rewards, we derive lower bounds and upper bounds for the probability of error and simple regret of the algorithm. With these bounds, existing asymptotic results become simple corollaries. We also show the performance of the algorithm for the multi-armed bandit (MAB) problem. These developments not only extend the existing analysis of the KG algorithm, but can also be used to analyze other improvement-based algorithms. Last, we use numerical experiments to further demonstrate the finite-time behavior of the KG algorithm.

We report a practical finite-time algorithmic scheme to compute approximately stationary points for nonconvex nonsmooth Lipschitz functions. In particular, we are interested in two kinds of approximate stationarity notions for nonconvex nonsmooth problems, i.e., Goldstein approximate stationarity (GAS) and near-approximate stationarity (NAS). For GAS, our scheme removes the unrealistic subgradient selection oracle assumption in (Zhang et al., 2020, Assumption 1) and computes GAS with the same finite-time complexity. For NAS, Davis & Drusvyatskiy (2019) showed that $\rho$-weakly convex functions admit finite-time computation, while Tian & So (2021) provided the matching impossibility results of dimension-free finite-time complexity for first-order methods. Complement to these developments, in this paper, we isolate a new class of functions that could be Clarke irregular (and thus not weakly convex anymore) and show that our new algorithmic scheme can compute NAS points for functions in that class within finite time. To demonstrate the wide applicability of our new theoretical framework, we show that $\rho$-margin SVM, $1$-layer, and $2$-layer ReLU neural networks, all being Clarke irregular, satisfy our new conditions.

This work formalizes the associational task of predicting node attribute evolution in temporal graphs from the perspective of learning equivariant representations. We show that node representations in temporal graphs can be cast into two distinct frameworks: (a) The most popular approach, which we denote as time-and-graph, where equivariant graph (e.g., GNN) and sequence (e.g., RNN) representations are intertwined to represent the temporal evolution of node attributes in the graph; and (b) an approach that we denote as time-then-graph, where the sequences describing the node and edge dynamics are represented first, then fed as node and edge attributes into a static equivariant graph representation that comes after. Interestingly, we show that time-then-graph representations have an expressivity advantage over time-and-graph representations when both use component GNNs that are not most-expressive (e.g., 1-Weisfeiler-Lehman GNNs). Moreover, while our goal is not necessarily to obtain state-of-the-art results, our experiments show that time-then-graph methods are capable of achieving better performance and efficiency than state-of-the-art time-and-graph methods in some real-world tasks, thereby showcasing that the time-then-graph framework is a worthy addition to the graph ML toolbox.

Data distortion is commonly applied in vision models during both training (e.g methods like MixUp and CutMix) and evaluation (e.g. shape-texture bias and robustness). This data modification can introduce artificial information. It is often assumed that the resulting artefacts are detrimental to training, whilst being negligible when analysing models. We investigate these assumptions and conclude that in some cases they are unfounded and lead to incorrect results. Specifically, we show current shape bias identification methods and occlusion robustness measures are biased and propose a fairer alternative for the latter. Subsequently, through a series of experiments we seek to correct and strengthen the community’s perception of how augmenting affects learning of vision models. Based on our empirical results we argue that the impact of the artefacts must be understood and exploited rather than eliminated.

Self-Supervised Learning (SSL) is an increasingly popular ML paradigm that trains models to transform complex inputs into representations without relying on explicit labels. These representations encode similarity structures that enable efficient learning of multiple downstream tasks. Recently, ML-as-a-Service providers have commenced offering trained SSL models over inference APIs, which transform user inputs into useful representations for a fee. However, the high cost involved to train these models and their exposure over APIs both make black-box extraction a realistic security threat. We thus explore model stealing attacks against SSL. Unlike traditional model extraction on classifiers that output labels, the victim models here output representations; these representations are of significantly higher dimensionality compared to the low-dimensional prediction scores output by classifiers. We construct several novel attacks and find that approaches that train directly on a victim’s stolen representations are query efficient and enable high accuracy for downstream models. We then show that existing defenses against model extraction are inadequate and not easily retrofitted to the specificities of SSL.

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.

Federated Learning has been actively studied due to its efficiency in numerous real-world applications in the past few years. However, the federated stochastic compositional optimization problem is still underexplored, even though it has widespread applications in machine learning. In this paper, we developed a novel local stochastic compositional gradient descent with momentum method, which facilitates Federated Learning for the stochastic compositional problem. Importantly, we investigated the convergence rate of our proposed method and proved that it can achieve the $O(1/\epsilon^4)$ sample complexity, which is better than existing methods. Meanwhile, our communication complexity $O(1/\epsilon^3)$ can match existing methods. To the best of our knowledge, this is the first work achieving such favorable sample and communication complexities. Additionally, extensive experimental results demonstrate the superior empirical performance over existing methods, confirming the efficacy of our method.

Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear system of equations at each iteration. In common applications of linear programming, particularly in machine learning and scientific computing, the size of this linear system can become prohibitively large, requiring the use of iterative solvers, which provide an approximate solution to the linear system. However, approximately solving the linear system at each iteration of an IPM invalidates the theoretical guarantees of common IPM analyses. To remedy this, we theoretically and empirically analyze (slightly modified) predictor-corrector IPMs when using approximate linear solvers: our approach guarantees that, when certain conditions are satisfied, the number of IPM iterations does not increase and that the final solution remains feasible. We also provide practical instantiations of approximate linear solvers that satisfy these conditions for special classes of constraint matrices using randomized linear algebra.

Algorithmic recourse seeks to provide actionable recommendations for individuals to overcome unfavorable classification outcomes from automated decision-making systems. Recourse recommendations should ideally be robust to reasonably small uncertainty in the features of the individual seeking recourse. In this work, we formulate the adversarially robust recourse problem and show that recourse methods that offer minimally costly recourse fail to be robust. We then present methods for generating adversarially robust recourse for linear and for differentiable classifiers. Finally, we show that regularizing the decision-making classifier to behave locally linearly and to rely more strongly on actionable features facilitates the existence of adversarially robust recourse.

We study the off-policy evaluation (OPE) problem in an infinite-horizon Markov decision process with continuous states and actions. We recast the $Q$-function estimation into a special form of the nonparametric instrumental variables (NPIV) estimation problem. We first show that under one mild condition the NPIV formulation of $Q$-function estimation is well-posed in the sense of $L^2$-measure of ill-posedness with respect to the data generating distribution, bypassing a strong assumption on the discount factor $\gamma$ imposed in the recent literature for obtaining the $L^2$ convergence rates of various $Q$-function estimators. Thanks to this new well-posed property, we derive the first minimax lower bounds for the convergence rates of nonparametric estimation of $Q$-function and its derivatives in both sup-norm and $L^2$-norm, which are shown to be the same as those for the classical nonparametric regression (Stone, 1982). We then propose a sieve two-stage least squares estimator and establish its rate-optimality in both norms under some mild conditions. Our general results on the well-posedness and the minimax lower bounds are of independent interest to study not only other nonparametric estimators for $Q$-function but also efficient estimation on the value of any target policy in off-policy settings.