ICML 2021 Papers

We address the problem of causal effect estima-tion in the presence of unobserved confounding,but where proxies for the latent confounder(s) areobserved. We propose two kernel-based meth-ods for nonlinear causal effect estimation in thissetting: (a) a two-stage regression approach, and(b) a maximum moment restriction approach. Wefocus on the proximal causal learning setting, butour methods can be used to solve a wider classof inverse problems characterised by a Fredholmintegral equation. In particular, we provide a uni-fying view of two-stage and moment restrictionapproaches for solving this problem in a nonlin-ear setting. We provide consistency guaranteesfor each algorithm, and demonstrate that these ap-proaches achieve competitive results on syntheticdata and data simulating a real-world task. In par-ticular, our approach outperforms earlier methodsthat are not suited to leveraging proxy variables.

It is widely believed that engineering a model to be invariant/equivariant improves generalisation. Despite the growing popularity of this approach, a precise characterisation of the generalisation benefit is lacking. By considering the simplest case of linear models, this paper provides the first provably non-zero improvement in generalisation for invariant/equivariant models when the target distribution is invariant/equivariant with respect to a compact group. Moreover, our work reveals an interesting relationship between generalisation, the number of training examples and properties of the group action. Our results rest on an observation of the structure of function spaces under averaging operators which, along with its consequences for feature averaging, may be of independent interest.

In label-noise learning, the transition matrix plays a key role in building statistically consistent classifiers. Existing consistent estimators for the transition matrix have been developed by exploiting anchor points. However, the anchor-point assumption is not always satisfied in real scenarios. In this paper, we propose an end-to-end framework for solving label-noise learning without anchor points, in which we simultaneously optimize two objectives: the cross entropy loss between the noisy label and the predicted probability by the neural network, and the volume of the simplex formed by the columns of the transition matrix. Our proposed framework can identify the transition matrix if the clean class-posterior probabilities are sufficiently scattered. This is by far the mildest assumption under which the transition matrix is provably identifiable and the learned classifier is statistically consistent. Experimental results on benchmark datasets demonstrate the effectiveness and robustness of the proposed method.

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.

The reward function is widely accepted as a succinct, robust, and transferable representation of a task. Typical approaches, at the basis of Inverse Reinforcement Learning (IRL), leverage on expert demonstrations to recover a reward function. In this paper, we study the theoretical properties of the class of reward functions that are compatible with the expert’s behavior. We analyze how the limited knowledge of the expert’s policy and of the environment affects the reward reconstruction phase. Then, we examine how the error propagates to the learned policy’s performance when transferring the reward function to a different environment. We employ these findings to devise a provably efficient active sampling approach, aware of the need for transferring the reward function, that can be paired with a large variety of IRL algorithms. Finally, we provide numerical simulations on benchmark environments.

While single-agent policy optimization in a fixed environment has attracted a lot of research attention recently in the reinforcement learning community, much less is known theoretically when there are multiple agents playing in a potentially competitive environment. We take steps forward by proposing and analyzing new fictitious play policy optimization algorithms for two-player zero-sum Markov games with structured but unknown transitions. We consider two classes of transition structures: factored independent transition and single-controller transition. For both scenarios, we prove tight $\widetilde{\mathcal{O}}(\sqrt{T})$ regret bounds after $T$ steps in a two-agent competitive game scenario. The regret of each player is measured against a potentially adversarial opponent who can choose a single best policy in hindsight after observing the full policy sequence. Our algorithms feature a combination of Upper Confidence Bound (UCB)-type optimism and fictitious play under the scope of simultaneous policy optimization in a non-stationary environment. When both players adopt the proposed algorithms, their overall optimality gap is $\widetilde{\mathcal{O}}(\sqrt{T})$.

We study multi-objective reinforcement learning (RL) where an agent’s reward is represented as a vector. In settings where an agent competes against opponents, its performance is measured by the distance of its average return vector to a target set. We develop statistically and computationally efficient algorithms to approach the associated target set. Our results extend Blackwell’s approachability theorem \citep{blackwell1956analog} to tabular RL, where strategic exploration becomes essential. The algorithms presented are adaptive; their guarantees hold even without Blackwell’s approachability condition. If the opponents use fixed policies, we give an improved rate of approaching the target set while also tackling the more ambitious goal of simultaneously minimizing a scalar cost function. We discuss our analysis for this special case by relating our results to previous works on constrained RL. To our knowledge, this work provides the first provably efficient algorithms for vector-valued Markov games and our theoretical guarantees are near-optimal.

Policy optimization methods remain a powerful workhorse in empirical Reinforcement Learning (RL), with a focus on neural policies that can easily reason over complex and continuous state and/or action spaces. Theoretical understanding of strategic exploration in policy-based methods with non-linear function approximation, however, is largely missing. In this paper, we address this question by designing ENIAC, an actor-critic method that allows non-linear function approximation in the critic. We show that under certain assumptions, e.g., a bounded eluder dimension $d$ for the critic class, the learner finds to a near-optimal policy in $\widetilde{O}(\mathrm{poly}(d))$ exploration rounds. The method is robust to model misspecification and strictly extends existing works on linear function approximation. We also develop some computational optimizations of our approach with slightly worse statistical guarantees, and an empirical adaptation building on existing deep RL tools. We empirically evaluate this adaptation, and show that it outperforms prior heuristics inspired by linear methods, establishing the value in correctly reasoning about the agent’s uncertainty under non-linear function approximation.

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.

Meta-learning, or learning-to-learn, seeks to design algorithms that can utilize previous experience to rapidly learn new skills or adapt to new environments. Representation learning—a key tool for performing meta-learning—learns a data representation that can transfer knowledge across multiple tasks, which is essential in regimes where data is scarce. Despite a recent surge of interest in the practice of meta-learning, the theoretical underpinnings of meta-learning algorithms are lacking, especially in the context of learning transferable representations. In this paper, we focus on the problem of multi-task linear regression—in which multiple linear regression models share a common, low-dimensional linear representation. Here, we provide provably fast, sample-efficient algorithms to address the dual challenges of (1) learning a common set of features from multiple, related tasks, and (2) transferring this knowledge to new, unseen tasks. Both are central to the general problem of meta-learning. Finally, we complement these results by providing information-theoretic lower bounds on the sample complexity of learning these linear features.

We present a scalable technique for upper bounding the Lipschitz constant of generative models. We relate this quantity to the maximal norm over the set of attainable vector-Jacobian products of a given generative model. We approximate this set by layerwise convex approximations using zonotopes. Our approach generalizes and improves upon prior work using zonotope transformers and we extend to Lipschitz estimation of neural networks with large output dimension. This provides efficient and tight bounds on small networks and can scale to generative models on VAE and DCGAN architectures.

We consider a one-hidden-layer leaky ReLU network of arbitrary width trained by stochastic gradient descent (SGD) following an arbitrary initialization. We prove that SGD produces neural networks that have classification accuracy competitive with that of the best halfspace over the distribution for a broad class of distributions that includes log-concave isotropic and hard margin distributions. Equivalently, such networks can generalize when the data distribution is linearly separable but corrupted with adversarial label noise, despite the capacity to overfit. To the best of our knowledge, this is the first work to show that overparameterized neural networks trained by SGD can generalize when the data is corrupted with adversarial label noise.

This submission considers the problem of updating the rank-$k$ truncated Singular Value Decomposition (SVD) of matrices subject to the addition of new rows and/or columns over time. Such matrix problems represent an important computational kernel in applications such as Latent Semantic Indexing and Recommender Systems. Nonetheless, the proposed framework is purely algebraic and targets general updating problems. The algorithm presented in this paper undertakes a projection viewpoint and focuses on building a pair of subspaces which approximate the linear span of the sought singular vectors of the updated matrix. We discuss and analyze two different choices to form the projection subspaces. Results on matrices from real applications suggest that the proposed algorithm can lead to higher accuracy, especially for the singular triplets associated with the largest modulus singular values. Several practical details and key differences with other approaches are also discussed.

Collecting and aggregating information from several probability measures or histograms is a fundamental task in machine learning. One of the popular solution methods for this task is to compute the barycenter of the probability measures under the Wasserstein metric. However, approximating the Wasserstein barycenter is numerically challenging because of the curse of dimensionality. This paper proposes the projection robust Wasserstein barycenter (PRWB) that has the potential to mitigate the curse of dimensionality, and a relaxed PRWB (RPRWB) model that is computationally more tractable. By combining the iterative Bregman projection algorithm and Riemannian optimization, we propose two algorithms for computing the RPRWB, which is a max-min problem over the Stiefel manifold. The complexity of arithmetic operations of the proposed algorithms for obtaining an $\epsilon$-stationary solution is analyzed. We incorporate the RPRWB into a discrete distribution clustering algorithm, and the numerical results on real text datasets confirm that our RPRWB model helps improve the clustering performance significantly.

Boundary based blackbox attack has been recognized as practical and effective, given that an attacker only needs to access the final model prediction. However, the query efficiency of it is in general high especially for high dimensional image data. In this paper, we show that such efficiency highly depends on the scale at which the attack is applied, and attacking at the optimal scale significantly improves the efficiency. In particular, we propose a theoretical framework to analyze and show three key characteristics to improve the query efficiency. We prove that there exists an optimal scale for projective gradient estimation. Our framework also explains the satisfactory performance achieved by existing boundary black-box attacks. Based on our theoretical framework, we propose Progressive-Scale enabled projective Boundary Attack (PSBA) to improve the query efficiency via progressive scaling techniques. In particular, we employ Progressive-GAN to optimize the scale of projections, which we call PSBA-PGAN. We evaluate our approach on both spatial and frequency scales. Extensive experiments on MNIST, CIFAR-10, CelebA, and ImageNet against different models including a real-world face recognition API show that PSBA-PGAN significantly outperforms existing baseline attacks in terms of query efficiency and attack success rate. We also observe relatively stable optimal scales for different models and datasets. The code is publicly available at https://github.com/AI-secure/PSBA.

We investigate the \textit{problem dependent regime} in the stochastic \emph{Thresholding Bandit problem} (\tbp) under several \emph{shape constraints}. In the \tbp the objective of the learner is to output, after interacting with the environment, the set of arms whose means are above a given threshold. The vanilla, unstructured, case is already well studied in the literature. Taking $K$ as the number of arms, we consider the case where (i) the sequence of arm’s means $(\mu_k){k=1}^K$ is monotonically increasing (\textit{MTBP}) and (ii) the case where $(\mu_k){k=1}^K$ is concave (\textit{CTBP}). We consider both cases in the \emph{problem dependent} regime and study the probability of error - i.e. the probability to mis-classify at least one arm. In the fixed budget setting, we provide nearly matching upper and lower bounds for the probability of error in both the concave and monotone settings, as well as associated algorithms. Of interest, is that for both the monotone and concave cases, optimal bounds on probability of error are of the same order as those for the two armed bandit problem.

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.

We tackle the problem of conditioning probabilistic programs on distributions of observable variables. Probabilistic programs are usually conditioned on samples from the joint data distribution, which we refer to as deterministic conditioning. However, in many real-life scenarios, the observations are given as marginal distributions, summary statistics, or samplers. Conventional probabilistic programming systems lack adequate means for modeling and inference in such scenarios. We propose a generalization of deterministic conditioning to stochastic conditioning, that is, conditioning on the marginal distribution of a variable taking a particular form. To this end, we first define the formal notion of stochastic conditioning and discuss its key properties. We then show how to perform inference in the presence of stochastic conditioning. We demonstrate potential usage of stochastic conditioning on several case studies which involve various kinds of stochastic conditioning and are difficult to solve otherwise. Although we present stochastic conditioning in the context of probabilistic programming, our formalization is general and applicable to other settings.

Generating functions, which are widely used in combinatorics and probability theory, encode function values into the coefficients of a polynomial. In this paper, we explore their use as a tractable probabilistic model, and propose probabilistic generating circuits (PGCs) for their efficient representation. PGCs are strictly more expressive efficient than many existing tractable probabilistic models, including determinantal point processes (DPPs), probabilistic circuits (PCs) such as sum-product networks, and tractable graphical models. We contend that PGCs are not just a theoretical framework that unifies vastly different existing models, but also show great potential in modeling realistic data. We exhibit a simple class of PGCs that are not trivially subsumed by simple combinations of PCs and DPPs, and obtain competitive performance on a suite of density estimation benchmarks. We also highlight PGCs’ connection to the theory of strongly Rayleigh distributions.