NeurIPS 2021 Papers

We study reinforcement learning (RL) with linear function approximation. Existing algorithms for this problem only have high-probability regret and/or Probably Approximately Correct (PAC) sample complexity guarantees, which cannot guarantee the convergence to the optimal policy. In this paper, in order to overcome the limitation of existing algorithms, we propose a new algorithm called FLUTE, which enjoys uniform-PAC convergence to the optimal policy with high probability. The uniform-PAC guarantee is the strongest possible guarantee for reinforcement learning in the literature, which can directly imply both PAC and high probability regret bounds, making our algorithm superior to all existing algorithms with linear function approximation. At the core of our algorithm is a novel minimax value function estimator and a multi-level partition scheme to select the training samples from historical observations. Both of these techniques are new and of independent interest.

Double Q-learning (Hasselt, 2010) has gained significant success in practice due to its effectiveness in overcoming the overestimation issue of Q-learning. However, the theoretical understanding of double Q-learning is rather limited. The only existing finite-time analysis was recently established in (Xiong et al. 2020), where the polynomial learning rate adopted in the analysis typically yields a slower convergence rate. This paper tackles the more challenging case of a constant learning rate, and develops new analytical tools that improve the existing convergence rate by orders of magnitude. Specifically, we show that synchronous double Q-learning attains an $\epsilon$-accurate global optimum with a time complexity of $\tilde{\Omega}\left(\frac{\ln D}{(1-\gamma)^7\epsilon^2} \right)$, and the asynchronous algorithm achieves a time complexity of $\tilde{\Omega}\left(\frac{L}{(1-\gamma)^7\epsilon^2} \right)$, where $D$ is the cardinality of the state-action space, $\gamma$ is the discount factor, and $L$ is a parameter related to the sampling strategy for asynchronous double Q-learning. These results improve the existing convergence rate by the order of magnitude in terms of its dependence on all major parameters $(\epsilon,1-\gamma, D, L)$. This paper presents a substantial step toward the full understanding of the fast convergence of double-Q learning.

Graph neural networks (GNNs) have limited expressive power, failing to represent many graph classes correctly. While more expressive graph representation learning (GRL) alternatives can distinguish some of these classes, they are significantly harder to implement, may not scale well, and have not been shown to outperform well-tuned GNNs in real-world tasks. Thus, devising simple, scalable, and expressive GRL architectures that also achieve real-world improvements remains an open challenge. In this work, we show the extent to which graph reconstruction---reconstructing a graph from its subgraphs---can mitigate the theoretical and practical problems currently faced by GRL architectures. First, we leverage graph reconstruction to build two new classes of expressive graph representations. Secondly, we show how graph reconstruction boosts the expressive power of any GNN architecture while being a (provably) powerful inductive bias for invariances to vertex removals. Empirically, we show how reconstruction can boost GNN's expressive power---while maintaining its invariance to permutations of the vertices---by solving seven graph property tasks not solvable by the original GNN. Further, we demonstrate how it boosts state-of-the-art GNN's performance across nine real-world benchmark datasets.

This paper investigates the problem of computing the equilibrium of competitive games, which is often modeled as a constrained saddle-point optimization problem with probability simplex constraints. Despite recent efforts in understanding the last-iterate convergence of extragradient methods in the unconstrained setting, the theoretical underpinnings of these methods in the constrained settings, especially those using multiplicative updates, remain highly inadequate, even when the objective function is bilinear. Motivated by the algorithmic role of entropy regularization in single-agent reinforcement learning and game theory, we develop provably efficient extragradient methods to find the quantal response equilibrium (QRE)---which are solutions to zero-sum two-player matrix games with entropy regularization---at a linear rate. The proposed algorithms can be implemented in a decentralized manner, where each player executes symmetric and multiplicative updates iteratively using its own payoff without observing the opponent's actions directly. In addition, by controlling the knob of entropy regularization, the proposed algorithms can locate an approximate Nash equilibrium of the unregularized matrix game at a sublinear rate without assuming the Nash equilibrium to be unique. Our methods also lead to efficient policy extragradient algorithms for solving entropy-regularized zero-sum Markov games at a linear rate. All of our convergence rates are nearly dimension-free, which are independent of the size of the state and action spaces up to logarithm factors, highlighting the positive role of entropy regularization for accelerating convergence.

We introduce TransformerFusion, a transformer-based 3D scene reconstruction approach. From an input monocular RGB video, the video frames are processed by a transformer network that fuses the observations into a volumetric feature grid representing the scene; this feature grid is then decoded into an implicit 3D scene representation. Key to our approach is the transformer architecture that enables the network to learn to attend to the most relevant image frames for each 3D location in the scene, supervised only by the scene reconstruction task. Features are fused in a coarse-to-fine fashion, storing fine-level features only where needed, requiring lower memory storage and enabling fusion at interactive rates. The feature grid is then decoded to a higher-resolution scene reconstruction, using an MLP-based surface occupancy prediction from interpolated coarse-to-fine 3D features. Our approach results in an accurate surface reconstruction, outperforming state-of-the-art multi-view stereo depth estimation methods, fully-convolutional 3D reconstruction approaches, and approaches using LSTM- or GRU-based recurrent networks for video sequence fusion.

Since its introduction a decade ago, relative entropy policy search (REPS) has demonstrated successful policy learning on a number of simulated and real-world robotic domains, not to mention providing algorithmic components used by many recently proposed reinforcement learning (RL) algorithms. While REPS is commonly known in the community, there exist no guarantees on its performance when using stochastic and gradient-based solvers. In this paper we aim to fill this gap by providing guarantees and convergence rates for the sub-optimality of a policy learned using first-order optimization methods applied to the REPS objective. We first consider the setting in which we are given access to exact gradients and demonstrate how near-optimality of the objective translates to near-optimality of the policy. We then consider the practical setting of stochastic gradients, and introduce a technique that uses generative access to the underlying Markov decision process to compute parameter updates that maintain favorable convergence to the optimal regularized policy.

Machine learning models trained on uncurated datasets can often end up adversely affecting inputs belonging to underrepresented groups. To address this issue, we consider the problem of adaptively constructing training sets which allow us to learn classifiers that are fair in a {\em minimax} sense. We first propose an adaptive sampling algorithm based on the principle of \emph{optimism}, and derive theoretical bounds on its performance. We also propose heuristic extensions of this algorithm suitable for application to large scale, practical problems. Next, by deriving algorithm independent lower-bounds for a specific class of problems, we show that the performance achieved by our adaptive scheme cannot be improved in general. We then validate the benefits of adaptively constructing training sets via experiments on synthetic tasks with logistic regression classifiers, as well as on several real-world tasks using convolutional neural networks (CNNs).

In this paper, we comparatively analyze the Bures-Wasserstein (BW) geometry with the popular Affine-Invariant (AI) geometry for Riemannian optimization on the symmetric positive definite (SPD) matrix manifold. Our study begins with an observation that the BW metric has a linear dependence on SPD matrices in contrast to the quadratic dependence of the AI metric. We build on this to show that the BW metric is a more suitable and robust choice for several Riemannian optimization problems over ill-conditioned SPD matrices. We show that the BW geometry has a non-negative curvature, which further improves convergence rates of algorithms over the non-positively curved AI geometry. Finally, we verify that several popular cost functions, which are known to be geodesic convex under the AI geometry, are also geodesic convex under the BW geometry. Extensive experiments on various applications support our findings.

We present 3DP3, a framework for inverse graphics that uses inference in a structured generative model of objects, scenes, and images. 3DP3 uses (i) voxel models to represent the 3D shape of objects, (ii) hierarchical scene graphs to decompose scenes into objects and the contacts between them, and (iii) depth image likelihoods based on real-time graphics. Given an observed RGB-D image, 3DP3's inference algorithm infers the underlying latent 3D scene, including the object poses and a parsimonious joint parametrization of these poses, using fast bottom-up pose proposals, novel involutive MCMC updates of the scene graph structure, and, optionally, neural object detectors and pose estimators. We show that 3DP3 enables scene understanding that is aware of 3D shape, occlusion, and contact structure. Our results demonstrate that 3DP3 is more accurate at 6DoF object pose estimation from real images than deep learning baselines and shows better generalization to challenging scenes with novel viewpoints, contact, and partial observability.

We study the gradient flow for a relaxed approximation to the Kullback-Leibler (KL) divergence between a moving source and a fixed target distribution. This approximation, termed the KALE (KL approximate lower-bound estimator), solves a regularized version of the Fenchel dual problem defining the KL over a restricted class of functions. When using a Reproducing Kernel Hilbert Space (RKHS) to define the function class, we show that the KALE continuously interpolates between the KL and the Maximum Mean Discrepancy (MMD). Like the MMD and other Integral Probability Metrics, the KALE remains well defined for mutually singular distributions. Nonetheless, the KALE inherits from the limiting KL a greater sensitivity to mismatch in the support of the distributions, compared with the MMD. These two properties make the KALE gradient flow particularly well suited when the target distribution is supported on a low-dimensional manifold. Under an assumption of sufficient smoothness of the trajectories, we show the global convergence of the KALE flow. We propose a particle implementation of the flow given initial samples from the source and the target distribution, which we use to empirically confirm the KALE's properties.

Modern neural networks are often quite wide, causing large memory and computation costs. It is thus of great interest to train a narrower network. However, training narrow neural nets remains a challenging task. We ask two theoretical questions: Can narrow networks have as strong expressivity as wide ones? If so, does the loss function exhibit a benign optimization landscape? In this work, we provide partially affirmative answers to both questions for 1-hidden-layer networks with fewer than $n$ (sample size) neurons when the activation is smooth. First, we prove that as long as the width $m \geq 2n/d$ (where $d$ is the input dimension), its expressivity is strong, i.e., there exists at least one global minimizer with zero training loss. Second, we identify a nice local region with no local-min or saddle points. Nevertheless, it is not clear whether gradient descent can stay in this nice region. Third, we consider a constrained optimization formulation where the feasible region is the nice local region, and prove that every KKT point is a nearly global minimizer. It is expected that projected gradient methods converge to KKT points under mild technical conditions, but we leave the rigorous convergence analysis to future work. Thorough numerical results show that projected gradient methods on this constrained formulation significantly outperform SGD for training narrow neural nets.

Existing deep hierarchical topic models are able to extract semantically meaningful topics from a text corpus in an unsupervised manner and automatically organize them into a topic hierarchy. However, it is unclear how to incorporate prior belief such as knowledge graph to guide the learning of the topic hierarchy. To address this issue, we introduce TopicNet as a deep hierarchical topic model that can inject prior structural knowledge as inductive bias to influence the learning. TopicNet represents each topic as a Gaussian-distributed embedding vector, projects the topics of all layers into a shared embedding space, and explores both the symmetric and asymmetric similarities between Gaussian embedding vectors to incorporate prior semantic hierarchies. With a variational auto-encoding inference network, the model parameters are optimized by minimizing the evidence lower bound and supervised loss via stochastic gradient descent. Experiments on widely used benchmark show that TopicNet outperforms related deep topic models on discovering deeper interpretable topics and mining better document representations.

Approximate Bayesian inference estimates descriptors of an intractable target distribution - in essence, an optimization problem within a family of distributions. For example, Langevin dynamics (LD) extracts asymptotically exact samples from a diffusion process because the time evolution of its marginal distributions constitutes a curve that minimizes the KL-divergence via steepest descent in the Wasserstein space. Parallel to LD, Stein variational gradient descent (SVGD) similarly minimizes the KL, albeit endowed with a novel Stein-Wasserstein distance, by deterministically transporting a set of particle samples, thus de-randomizes the stochastic diffusion process. We propose de-randomized kernel-based particle samplers to all diffusion-based samplers known as MCMC dynamics. Following previous work in interpreting MCMC dynamics, we equip the Stein-Wasserstein space with a fiber-Riemannian Poisson structure, with the capacity of characterizing a fiber-gradient Hamiltonian flow that simulates MCMC dynamics. Such dynamics discretizes into generalized SVGD (GSVGD), a Stein-type deterministic particle sampler, with particle updates coinciding with applying the diffusion Stein operator to a kernel function. We demonstrate empirically that GSVGD can de-randomize complex MCMC dynamics, which combine the advantages of auxiliary momentum variables and Riemannian structure, while maintaining the high sample quality from an interacting particle system.

Recent work demonstrates that deep neural networks trained using Empirical Risk Minimization (ERM) can generalize under distribution shift, outperforming specialized training algorithms for domain generalization. The goal of this paper is to further understand this phenomenon. In particular, we study the extent to which the seminal domain adaptation theory of Ben-David et al. (2007) explains the performance of ERMs. Perhaps surprisingly, we find that this theory does not provide a tight explanation of the out-of-domain generalization observed across a large number of ERM models trained on three popular domain generalization datasets. This motivates us to investigate other possible measures—that, however, lack theory—which could explain generalization in this setting. Our investigation reveals that measures relating to the Fisher information, predictive entropy, and maximum mean discrepancy are good predictors of the out-of-distribution generalization of ERM models. We hope that our work helps galvanize the community towards building a better understanding of when deep networks trained with ERM generalize out-of-distribution.

Machine learning is vulnerable to a wide variety of attacks. It is now well understood that by changing the underlying data distribution, an adversary can poison the model trained with it or introduce backdoors. In this paper we present a novel class of training-time attacks that require no changes to the underlying dataset or model architecture, but instead only change the order in which data are supplied to the model. In particular, we find that the attacker can either prevent the model from learning, or poison it to learn behaviours specified by the attacker. Furthermore, we find that even a single adversarially-ordered epoch can be enough to slow down model learning, or even to reset all of the learning progress. Indeed, the attacks presented here are not specific to the model or dataset, but rather target the stochastic nature of modern learning procedures. We extensively evaluate our attacks on computer vision and natural language benchmarks to find that the adversary can disrupt model training and even introduce backdoors.

Visual question answering (VQA) is designed to examine the visual-textual reasoning ability of an intelligent agent. However, recent observations show that many VQA models may only capture the biases between questions and answers in a dataset rather than showing real reasoning abilities. For example, given a question, some VQA models tend to output the answer that occurs frequently in the dataset and ignore the images. To reduce this tendency, existing methods focus on weakening the language bias. Meanwhile, only a few works also consider vision bias implicitly. However, these methods introduce additional annotations or show unsatisfactory performance. Moreover, not all biases are harmful to the models. Some “biases” learnt from datasets represent natural rules of the world and can help limit the range of answers. Thus, how to filter and remove the true negative biases in language and vision modalities remain a major challenge. In this paper, we propose a method named D-VQA to alleviate the above challenges from the feature and sample perspectives. Specifically, from the feature perspective, we build a question-to-answer and vision-to-answer branch to capture the language and vision biases, respectively. Next, we apply two unimodal bias detection modules to explicitly recognise and remove the negative biases. From the sample perspective, we construct two types of negative samples to assist the training of the models, without introducing additional annotations. Extensive experiments on the VQA-CP v2 and VQA v2 datasets demonstrate the effectiveness of our D-VQA method.

Many reinforcement learning (RL) problems in practice are offline, learning purely from observational data. A key challenge is how to ensure the learned policy is safe, which requires quantifying the risk associated with different actions. In the online setting, distributional RL algorithms do so by learning the distribution over returns (i.e., cumulative rewards) instead of the expected return; beyond quantifying risk, they have also been shown to learn better representations for planning. We propose Conservative Offline Distributional Actor Critic (CODAC), an offline RL algorithm suitable for both risk-neutral and risk-averse domains. CODAC adapts distributional RL to the offline setting by penalizing the predicted quantiles of the return for out-of-distribution actions. We prove that CODAC learns a conservative return distribution---in particular, for finite MDPs, CODAC converges to an uniform lower bound on the quantiles of the return distribution; our proof relies on a novel analysis of the distributional Bellman operator. In our experiments, on two challenging robot navigation tasks, CODAC successfully learns risk-averse policies using offline data collected purely from risk-neutral agents. Furthermore, CODAC is state-of-the-art on the D4RL MuJoCo benchmark in terms of both expected and risk-sensitive performance.

Deep Markov models (DMM) are generative models which are scalable and expressive generalization of Markov models for representation, learning, and inference problems. However, the fundamental stochastic stability guarantees of such models have not been thoroughly investigated. In this paper, we present a novel stability analysis method and provide sufficient conditions of DMM's stochastic stability. The proposed stability analysis is based on the contraction of probabilistic maps modeled by deep neural networks. We make connections between the spectral properties of neural network's weights and different types of used activation function on the stability and overall dynamic behavior of DMMs with Gaussian distributions. Based on the theory, we propose a few practical methods for designing constrained DMMs with guaranteed stability. We empirically substantiate our theoretical results via intuitive numerical experiments using the proposed stability constraints.

Modern convolutional neural networks (CNNs) have massive identical convolution blocks, and, hence, recursive sharing of parameters across these blocks has been proposed to reduce the amount of parameters. However, naive sharing of parameters poses many challenges such as limited representational power and the vanishing/exploding gradients problem of recursively shared parameters. In this paper, we present a recursive convolution block design and training method, in which a recursively shareable part, or a filter basis, is separated and learned while effectively avoiding the vanishing/exploding gradients problem during training. We show that the unwieldy vanishing/exploding gradients problem can be controlled by enforcing the elements of the filter basis orthonormal, and empirically demonstrate that the proposed orthogonality regularization improves the flow of gradients during training. Experimental results on image classification and object detection show that our approach, unlike previous parameter-sharing approaches, does not trade performance to save parameters and consistently outperforms over parameterized counterpart networks. This superior performance demonstrates that the proposed recursive convolution block design and the orthogonality regularization not only prevent performance degradation, but also consistently improve the representation capability while a significant amount of parameters are recursively shared.