NeurIPS 2019 Papers

We unify the theory of optimal control of transport equations with the practice of training and testing of ResNets. Based on this unified viewpoint, we propose a simple yet effective ResNets ensemble algorithm to boost the accuracy of the robustly trained model on both clean and adversarial images. The proposed algorithm consists of two components: First, we modify the base ResNets by injecting a variance specified Gaussian noise to the output of each residual mapping. Second, we average over the production of multiple jointly trained modified ResNets to get the final prediction. These two steps give an approximation to the Feynman-Kac formula for representing the solution of a convection-diffusion equation. For the CIFAR10 benchmark, this simple algorithm leads to a robust model with a natural accuracy of {\bf 85.62}\% on clean images and a robust accuracy of ${\bf 57.94 \%}$ under the 20 iterations of the IFGSM attack, which outperforms the current state-of-the-art in defending against IFGSM attack on the CIFAR10.

We propose and investigate new complementary methodologies for estimating predictive variance networks in regression neural networks. We derive a locally aware mini-batching scheme that results in sparse robust gradients, and we show how to make unbiased weight updates to a variance network. Further, we formulate a heuristic for robustly fitting both the mean and variance networks post hoc. Finally, we take inspiration from posterior Gaussian processes and propose a network architecture with similar extrapolation properties to Gaussian processes. The proposed methodologies are complementary, and improve upon baseline methods individually. Experimentally, we investigate the impact of predictive uncertainty on multiple datasets and tasks ranging from regression, active learning and generative modeling. Experiments consistently show significant improvements in predictive uncertainty estimation over state-of-the-art methods across tasks and datasets.

In standard reinforcement learning (RL), a learning agent seeks to optimize the overall reward. However, many key aspects of a desired behavior are more naturally expressed as constraints. For instance, the designer may want to limit the use of unsafe actions, increase the diversity of trajectories to enable exploration, or approximate expert trajectories when rewards are sparse. In this paper, we propose an algorithmic scheme that can handle a wide class of constraints in RL tasks: specifically, any constraints that require expected values of some vector measurements (such as the use of an action) to lie in a convex set. This captures previously studied constraints (such as safety and proximity to an expert), but also enables new classes of constraints (such as diversity). Our approach comes with rigorous theoretical guarantees and only relies on the ability to approximately solve standard RL tasks. As a result, it can be easily adapted to work with any model-free or model-based RL. In our experiments, we show that it matches previous algorithms that enforce safety via constraints, but can also enforce new properties that these algorithms do not incorporate, such as diversity.

Trajectory optimization using a learned model of the environment is one of the core elements of model-based reinforcement learning. This procedure often suffers from exploiting inaccuracies of the learned model. We propose to regularize trajectory optimization by means of a denoising autoencoder that is trained on the same trajectories as the model of the environment. We show that the proposed regularization leads to improved planning with both gradient-based and gradient-free optimizers. We also demonstrate that using regularized trajectory optimization leads to rapid initial learning in a set of popular motor control tasks, which suggests that the proposed approach can be a useful tool for improving sample efficiency.

The classical low rank approximation problem is to find a rank $k$ matrix $UV$ (where $U$ has $k$ columns and $V$ has $k$ rows) that minimizes the Frobenius norm of $A - UV$. Although this problem can be solved efficiently, we study an NP-hard variant of this problem that involves weights and regularization. A previous paper of [Razenshteyn et al. '16] derived a polynomial time algorithm for weighted low rank approximation with constant rank. We derive provably sharper guarantees for the regularized version by obtaining parameterized complexity bounds in terms of the statistical dimension rather than the rank, allowing for a rank-independent runtime that can be significantly faster. Our improvement comes from applying sharper matrix concentration bounds, using a novel conditioning technique, and proving structural theorems for regularized low rank problems.

Gradient Boosting (\GB) is a popular and very successful ensemble method for binary trees. While various types of regularization of the base predictors are used with this algorithm, the theory that connects such regularizations with generalization guarantees is poorly understood. We fill this gap by deriving data-dependent learning guarantees for \GB\ used with \emph{regularization}, expressed in terms of the Rademacher complexities of the constrained families of base predictors. We introduce a new algorithm, called \rgb\, that directly benefits from these generalization bounds and that, at every boosting round, applies the \emph{Structural Risk Minimization} principle to search for a base predictor with the best empirical fit versus complexity trade-off. Inspired by \emph{Randomized Coordinate Descent} we provide a scalable implementation of our algorithm, able to search over large families of base predictors. Finally, we provide experimental results, demonstrating that our algorithm achieves significantly better out-of-sample performance on multiple datasets than the standard \GB\ algorithm used with its regularization.

Model-free deep reinforcement learning (RL) algorithms have been widely used for a range of complex control tasks. However, slow convergence and sample inefficiency remain challenging problems in RL, especially when handling continuous and high-dimensional state spaces. To tackle this problem, we propose a general acceleration method for model-free, off-policy deep RL algorithms by drawing the idea underlying regularized Anderson acceleration (RAA), which is an effective approach to accelerating the solving of fixed point problems with perturbations. Specifically, we first explain how policy iteration can be applied directly with Anderson acceleration. Then we extend RAA to the case of deep RL by introducing a regularization term to control the impact of perturbation induced by function approximation errors. We further propose two strategies, i.e., progressive update and adaptive restart, to enhance the performance. The effectiveness of our method is evaluated on a variety of benchmark tasks, including Atari 2600 and MuJoCo. Experimental results show that our approach substantially improves both the learning speed and final performance of state-of-the-art deep RL algorithms.

We consider an agent who is involved in an online Markov decision process, and receives a vector of outcomes every round. The agent aims to simultaneously optimize multiple objectives associated with the multi-dimensional outcomes. Due to state transitions, it is challenging to balance the vectorial outcomes for achieving near-optimality. In particular, contrary to the single objective case, stationary policies are generally sub-optimal. We propose a no-regret algorithm based on the Frank-Wolfe algorithm (Frank and Wolfe 1956), UCRL2 (Jaksch et al. 2010), as well as a crucial and novel gradient threshold procedure. The procedure involves carefully delaying gradient updates, and returns a non-stationary policy that diversifies the outcomes for optimizing the objectives.

We present an algorithm based on the \emph{Optimism in the Face of Uncertainty} (OFU) principle which is able to learn Reinforcement Learning (RL) modeled by Markov decision process (MDP) with finite state-action space efficiently. By evaluating the state-pair difference of the optimal bias function $h^{*}$, the proposed algorithm achieves a regret bound of $\tilde{O}(\sqrt{SATH})$\footnote{The symbol $\tilde{O}$ means $O$ with log factors ignored. } for MDP with S states and A actions, in the case that an upper bound $H$ on the span of $h^{*}$, i.e., $sp(h^{*})$ is known. This result outperforms the best previous regret bounds $\tilde{O}(HS\sqrt{AT})$\cite{bartlett2009regal} by a factor of $\sqrt{SH}$. Furthermore, this regret bound matches the lower bound of $\Omega(\sqrt{SATH})$\cite{jaksch2010near} up to a logarithmic factor. As a consequence, we show that there is a near optimal regret bound of $\tilde{O}(\sqrt{DSAT})$ for MDPs with finite diameter $D$ compared to the lower bound of $\Omega(\sqrt{DSAT})$\cite{jaksch2010near}.

Restless bandit problems are instances of non-stationary multi-armed bandits. These problems have been studied well from the optimization perspective, where the goal is to efficiently find a near-optimal policy when system parameters are known. However, very few papers adopt a learning perspective, where the parameters are unknown. In this paper, we analyze the performance of Thompson sampling in episodic restless bandits with unknown parameters. We consider a general policy map to define our competitor and prove an $\tilde{\bigO}(\sqrt{T})$ Bayesian regret bound. Our competitor is flexible enough to represent various benchmarks including the best fixed action policy, the optimal policy, the Whittle index policy, or the myopic policy. We also present empirical results that support our theoretical findings.

We consider the problem of online reinforcement learning when several state representations (mapping histories to a discrete state space) are available to the learning agent. At least one of these representations is assumed to induce a Markov decision process (MDP), and the performance of the agent is measured in terms of cumulative regret against the optimal policy giving the highest average reward in this MDP representation. We propose an algorithm (UCB-MS) with O(sqrt(T)) regret in any communicating Markov decision process. The regret bound shows that UCB-MS automatically adapts to the Markov model. This improves over the currently known best results in the literature that gave regret bounds of order O(T^(2/3)).

Recent learning-to-plan methods have shown promising results on planning directly from observation space. Yet, their ability to plan for long-horizon tasks is limited by the accuracy of the prediction model. On the other hand, classical symbolic planners show remarkable capabilities in solving long-horizon tasks, but they require predefined symbolic rules and symbolic states, restricting their real-world applicability. In this work, we combine the benefits of these two paradigms and propose a learning-to-plan method that can directly generate a long-term symbolic plan conditioned on high-dimensional observations. We borrow the idea of regression (backward) planning from classical planning literature and introduce Regression Planning Networks (RPN), a neural network architecture that plans backward starting at a task goal and generates a sequence of intermediate goals that reaches the current observation. We show that our model not only inherits many favorable traits from symbolic planning --including the ability to solve previously unseen tasks-- but also can learn from visual inputs in an end-to-end manner. We evaluate the capabilities of RPN in a grid world environment and a simulated 3D kitchen environment featuring complex visual scenes and long task horizon, and show that it achieves near-optimal performance in completely new task instances.

We introduce a region-specific diffeomorphic metric mapping (RDMM) registration approach. RDMM is non-parametric, estimating spatio-temporal velocity fields which parameterize the sought-for spatial transformation. Regularization of these velocity fields is necessary. In contrast to existing non-parametric registration approaches using a fixed spatially-invariant regularization, for example, the large displacement diffeomorphic metric mapping (LDDMM) model, our approach allows for spatially-varying regularization which is advected via the estimated spatio-temporal velocity field. Hence, not only can our model capture large displacements, it does so with a spatio-temporal regularizer that keeps track of how regions deform, which is a more natural mathematical formulation. We explore a family of RDMM registration approaches: 1) a registration model where regions with separate regularizations are pre-defined (e.g., in an atlas space or for distinct foreground and background regions), 2) a registration model where a general spatially-varying regularizer is estimated, and 3) a registration model where the spatially-varying regularizer is obtained via an end-to-end trained deep learning (DL) model. We provide a variational derivation of RDMM, showing that the model can assure diffeomorphic transformations in the continuum, and that LDDMM is a particular instance of RDMM. To evaluate RDMM performance we experiment 1) on synthetic 2D data and 2) on two 3D datasets: knee magnetic resonance images (MRIs) of the Osteoarthritis Initiative (OAI) and computed tomography images (CT) of the lung. Results show that our framework achieves comparable performance to state-of-the-art image registration approaches, while providing additional information via a learned spatio-temporal regularizer. Further, our deep learning approach allows for very fast RDMM and LDDMM estimations. Code is available at https://github.com/uncbiag/registration.

Semantic segmentation is a fundamental problem in computer vision. It is considered as a pixel-wise classification problem in practice, and most segmentation models use a pixel-wise loss as their optimization criterion. However, the pixel-wise loss ignores the dependencies between pixels in an image. Several ways to exploit the relationship between pixels have been investigated, \eg, conditional random fields (CRF) and pixel affinity based methods. Nevertheless, these methods usually require additional model branches, large extra memories, or more inference time. In this paper, we develop a region mutual information (RMI) loss to model the dependencies among pixels more simply and efficiently. In contrast to the pixel-wise loss which treats the pixels as independent samples, RMI uses one pixel and its neighbour pixels to represent this pixel. Then for each pixel in an image, we get a multi-dimensional point that encodes the relationship between pixels, and the image is cast into a multi-dimensional distribution of these high-dimensional points. The prediction and ground truth thus can achieve high order consistency through maximizing the mutual information (MI) between their multi-dimensional distributions. Moreover, as the actual value of the MI is hard to calculate, we derive a lower bound of the MI and maximize the lower bound to maximize the real value of the MI. RMI only requires a few extra computational resources in the training stage, and there is no overhead during testing. Experimental results demonstrate that RMI can achieve substantial and consistent improvements in performance on PASCAL VOC 2012 and CamVid datasets. The code is available at \url{https://github.com/ZJULearning/RMI}.

We study the effect of the stochastic gradient noise on the training of generative adversarial networks (GANs) and show that it can prevent the convergence of standard game optimization methods, while the batch version converges. We address this issue with a novel stochastic variance-reduced extragradient (SVRE) optimization algorithm, which for a large class of games improves upon the previous convergence rates proposed in the literature. We observe empirically that SVRE performs similarly to a batch method on MNIST while being computationally cheaper, and that SVRE yields more stable GAN training on standard datasets.

Learning in the space-time domain remains a very challenging problem in machine learning and computer vision. Current computational models for understanding spatio-temporal visual data are heavily rooted in the classical single-image based paradigm. It is not yet well understood how to integrate information in space and time into a single, general model. We propose a neural graph model, recurrent in space and time, suitable for capturing both the local appearance and the complex higher-level interactions of different entities and objects within the changing world scene. Nodes and edges in our graph have dedicated neural networks for processing information. Nodes operate over features extracted from local parts in space and time and over previous memory states. Edges process messages between connected nodes at different locations and spatial scales or between past and present time. Messages are passed iteratively in order to transmit information globally and establish long range interactions. Our model is general and could learn to recognize a variety of high level spatio-temporal concepts and be applied to different learning tasks. We demonstrate, through extensive experiments and ablation studies, that our model outperforms strong baselines and top published methods on recognizing complex activities in video. Moreover, we obtain state-of-the-art performance on the challenging Something-Something human-object interaction dataset.

Parametric spatial transformation models have been successfully applied to image registration tasks. In such models, the transformation of interest is parameterized by a fixed set of basis functions as for example B-splines. Each basis function is located on a fixed regular grid position among the image domain because the transformation of interest is not known in advance. As a consequence, not all basis functions will necessarily contribute to the final transformation which results in a non-compact representation of the transformation. We reformulate the pairwise registration problem as a recursive sequence of successive alignments. For each element in the sequence, a local deformation defined by its position, shape, and weight is computed by our recurrent registration neural network. The sum of all lo- cal deformations yield the final spatial alignment of both images. Formulating the registration problem in this way allows the network to detect non-aligned regions in the images and to learn how to locally refine the registration properly. In contrast to current non-sequence-based registration methods, our approach iteratively applies local spatial deformations to the images until the desired registration accuracy is achieved. We trained our network on 2D magnetic resonance images of the lung and compared our method to a standard parametric B-spline registration. The experiments show, that our method performs on par for the accuracy but yields a more compact representation of the transformation. Furthermore, we achieve a speedup of around 15 compared to the B-spline registration.

Substring kernels are classical tools for representing biological sequences or text. However, when large amounts of annotated data is available, models that allow end-to-end training such as neural networks are often prefered. Links between recurrent neural networks (RNNs) and substring kernels have recently been drawn, by formally showing that RNNs with specific activation functions were points in a reproducing kernel Hilbert space (RKHS). In this paper, we revisit this link by generalizing convolutional kernel networks---originally related to a relaxation of the mismatch kernel---to model gaps in sequences. It results in a new type of recurrent neural network which can be trained end-to-end with backpropagation, or without supervision by using kernel approximation techniques. We experimentally show that our approach is well suited to biological sequences, where it outperforms existing methods for protein classification tasks.

Modern deep reinforcement learning methods have departed from the incremental learning required for eligibility traces, rendering the implementation of the λ-return difficult in this context. In particular, off-policy methods that utilize experience replay remain problematic because their random sampling of minibatches is not conducive to the efficient calculation of λ-returns. Yet replay-based methods are often the most sample efficient, and incorporating λ-returns into them is a viable way to achieve new state-of-the-art performance. Towards this, we propose the first method to enable practical use of λ-returns in arbitrary replay-based methods without relying on other forms of decorrelation such as asynchronous gradient updates. By promoting short sequences of past transitions into a small cache within the replay memory, adjacent λ-returns can be efficiently precomputed by sharing Q-values. Computation is not wasted on experiences that are never sampled, and stored λ-returns behave as stable temporal-difference (TD) targets that replace the target network. Additionally, our method grants the unique ability to observe TD errors prior to sampling; for the first time, transitions can be prioritized by their true significance rather than by a proxy to it. Furthermore, we propose the novel use of the TD error to dynamically select λ-values that facilitate faster learning. We show that these innovations can enhance the performance of DQN when playing Atari 2600 games, even under partial observability. While our work specifically focuses on λ-returns, these ideas are applicable to any multi-step return estimator.