NeurIPS 2019 论文列表

Real-world event sequences consist of complex mixtures of different types of events occurring in time. An event may depend on past events of the same type, as well as, the other types. Point processes define a general class of models for event sequences. ``Regressive point processes'' refer to point processes that directly model the dependency between an event and any past event, an example of which is a Hawkes process. In this work, we propose and develop a new nonparametric regressive point process model based on Gaussian processes. We show that our model can represent better many commonly observed real-world event sequences and capture the dependencies between events that are difficult to model using existing nonparametric Hawkes process variants. We demonstrate the improved predictive performance of our model against state-of-the-art baselines on multiple synthetic and real-world datasets.

Consider a nonparametric contextual multi-arm bandit problem where each arm $a \in [K]$ is associated to a nonparametric reward function $f_a: [0,1] \to \mathbb{R}$ mapping from contexts to the expected reward. Suppose that there is a large set of arms, yet there is a simple but unknown structure amongst the arm reward functions, e.g. finite types or smooth with respect to an unknown metric space. We present a novel algorithm which learns data-driven similarities amongst the arms, in order to implement adaptive partitioning of the context-arm space for more efficient learning. We provide regret bounds along with simulations that highlight the algorithm's dependence on the local geometry of the reward functions.

In many sensory systems, information transmission is constrained by a bottleneck, where the number of output neurons is vastly smaller than the number of input neurons. Efficient coding theory predicts that in these scenarios the brain should allocate its limited resources by removing redundant information. Previous work has typically assumed that receptors are uniformly distributed across the sensory sheet, when in reality these vary in density, often by an order of magnitude. How, then, should the brain efficiently allocate output neurons when the density of input neurons is nonuniform? Here, we show analytically and numerically that resource allocation scales nonlinearly in efficient coding models that maximize information transfer, when inputs arise from separate regions with different receptor densities. Importantly, the proportion of output neurons allocated to a given input region changes depending on the width of the bottleneck, and thus cannot be predicted from input density or region size alone. Narrow bottlenecks favor magnification of high density input regions, while wider bottlenecks often cause contraction. Our results demonstrate that both expansion and contraction of sensory input regions can arise in efficient coding models and that the final allocation crucially depends on the neural resources made available.

We study a completion problem of broad practical interest: the reconstruction of a low-rank symmetric tensor from highly incomplete and randomly corrupted observations of its entries. While a variety of prior work has been dedicated to this problem, prior algorithms either are computationally too expensive for large-scale applications, or come with sub-optimal statistical guarantees. Focusing on ``incoherent'' and well-conditioned tensors of a constant CP rank, we propose a two-stage nonconvex algorithm --- (vanilla) gradient descent following a rough initialization --- that achieves the best of both worlds. Specifically, the proposed nonconvex algorithm faithfully completes the tensor and retrieves all low-rank tensor factors within nearly linear time, while at the same time enjoying near-optimal statistical guarantees (i.e.~minimal sample complexity and optimal $\ell_2$ and $\ell_{\infty}$ statistical accuracy). The insights conveyed through our analysis of nonconvex optimization might have implications for other tensor estimation problems.

A recent strategy to circumvent the exploding and vanishing gradient problem in RNNs, and to allow the stable propagation of signals over long time scales, is to constrain recurrent connectivity matrices to be orthogonal or unitary. This ensures eigenvalues with unit norm and thus stable dynamics and training. However this comes at the cost of reduced expressivity due to the limited variety of orthogonal transformations. We propose a novel connectivity structure based on the Schur decomposition and a splitting of the Schur form into normal and non-normal parts. This allows to parametrize matrices with unit-norm eigenspectra without orthogonality constraints on eigenbases. The resulting architecture ensures access to a larger space of spectrally constrained matrices, of which orthogonal matrices are a subset. This crucial difference retains the stability advantages and training speed of orthogonal RNNs while enhancing expressivity, especially on tasks that require computations over ongoing input sequences.

Stochastic Proximal Gradient (SPG) methods have been widely used for solving optimization problems with a simple (possibly non-smooth) regularizer in machine learning and statistics. However, to the best of our knowledge no non-asymptotic convergence analysis of SPG exists for non-convex optimization with a non-smooth and non-convex regularizer. All existing non-asymptotic analysis of SPG for solving non-smooth non-convex problems require the non-smooth regularizer to be a convex function, and hence are not applicable to a non-smooth non-convex regularized problem. This work initiates the analysis to bridge this gap and opens the door to non-asymptotic convergence analysis of non-smooth non-convex regularized problems. We analyze several variants of mini-batch SPG methods for minimizing a non-convex objective that consists of a smooth non-convex loss and a non-smooth non-convex regularizer. Our contributions are two-fold: (i) we show that they enjoy the same complexities as their counterparts for solving convex regularized non-convex problems in terms of finding an approximate stationary point; (ii) we develop more practical variants using dynamic mini-batch size instead of a fixed mini-batch size without requiring the target accuracy level of solution. The significance of our results is that they improve upon the-state-of-art results for solving non-smooth non-convex regularized problems. We also empirically demonstrate the effectiveness of the considered SPG methods in comparison with other peer stochastic methods.

This work tackles the problem of robust zero-shot planning in non-stationary stochastic environments. We study Markov Decision Processes (MDPs) evolving over time and consider Model-Based Reinforcement Learning algorithms in this setting. We make two hypotheses: 1) the environment evolves continuously with a bounded evolution rate; 2) a current model is known at each decision epoch but not its evolution. Our contribution can be presented in four points. 1) we define a specific class of MDPs that we call Non-Stationary MDPs (NSMDPs). We introduce the notion of regular evolution by making an hypothesis of Lipschitz-Continuity on the transition and reward functions w.r.t. time; 2) we consider a planning agent using the current model of the environment but unaware of its future evolution. This leads us to consider a worst-case method where the environment is seen as an adversarial agent; 3) following this approach, we propose the Risk-Averse Tree-Search (RATS) algorithm, a zero-shot Model-Based method similar to Minimax search; 4) we illustrate the benefits brought by RATS empirically and compare its performance with reference Model-Based algorithms.

Making decisions in the presence of a strategic opponent requires one to take into account the opponent’s ability to actively mask its intended objective. To describe such strategic situations, we introduce the non-cooperative inverse reinforcement learning (N-CIRL) formalism. The N-CIRL formalism consists of two agents with completely misaligned objectives, where only one of the agents knows the true objective function. Formally, we model the N-CIRL formalism as a zero-sum Markov game with one-sided incomplete information. Through interacting with the more informed player, the less informed player attempts to both infer and optimize the true objective function. As a result of the one-sided incomplete information, the multi-stage game can be decomposed into a sequence of single- stage games expressed by a recursive formula. Solving this recursive formula yields the value of the N-CIRL game and the more informed player’s equilibrium strategy. Another recursive formula, constructed by forming an auxiliary game, termed the dual game, yields the less informed player’s strategy. Building upon these two recursive formulas, we develop a computationally tractable algorithm to approximately solve for the equilibrium strategies. Finally, we demonstrate the benefits of our N-CIRL formalism over the existing multi-agent IRL formalism via extensive numerical simulation in a novel cyber security setting.

Pure exploration (aka active testing) is the fundamental task of sequentially gathering information to answer a query about a stochastic environment. Good algorithms make few mistakes and take few samples. Lower bounds (for multi-armed bandit models with arms in an exponential family) reveal that the sample complexity is determined by the solution to an optimisation problem. The existing state of the art algorithms achieve asymptotic optimality by solving a plug-in estimate of that optimisation problem at each step. We interpret the optimisation problem as an unknown game, and propose sampling rules based on iterative strategies to estimate and converge to its saddle point. We apply no-regret learners to obtain the first finite confidence guarantees that are adapted to the exponential family and which apply to any pure exploration query and bandit structure. Moreover, our algorithms only use a best response oracle instead of fully solving the optimisation problem.

This paper establishes that optimistic algorithms attain gap-dependent and non-asymptotic logarithmic regret for episodic MDPs. In contrast to prior work, our bounds do not suffer a dependence on diameter-like quantities or ergodicity, and smoothly interpolate between the gap dependent logarithmic-regret, and the $\widetilde{\mathcal{O}}(\sqrt{HSAT})$-minimax rate. The key technique in our analysis is a novel ``clipped'' regret decomposition which applies to a broad family of recent optimistic algorithms for episodic MDPs.

Fairness-aware learning involves designing algorithms that do not discriminate with respect to some sensitive feature (e.g., race or gender). Existing work on the problem operates under the assumption that the sensitive feature available in one's training sample is perfectly reliable. This assumption may be violated in many real-world cases: for example, respondents to a survey may choose to conceal or obfuscate their group identity out of fear of potential discrimination. This poses the question of whether one can still learn fair classifiers given noisy sensitive features. In this paper, we answer the question in the affirmative: we show that if one measures fairness using the mean-difference score, and sensitive features are subject to noise from the mutually contaminated learning model, then owing to a simple identity we only need to change the desired fairness-tolerance. The requisite tolerance can be estimated by leveraging existing noise-rate estimators from the label noise literature. We finally show that our procedure is empirically effective on two case-studies involving sensitive feature censoring.

We consider the problem of learning to play a repeated multi-agent game with an unknown reward function. Single player online learning algorithms attain strong regret bounds when provided with full information feedback, which unfortunately is unavailable in many real-world scenarios. Bandit feedback alone, i.e., observing outcomes only for the selected action, yields substantially worse performance. In this paper, we consider a natural model where, besides a noisy measurement of the obtained reward, the player can also observe the opponents' actions. This feedback model, together with a regularity assumption on the reward function, allows us to exploit the correlations among different game outcomes by means of Gaussian processes (GPs). We propose a novel confidence-bound based bandit algorithm GP-MW, which utilizes the GP model for the reward function and runs a multiplicative weight (MW) method. We obtain novel kernel-dependent regret bounds that are comparable to the known bounds in the full information setting, while substantially improving upon the existing bandit results. We experimentally demonstrate the effectiveness of GP-MW in random matrix games, as well as real-world problems of traffic routing and movie recommendation. In our experiments, GP-MW consistently outperforms several baselines, while its performance is often comparable to methods that have access to full information feedback.

Diplomacy is a seven-player non-stochastic, non-cooperative game, where agents acquire resources through a mix of teamwork and betrayal. Reliance on trust and coordination makes Diplomacy the first non-cooperative multi-agent benchmark for complex sequential social dilemmas in a rich environment. In this work, we focus on training an agent that learns to play the No Press version of Diplomacy where there is no dedicated communication channel between players. We present DipNet, a neural-network-based policy model for No Press Diplomacy. The model was trained on a new dataset of more than 150,000 human games. Our model is trained by supervised learning (SL) from expert trajectories, which is then used to initialize a reinforcement learning (RL) agent trained through self-play. Both the SL and the RL agent demonstrate state-of-the-art No Press performance by beating popular rule-based bots.

Nonlinear embedding manifold learning methods provide invaluable visual insights into a structure of high-dimensional data. However, due to a complicated nonconvex objective function, these methods can easily get stuck in local minima and their embedding quality can be poor. We propose a natural extension to several manifold learning methods aimed at identifying pressured points, i.e. points stuck in the poor local minima and have poor embedding quality. We show that the objective function can be decreased by temporarily allowing these points to make use of an extra dimension in the embedding space. Our method is able to improve the objective function value of existing methods even after they get stuck in a poor local minimum.

Discovery of causal relations from observational data is essential for many disciplines of science and real-world applications. However, unlike other machine learning algorithms, whose development has been greatly fostered by a large amount of available benchmark datasets, causal discovery algorithms are notoriously difficult to be systematically evaluated because few datasets with known ground-truth causal relations are available. In this work, we handle the problem of evaluating causal discovery algorithms by building a flexible simulator in the medical setting. We develop a neuropathic pain diagnosis simulator, inspired by the fact that the biological processes of neuropathic pathophysiology are well studied with well-understood causal influences. Our simulator exploits the causal graph of the neuropathic pain pathology and its parameters in the generator are estimated from real-life patient cases. We show that the data generated from our simulator have similar statistics as real-world data. As a clear advantage, the simulator can produce infinite samples without jeopardizing the privacy of real-world patients. Our simulator provides a natural tool for evaluating various types of causal discovery algorithms, including those to deal with practical issues in causal discovery, such as unknown confounders, selection bias, and missing data. Using our simulator, we have evaluated extensively causal discovery algorithms under various settings.

Living neural networks emerge through a process of growth and self-organization that begins with a single cell and results in a brain, an organized and functional computational device. Artificial neural networks, however, rely on human-designed, hand-programmed architectures for their remarkable performance. Can we develop artificial computational devices that can grow and self-organize without human intervention? In this paper, we propose a biologically inspired developmental algorithm that can ‘grow’ a functional, layered neural network from a single initial cell. The algorithm organizes inter-layer connections to construct retinotopic pooling layers. Our approach is inspired by the mechanisms employed by the early visual system to wire the retina to the lateral geniculate nucleus (LGN), days before animals open their eyes. The key ingredients for robust self-organization are an emergent spontaneous spatiotemporal activity wave in the first layer and a local learning rule in the second layer that ‘learns’ the underlying activity pattern in the first layer. The algorithm is adaptable to a wide-range of input-layer geometries, robust to malfunctioning units in the first layer, and so can be used to successfully grow and self-organize pooling architectures of different pool-sizes and shapes. The algorithm provides a primitive procedure for constructing layered neural networks through growth and self-organization. We also demonstrate that networks grown from a single unit perform as well as hand-crafted networks on MNIST. Broadly, our work shows that biologically inspired developmental algorithms can be applied to autonomously grow functional `brains' in-silico.

Proximal policy optimization and trust region policy optimization (PPO and TRPO) with actor and critic parametrized by neural networks achieve significant empirical success in deep reinforcement learning. However, due to nonconvexity, the global convergence of PPO and TRPO remains less understood, which separates theory from practice. In this paper, we prove that a variant of PPO and TRPO equipped with overparametrized neural networks converges to the globally optimal policy at a sublinear rate. The key to our analysis is the global convergence of infinite-dimensional mirror descent under a notion of one-point monotonicity, where the gradient and iterate are instantiated by neural networks. In particular, the desirable representation power and optimization geometry induced by the overparametrization of such neural networks allow them to accurately approximate the infinite-dimensional gradient and iterate.

Temporal-difference learning (TD), coupled with neural networks, is among the most fundamental building blocks of deep reinforcement learning. However, due to the nonlinearity in value function approximation, such a coupling leads to nonconvexity and even divergence in optimization. As a result, the global convergence of neural TD remains unclear. In this paper, we prove for the first time that neural TD converges at a sublinear rate to the global optimum of the mean-squared projected Bellman error for policy evaluation. In particular, we show how such global convergence is enabled by the overparametrization of neural networks, which also plays a vital role in the empirical success of neural TD. Beyond policy evaluation, we establish the global convergence of neural (soft) Q-learning, which is further connected to that of policy gradient algorithms.

Convolutional neural networks (CNNs) trained for object classification have been widely used to account for visually-driven neural responses in both human and primate brains. However, because of the generality and complexity of object classification, despite the effectiveness of CNNs in predicting brain activity, it is difficult to draw specific inferences about neural information processing using CNN-derived representations. To address this problem, we used learned representations drawn from 21 computer vision tasks to construct encoding models for predicting brain responses from BOLD5000---a large-scale dataset comprised of fMRI scans collected while observers viewed over 5000 naturalistic scene and object images. Encoding models based on task features predict activity in different regions across the whole brain. Features from 3D tasks such as keypoint/edge detection explain greater variance compared to 2D tasks---a pattern observed across the whole brain. Using results across all 21 task representations, we constructed a ``task graph’’ based on the spatial layout of well-predicted brain areas from each task. A comparison of this brain-derived task structure to the task structure derived from transfer learning accuracy demonstrate that tasks with higher transferability make similar predictions for brain responses from different regions. These results---arising out of state-of-the-art computer vision methods---help reveal the task-specific architecture of the human visual system.