NeurIPS 2019 Papers

Efficient exploration is crucial to achieving good performance in reinforcement learning. Existing systematic exploration strategies (R-MAX, MBIE, UCRL, etc.), despite being promising theoretically, are essentially greedy strategies that follow some predefined heuristics. When the heuristics do not match the dynamics of Markov decision processes (MDPs) well, an excessive amount of time can be wasted in travelling through already-explored states, lowering the overall efficiency. We argue that explicit planning for exploration can help alleviate such a problem, and propose a Value Iteration for Exploration Cost (VIEC) algorithm which computes the optimal exploration scheme by solving an augmented MDP. We then present a detailed analysis of the exploration behaviour of some popular strategies, showing how these strategies can fail and spend O(n^2 md) or O(n^2 m + nmd) steps to collect sufficient data in some tower-shaped MDPs, while the optimal exploration scheme, which can be obtained by VIEC, only needs O(nmd), where n, m are the numbers of states and actions and d is the data demand. The analysis not only points out the weakness of existing heuristic-based strategies, but also suggests a remarkable potential in explicit planning for exploration.

We present a new model-based algorithm for reinforcement learning (RL) which consists of explicit exploration and exploitation phases, and is applicable in large or infinite state spaces. The algorithm maintains a set of dynamics models consistent with current experience and explores by finding policies which induce high dis- agreement between their state predictions. It then exploits using the refined set of models or experience gathered during exploration. We show that under realizability and optimal planning assumptions, our algorithm provably finds a near-optimal policy with a number of samples that is polynomial in a structural complexity measure which we show to be low in several natural settings. We then give a practical approximation using neural networks and demonstrate its performance and sample efficiency in practice.

Disentangled representation learning finds compact, independent and easy-to-interpret factors of the data. Learning such has been shown to require an inductive bias, which we explicitly encode in a generative model of images. Specifically, we propose a model with two latent spaces: one that represents spatial transformations of the input data, and another that represents the transformed data. We find that the latter naturally captures the intrinsic appearance of the data. To realize the generative model, we propose a Variationally Inferred Transformational Autoencoder (VITAE) that incorporates a spatial ransformer into a variational autoencoder. We show how to perform inference in the model efficiently by carefully designing the encoders and restricting the transformation class to be diffeomorphic. Empirically, our model separates the visual style from digit type on MNIST, separates shape and pose in images of human bodies and facial features from facial shape on CelebA.

Explanation methods aim to make neural networks more trustworthy and interpretable. In this paper, we demonstrate a property of explanation methods which is disconcerting for both of these purposes. Namely, we show that explanations can be manipulated arbitrarily by applying visually hardly perceptible perturbations to the input that keep the network's output approximately constant. We establish theoretically that this phenomenon can be related to certain geometrical properties of neural networks. This allows us to derive an upper bound on the susceptibility of explanations to manipulations. Based on this result, we propose effective mechanisms to enhance the robustness of explanations.

Mode connectivity is a surprising phenomenon in the loss landscape of deep nets. Optima---at least those discovered by gradient-based optimization---turn out to be connected by simple paths on which the loss function is almost constant. Often, these paths can be chosen to be piece-wise linear, with as few as two segments.

Interacting with a complex world involves continual learning, in which tasks and data distributions change over time. A continual learning system should demonstrate both plasticity (acquisition of new knowledge) and stability (preservation of old knowledge). Catastrophic forgetting is the failure of stability, in which new experience overwrites previous experience. In the brain, replay of past experience is widely believed to reduce forgetting, yet it has been largely overlooked as a solution to forgetting in deep reinforcement learning. Here, we introduce CLEAR, a replay-based method that greatly reduces catastrophic forgetting in multi-task reinforcement learning. CLEAR leverages off-policy learning and behavioral cloning from replay to enhance stability, as well as on-policy learning to preserve plasticity. We show that CLEAR performs better than state-of-the-art deep learning techniques for mitigating forgetting, despite being significantly less complicated and not requiring any knowledge of the individual tasks being learned.

We study the complexity of sampling from a distribution over all index subsets of the set {1, ..., n} with the probability of a subset S proportional to the determinant of the submatrix L

Structured prediction can be thought of as a simultaneous prediction of multiple labels. This is often done by maximizing a score function on the space of labels, which decomposes as a sum of pairwise and unary potentials. The above is naturally modeled with a graph, where edges and vertices are related to pairwise and unary potentials, respectively. We consider the generative process proposed by Globerson et al. (2015) and apply it to general connected graphs. We analyze the structural conditions of the graph that allow for the exact recovery of the labels. Our results show that exact recovery is possible and achievable in polynomial time for a large class of graphs. In particular, we show that graphs that are bad expanders can be exactly recovered by adding small edge perturbations coming from the \Erdos-\Renyi model. Finally, as a byproduct of our analysis, we provide an extension of Cheeger's inequality.

Compression is at the heart of effective representation learning. However, lossy compression is typically achieved through simple parametric models like Gaussian noise to preserve analytic tractability, and the limitations this imposes on learning are largely unexplored. Further, the Gaussian prior assumptions in models such as variational autoencoders (VAEs) provide only an upper bound on the compression rate in general. We introduce a new noise channel, Echo noise, that admits a simple, exact expression for mutual information for arbitrary input distributions. The noise is constructed in a data-driven fashion that does not require restrictive distributional assumptions. With its complex encoding mechanism and exact rate regularization, Echo leads to improved bounds on log-likelihood and dominates beta-VAEs across the achievable range of rate-distortion trade-offs. Further, we show that Echo noise can outperform flow-based methods without the need to train additional distributional transformations.

Gaussian processes (GPs) are flexible non-parametric models, with a capacity that grows with the available data. However, computational constraints with standard inference procedures have limited exact GPs to problems with fewer than about ten thousand training points, necessitating approximations for larger datasets. In this paper, we develop a scalable approach for exact GPs that leverages multi-GPU parallelization and methods like linear conjugate gradients, accessing the kernel matrix only through matrix multiplication. By partitioning and distributing kernel matrix multiplies, we demonstrate that an exact GP can be trained on over a million points, a task previously thought to be impossible with current computing hardware. Moreover, our approach is generally applicable, without constraints to grid data or specific kernel classes. Enabled by this scalability, we perform the first-ever comparison of exact GPs against scalable GP approximations on datasets with $10^4 \!-\! 10^6$ data points, showing dramatic performance improvements.

Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural variable-constraint bipartite graph representation of mixed-integer linear programs. We train our model via imitation learning from the strong branching expert rule, and demonstrate on a series of hard problems that our approach produces policies that improve upon state-of-the-art machine-learning methods for branching and generalize to instances significantly larger than seen during training. Moreover, we improve for the first time over expert-designed branching rules implemented in a state-of-the-art solver on large problems. Code for reproducing all the experiments can be found at https://github.com/ds4dm/learn2branch.

Protein modeling is an increasingly popular area of machine learning research. Semi-supervised learning has emerged as an important paradigm in protein modeling due to the high cost of acquiring supervised protein labels, but the current literature is fragmented when it comes to datasets and standardized evaluation techniques. To facilitate progress in this field, we introduce the Tasks Assessing Protein Embeddings (TAPE), a set of five biologically relevant semi-supervised learning tasks spread across different domains of protein biology. We curate tasks into specific training, validation, and test splits to ensure that each task tests biologically relevant generalization that transfers to real-life scenarios. We benchmark a range of approaches to semi-supervised protein representation learning, which span recent work as well as canonical sequence learning techniques. We find that self-supervised pretraining is helpful for almost all models on all tasks, more than doubling performance in some cases. Despite this increase, in several cases features learned by self-supervised pretraining still lag behind features extracted by state-of-the-art non-neural techniques. This gap in performance suggests a huge opportunity for innovative architecture design and improved modeling paradigms that better capture the signal in biological sequences. TAPE will help the machine learning community focus effort on scientifically relevant problems. Toward this end, all data and code used to run these experiments is available at https://github.com/songlab-cal/tape

We consider the task of estimating the entropy of $k$-ary distributions from samples in the streaming model, where space is limited. Our main contribution is an algorithm that requires $O\left(\frac{k \log (1/\varepsilon)^2}{\varepsilon^3}\right)$ samples and a constant $O(1)$ memory words of space and outputs a $\pm\varepsilon$ estimate of $H(p)$. Without space limitations, the sample complexity has been established as $S(k,\varepsilon)=\Theta\left(\frac k{\varepsilon\log k}+\frac{\log^2 k}{\varepsilon^2}\right)$, which is sub-linear in the domain size $k$, and the current algorithms that achieve optimal sample complexity also require nearly-linear space in $k$. Our algorithm partitions $[0,1]$ into intervals and estimates the entropy contribution of probability values in each interval. The intervals are designed to trade bias and variance. Distribution property estimation and testing with limited memory is a largely unexplored research area. We hope our work will motivate research in this field.

Markov chain Monte Carlo (MCMC) methods generate samples that are asymptotically distributed from a target distribution of interest as the number of iterations goes to infinity. Various theoretical results provide upper bounds on the distance between the target and marginal distribution after a fixed number of iterations. These upper bounds are on a case by case basis and typically involve intractable quantities, which limits their use for practitioners. We introduce L-lag couplings to generate computable, non-asymptotic upper bound estimates for the total variation or the Wasserstein distance of general Markov chains. We apply L-lag couplings to the tasks of (i) determining MCMC burn-in, (ii) comparing different MCMC algorithms with the same target, and (iii) comparing exact and approximate MCMC. Lastly, we (iv) assess the bias of sequential Monte Carlo and self-normalized importance samplers.

We consider minimizing a nonconvex, smooth function $f$ on a Riemannian manifold $\mathcal{M}$. We show that a perturbed version of the gradient descent algorithm converges to a second-order stationary point for this problem (and hence is able to escape saddle points on the manifold). While the unconstrained problem is well-studied, our result is the first to prove such a rate for nonconvex, manifold-constrained problems. The rate of convergence depends as $1/\epsilon^2$ on the accuracy $\epsilon$, which matches a rate known only for unconstrained smooth minimization. The convergence rate also has a polynomial dependence on the parameters denoting the curvature of the manifold and the smoothness of the function.

Modern machine learning systems are susceptible to adversarial examples; inputs which clearly preserve the characteristic semantics of a given class, but whose classification is (usually confidently) incorrect. Existing approaches to adversarial defense generally rely on modifying the input, e.g. quantization, or the learned model parameters, e.g. via adversarial training. However, recent research has shown that most such approaches succumb to adversarial examples when different norms or more sophisticated adaptive attacks are considered. In this paper, we propose a fundamentally different approach which instead changes the way the output is represented and decoded. This simple approach achieves state-of-the-art robustness to adversarial examples for L 2 and L ∞ based adversarial perturbations on MNIST and CIFAR10. In addition, even under strong white-box attacks, we find that our model often assigns adversarial examples a low probability; those with high probability are usually interpretable, i.e. perturbed towards the perceptual boundary between the original and adversarial class. Our approach has several advantages: it yields more meaningful probability estimates, is extremely fast during training and testing, requires essentially no architectural changes to existing discriminative learning pipelines, is wholly complementary to other defense approaches including adversarial training, and does not sacrifice benign test set performance

Can a stable matching that achieves high equity among the two sides of a market be reached in quadratic time? The Deferred Acceptance (DA) algorithm finds a stable matching that is biased in favor of one side; optimizing apt equity measures is strongly NP-hard. A proposed approximation algorithm offers a guarantee only with respect to the DA solutions. Recent work introduced Deferred Acceptance with Compensation Chains (DACC), a class of algorithms that can reach any stable matching in O(n^4) time, but did not propose a way to achieve good equity. In this paper, we propose an alternative that is computationally simpler and achieves high equity too. We introduce Monotonic Deferred Acceptance (MDA), a class of algorithms that progresses monotonically towards a stable matching; we couple MDA with a mechanism we call Strongly Deferred Acceptance (SDA), to build an algorithm that reaches an equitable stable matching in quadratic time; we amend this algorithm with a few low-cost local search steps to what we call Deferred Local Search (DLS), and demonstrate experimentally that it outperforms previous solutions in terms of equity measures and matches the most efficient ones in runtime.

We propose the first black-box approach to obtaining long-term memory guarantees for online learning in the sense of Bousquet and Warmuth, 2002, by reducing the problem to achieving typical switching regret. Specifically, for the classical expert problem with $K$ actions and $T$ rounds, using our general framework we develop various algorithms with a regret bound of order $\order(\sqrt{T(S\ln T + n \ln K)})$ compared to any sequence of experts with $S-1$ switches among $n \leq \min\{S, K\}$ distinct experts. In addition, by plugging specific adaptive algorithms into our framework we also achieve the best of both stochastic and adversarial environments simultaneously, which resolves an open problem of Warmuth and Koolen 2014. Furthermore, we extend our results to the sparse multi-armed bandit setting and show both negative and positive results for long-term memory guarantees. As a side result, our lower bound also implies that sparse losses do not help improve the worst-case regret for contextual bandit, a sharp contrast with the non-contextual case.

We study an online classification problem with partial feedback in which individuals arrive one at a time from a fixed but unknown distribution, and must be classified as positive or negative. Our algorithm only observes the true label of an individual if they are given a positive classification. This setting captures many classification problems for which fairness is a concern: for example, in criminal recidivism prediction, recidivism is only observed if the inmate is released; in lending applications, loan repayment is only observed if the loan is granted. We require that our algorithms satisfy common statistical fairness constraints (such as equalizing false positive or negative rates --- introduced as "equal opportunity" in Hardt et al. (2016)) at every round, with respect to the underlying distribution. We give upper and lower bounds characterizing the cost of this constraint in terms of the regret rate (and show that it is mild), and give an oracle efficient algorithm that achieves the upper bound.