ICML 2020 论文列表

We consider un-discounted reinforcement learning (RL) in Markov decision processes (MDPs) under drifting non-stationarity, \ie, both the reward and state transition distributions are allowed to evolve over time, as long as their respective total variations, quantified by suitable metrics, do not exceed certain \emph{variation budgets}. We first develop the Sliding Window Upper-Confidence bound for Reinforcement Learning with Confidence Widening (\texttt{SWUCRL2-CW}) algorithm, and establish its dynamic regret bound when the variation budgets are known. In addition, we propose the Bandit-over-Reinforcement Learning (\texttt{BORL}) algorithm to adaptively tune the \sw to achieve the same dynamic regret bound, but in a \emph{parameter-free} manner, \ie, without knowing the variation budgets. Notably, learning drifting MDPs via conventional optimistic exploration presents a unique challenge absent in existing (non-stationary) bandit learning settings. We overcome the challenge by a novel confidence widening technique that incorporates additional optimism.

Automating molecular design using deep reinforcement learning (RL) holds the promise of accelerating the discovery of new chemical compounds. Existing approaches work with molecular graphs and thus ignore the location of atoms in space, which restricts them to 1) generating single organic molecules and 2) heuristic reward functions. To address this, we present a novel RL formulation for molecular design in Cartesian coordinates, thereby extending the class of molecules that can be built. Our reward function is directly based on fundamental physical properties such as the energy, which we approximate via fast quantum-chemical methods. To enable progress towards de-novo molecular design, we introduce MolGym, an RL environment comprising several challenging molecular design tasks along with baselines. In our experiments, we show that our agent can efficiently learn to solve these tasks from scratch by working in a translation and rotation invariant state-action space.

Integer programming is a general optimization framework with a wide variety of applications, e.g., in scheduling, production planning, and graph optimization. As Integer Programs (IPs) model many provably hard to solve problems, modern IP solvers rely on heuristics. These heuristics are often human-designed, and tuned over time using experience and data. The goal of this work is to show that the performance of those solvers can be greatly enhanced using reinforcement learning (RL). In particular, we investigate a specific methodology for solving IPs, known as the Cutting Plane Method. This method is employed as a subroutine by all modern IP solvers. We present a deep RL formulation, network architecture, and algorithms for intelligent adaptive selection of cutting planes (aka cuts). Across a wide range of IP tasks, we show that our trained RL agent significantly outperforms human-designed heuristics, and effectively generalizes to larger instances and across IP problem classes. The trained agent is also demonstrated to benefit the popular downstream application of cutting plane methods in Branch-and-Cut algorithm, which is the backbone of state-of-the-art commercial IP solvers.

Regularizing the optimal transport (OT) problem has proven crucial for OT theory to impact the field of machine learning. For instance, it is known that regularizing OT problems with entropy leads to faster computations and better differentiation using the Sinkhorn algorithm, as well as better sample complexity bounds than classic OT. In this work we depart from this practical perspective and propose a new interpretation of regularization as a robust mechanism, and show using Fenchel duality that any convex regularization of OT can be interpreted as ground cost adversarial. This incidentally gives access to a robust dissimilarity measure on the ground space, which can in turn be used in other applications. We propose algorithms to compute this robust cost, and illustrate the interest of this approach empirically.

Automating algorithm configuration is growing increasingly necessary as algorithms come with more and more tunable parameters. It is common to tune parameters using machine learning, optimizing algorithmic performance (runtime or solution quality, for example) using a training set of problem instances from the specific domain at hand. We investigate a fundamental question about these techniques: how large should the training set be to ensure that a parameter’s average empirical performance over the training set is close to its expected, future performance? We answer this question for algorithm configuration problems that exhibit a widely-applicable structure: the algorithm’s performance as a function of its parameters can be approximated by a “simple” function. We show that if this approximation holds under the L$\infty$-norm, we can provide strong sample complexity bounds, but if the approximation holds only under the Lp-norm for p < $\infty$, it is not possible to provide meaningful sample complexity bounds in the worst case. We empirically evaluate our bounds in the context of integer programming, obtaining sample complexity bounds that are up to 700 times smaller than the previously best-known bounds.

Temporal difference (TD) learning is one of the main foundations of modern reinforcement learning. This paper studies the use of TD(0), a canonical TD algorithm, to estimate the value function of a given policy from a batch of data. In this batch setting, we show that TD(0) may converge to an inaccurate value function because the update following an action is weighted according to the number of times that action occurred in the batch – not the true probability of the action under the given policy. To address this limitation, we introduce \emph{policy sampling error corrected}-TD(0) (PSEC-TD(0)). PSEC-TD(0) first estimates the empirical distribution of actions in each state in the batch and then uses importance sampling to correct for the mismatch between the empirical weighting and the correct weighting for updates following each action. We refine the concept of a certainty-equivalence estimate and argue that PSEC-TD(0) is a more data efficient estimator than TD(0) for a fixed batch of data. Finally, we conduct an empirical evaluation of PSEC-TD(0) on three batch value function learning tasks, with a hyperparameter sensitivity analysis, and show that PSEC-TD(0) produces value function estimates with lower mean squared error than TD(0).

To simultaneously capture syntax and global semantics from a text corpus, we propose a new larger-context recurrent neural network (RNN) based language model, which extracts recurrent hierarchical semantic structure via a dynamic deep topic model to guide natural language generation. Moving beyond a conventional RNN-based language model that ignores long-range word dependencies and sentence order, the proposed model captures not only intra-sentence word dependencies, but also temporal transitions between sentences and inter-sentence topic dependencies. For inference, we develop a hybrid of stochastic-gradient Markov chain Monte Carlo and recurrent autoencoding variational Bayes. Experimental results on a variety of real-world text corpora demonstrate that the proposed model not only outperforms larger-context RNN-based language models, but also learns interpretable recurrent multilayer topics and generates diverse sentences and paragraphs that are syntactically correct and semantically coherent.

Mixture of linear regressions is a popular learning theoretic model that is used widely to represent heterogeneous data. In the simplest form, this model assumes that the labels are generated from either of two different linear models and mixed together. Recent works of Yin et al. and Krishnamurthy et al., 2019, focus on an experimental design setting of model recovery for this problem. It is assumed that the features can be designed and queried with to obtain their label. When queried, an oracle randomly selects one of the two different sparse linear models and generates a label accordingly. How many such oracle queries are needed to recover both of the models simultaneously? This question can also be thought of as a generalization of the well-known compressed sensing problem (Candès and Tao, 2005, Donoho, 2006). In this work we address this query complexity problem and provide efficient algorithms that improves on the previously best known results.

Stochastic optimization algorithms have become indispensable in modern machine learning. An unresolved foundational question in this area is the difference between with-replacement sampling and without-replacement sampling — does the latter have superior convergence rate compared to the former? A groundbreaking result of Recht and Ré reduces the problem to a noncommutative analogue of the arithmetic-geometric mean inequality where $n$ positive numbers are replaced by $n$ positive definite matrices. If this inequality holds for all $n$, then without-replacement sampling (also known as random reshuffling) indeed outperforms with-replacement sampling in some important optimization problems. The conjectured Recht–Ré inequality has so far only been established for $n = 2$ and a special case of $n = 3$. We will show that the Recht–Ré conjecture is false for general $n$. Our approach relies on the noncommutative Positivstellensatz, which allows us to reduce the conjectured inequality to a semidefinite program and the validity of the conjecture to certain bounds for the optimum values, which we show are false as soon as $n = 5$.

In display advertising, a small group of sellers and bidders face each other in up to $10^{12}$ auctions a day. In this context, revenue maximisation via monopoly price learning is a high-value problem for sellers. By nature, these auctions are online and produce a very high frequency stream of data. This results in a computational strain that requires algorithms be real-time. Unfortunately, existing methods inherited from the batch setting suffer $O(\sqrt{t})$ time/memory complexity at each update, prohibiting their use. In this paper, we provide the first algorithm for online learning of monopoly prices in online auctions whose update is constant in time and memory.

Model-Based Reinforcement Learning (MBRL) offers a promising direction for sample efficient learning, often achieving state of the art results for continuous control tasks. However many existing MBRL methods rely on combining greedy policies with exploration heuristics, and even those which utilize principled exploration bonuses construct dual objectives in an ad hoc fashion. In this paper we introduce Ready Policy One (RP1), a framework that views MBRL as an active learning problem, where we aim to improve the world model in the fewest samples possible. RP1 achieves this by utilizing a hybrid objective function, which crucially adapts during optimization, allowing the algorithm to trade off reward v.s. exploration at different stages of learning. In addition, we introduce a principled mechanism to terminate sample collection once we have a rich enough trajectory batch to improve the model. We rigorously evaluate our method on a variety of continuous control tasks, and demonstrate statistically significant gains over existing approaches.

To analyze high-dimensional and complex data in the real world, deep generative models, such as variational autoencoder (VAE) embed data in a low-dimensional space (latent space) and learn a probabilistic model in the latent space. However, they struggle to accurately reproduce the probability distribution function (PDF) in the input space from that in the latent space. If the embedding were isometric, this issue can be solved, because the relation of PDFs can become tractable. To achieve isometric property, we propose Rate-Distortion Optimization guided autoencoder inspired by orthonormal transform coding. We show our method has the following properties: (i) the Jacobian matrix between the input space and a Euclidean latent space forms a constantly-scaled orthonormal system and enables isometric data embedding; (ii) the relation of PDFs in both spaces can become tractable one such as proportional relation. Furthermore, our method outperforms state-of-the-art methods in unsupervised anomaly detection with four public datasets.

Rank aggregation from pairwise preferences has widespread applications in recommendation systems and information retrieval. Given the enormous economic and societal impact of these applications, and the consequent incentives for malicious players to manipulate ranking outcomes in their favor, an important challenge is to make rank aggregation algorithms robust to adversarial manipulations in data. In this paper, we initiate the study of robustness in rank aggregation under the popular Bradley-Terry-Luce (BTL) model for pairwise comparisons. We consider a setting where pairwise comparisons are initially generated according to a BTL model, but a fraction of these comparisons are corrupted by an adversary prior to being reported to us. We consider a strong contamination model, where an adversary having complete knowledge of the initial truthful data and the underlying true BTL parameters, can subsequently corrupt the truthful data by inserting, deleting, or changing data points. The goal is to estimate the true score/weight of each item under the BTL model, even in the presence of these corruptions. We characterize the extent of adversarial corruption under which the true BTL parameters are uniquely identifiable. We also provide a novel pruning algorithm that provably cleans the data of adversarial corruption under reasonable conditions on data generation and corruption. We corroborate our theory with experiments on both synthetic as well as real data showing that previous algorithms are vulnerable to even small amounts of corruption, whereas our algorithm can clean a reasonably high amount of corruption.

Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low dimensional projection can help alleviate this curse of dimensionality, but introduces many trainable hyperparameters, which can be cumbersome, especially in the small data regime. We use additive sums of kernels for GP regression, where each kernel operates on a different random projection of its inputs. Surprisingly, we find that as the number of random projections increases, the predictive performance of this approach quickly converges to the performance of a kernel operating on the original full dimensional inputs, over a wide range of data sets, even if we are projecting into a single dimension. As a consequence, many problems can remarkably be reduced to one dimensional input spaces, without learning a transformation. We prove this convergence and its rate, and additionally propose a deterministic approach that converges more quickly than purely random projections. Moreover, we demonstrate our approach can achieve faster inference and improved predictive accuracy for high-dimensional inputs compared to kernels in the original input space.

Randomized smoothing is the current state-of-the-art defense with provable robustness against $\ell_2$ adversarial attacks. Many works have devised new randomized smoothing schemes for other metrics, such as $\ell_1$ or $\ell_\infty$; however, substantial effort was needed to derive such new guarantees. This begs the question: can we find a general theory for randomized smoothing? We propose a novel framework for devising and analyzing randomized smoothing schemes, and validate its effectiveness in practice. Our theoretical contributions are: (1) we show that for an appropriate notion of "optimal", the optimal smoothing distributions for any "nice" norms have level sets given by the norm’s *Wulff Crystal*; (2) we propose two novel and complementary methods for deriving provably robust radii for any smoothing distribution; and, (3) we show fundamental limits to current randomized smoothing techniques via the theory of *Banach space cotypes*. By combining (1) and (2), we significantly improve the state-of-the-art certified accuracy in $\ell_1$ on standard datasets. Meanwhile, we show using (3) that with only label statistics under random input perturbations, randomized smoothing cannot achieve nontrivial certified accuracy against perturbations of $\ell_p$-norm $\Omega(\min(1, d^{\frac{1}{p} - \frac{1}{2}}))$, when the input dimension $d$ is large. We provide code in github.com/tonyduan/rs4a.

We study preconditioned gradient-based optimization methods where the preconditioning matrix has block-diagonal form. Such a structural constraint comes with the advantage that the update computation can be parallelized across multiple independent tasks. Our main contribution is to demonstrate that the convergence of these methods can significantly be improved by a randomization technique which corresponds to repartitioning coordinates across tasks during the optimization procedure. We provide a theoretical analysis that accurately characterizes the expected convergence gains of repartitioning and validate our findings empirically on various traditional machine learning tasks. From an implementation perspective, block-separable models are well suited for parallelization and, when shared memory is available, randomization can be implemented on top of existing methods very efficiently to improve convergence.

\emph{Is there a classifier that ensures optimal robustness against all adversarial attacks?} This paper tackles this question by adopting a game-theoretic point of view. We present the adversarial attacks and defenses problem as an \emph{infinite} zero-sum game where classical results (\emph{e.g.} Nash or Sion theorems) do not apply. We demonstrate the non-existence of a Nash equilibrium in our game when the classifier and the Adversary are both deterministic, hence giving a negative answer to the above question in the deterministic regime. Nonetheless, the question remains open in the randomized regime. We tackle this problem by showing that any deterministic classifier can be outperformed by a randomized one. This gives arguments for using randomization, and leads us to a simple method for building randomized classifiers that are robust to state-or-the-art adversarial attacks. Empirical results validate our theoretical analysis, and show that our defense method considerably outperforms Adversarial Training against strong adaptive attacks, by achieving 0.55 accuracy under adaptive PGD-attack on CIFAR10, compared to 0.42 for Adversarial training.

We introduce a randomly extrapolated primal-dual coordinate descent method that adapts to sparsity of the data matrix and the favorable structures of the objective function. Our method updates only a subset of primal and dual variables with sparse data, and it uses large step sizes with dense data, retaining the benefits of the specific methods designed for each case. In addition to adapting to sparsity, our method attains fast convergence guarantees in favorable cases \emph{without any modifications}. In particular, we prove linear convergence under metric subregularity, which applies to strongly convex-strongly concave problems and piecewise linear quadratic functions. We show almost sure convergence of the sequence and optimal sublinear convergence rates for the primal-dual gap and objective values, in the general convex-concave case. Numerical evidence demonstrates the state-of-the-art empirical performance of our method in sparse and dense settings, matching and improving the existing methods.

This paper shows that deep learning (DL) representations of data produced by generative adversarial nets (GANs) are random vectors which fall within the class of so-called \emph{concentrated} random vectors. Further exploiting the fact that Gram matrices, of the type $G = X^\intercal X$ with $X=[x_1,\ldots,x_n]\in \mathbb{R}^{p\times n}$ and $x_i$ independent concentrated random vectors from a mixture model, behave asymptotically (as $n,p\to \infty$) as if the $x_i$ were drawn from a Gaussian mixture, suggests that DL representations of GAN-data can be fully described by their first two statistical moments for a wide range of standard classifiers. Our theoretical findings are validated by generating images with the BigGAN model and across different popular deep representation networks.