We study multi-objective reinforcement learning (RL) where an agent's reward is represented as a vector. In settings where an agent competes against opponents, its performance is measured by the distance of its average return vector to a target set. We develop statistically and computationally efficient algorithms to approach the associated target set. Our results extend Blackwell's approachability theorem (Blackwell, 1956) to tabular RL, where strategic exploration becomes essential. The algorithms presented are adaptive; their guarantees hold even without Blackwell's approachability condition. If the opponents use fixed policies, we give an improved rate of approaching the target set while also tackling the more ambitious goal of simultaneously minimizing a scalar cost function. We discuss our analysis for this special case by relating our results to previous works on constrained RL. To our knowledge, this work provides the first provably efficient algorithms for vector-valued Markov games and our theoretical guarantees are near-optimal.
Divide and Conquer: Provably Unveiling the Pareto Front with Multi-Objective Reinforcement Learning
Vrije Universiteit Brussel（布鲁塞尔自由大学）；Université de Montréal（蒙特利尔大学）；Mila - Quebec AI Institute（米拉-魁北克人工智能研究所）；University of Galway（戈尔韦大学）；City of Amsterdam（阿姆斯特丹市）；Utrecht University（乌得勒支大学）
We consider primal-dual-based reinforcement learning (RL) in episodic constrained Markov decision processes (CMDPs) with non-stationary objectives and constraints, which plays a central role in ensuring the safety of RL in time-varying environments. In this problem, the reward/utility functions and the state transition functions are both allowed to vary arbitrarily over time as long as their cumulative variations do not exceed certain known variation budgets. Designing safe RL algorithms in time-varying environments is particularly challenging because of the need to integrate the constraint vi…
Princeton University（普林斯顿大学）；University of Washington（华盛顿大学）；Google AI（谷歌人工智能）
Suppose an agent is in a (possibly unknown) Markov Decision Process in the absence of a reward signal, what might we hope that an agent can efficiently learn to do? This work studies a broad class of objectives that are defined solely as functions of the state-visitation frequencies that are induced by how the agent behaves. For example, one natural, intrinsically defined, objective problem is for the agent to learn a policy which induces a distribution over state space that is as uniform as possible, which can be measured in an entropic sense. We provide an efficient algorithm to optimize suc…
University of Chicago（芝加哥大学）；Meta Platforms, Inc.（元平台公司）；University of Michigan（密歇根大学）；Northwestern University（西北大学）；Yale University（耶鲁大学）
While single-agent policy optimization in a fixed environment has attracted a lot of research attention recently in the reinforcement learning community, much less is known theoretically when there are multiple agents playing in a potentially competitive environment. We take steps forward by proposing and analyzing new fictitious play policy optimization algorithms for zero-sum Markov games with structured but unknown transitions. We consider two classes of transition structures: factored independent transition and single-controller transition. For both scenarios, we prove tight $\widetilde{\m…
Self-play, where the algorithm learns by playing against itself without requiring any direct supervision, has become the new weapon in modern Reinforcement Learning (RL) for achieving superhuman performance in practice. However, the majority of exisiting theory in reinforcement learning only applies to the setting where the agent plays against a fixed environment; it remains largely open whether self-play algorithms can be provably effective, especially when it is necessary to manage the exploration/exploitation tradeoff. We study self-play in competitive reinforcement learning under the setti…
Facebook AI Research（Facebook AI研究院）；Inria Lille（里尔法国国家信息与自动化研究所）；DeepMind
One of the challenges in online reinforcement learning (RL) is that the agent needs to trade off the exploration of the environment and the exploitation of the samples to optimize its behavior. Whether we optimize for regret, sample complexity, state-space coverage or model estimation, we need to strike a different exploration-exploitation trade-off. In this paper, we propose to tackle the exploration-exploitation problem following a decoupled approach composed of: 1) An "objective-specific" algorithm that (adaptively) prescribes how many samples to collect at which states, as if it has access…
University of Wisconsin, Madison（威斯康星大学麦迪逊分校）；Rice University（莱斯大学）；University of Washington（华盛顿大学）
We consider interactive learning in the realizable setting and develop a general framework to handle problems ranging from best arm identification to active classification. We begin our investigation with the observation that agnostic algorithms \emph{cannot} be minimax-optimal in the realizable setting. Hence, we design novel computationally efficient algorithms for the realizable setting that match the minimax lower bound up to logarithmic factors and are general-purpose, accommodating a wide variety of function classes including kernel methods, H{ö}lder smooth functions, and convex function…
In deep reinforcement learning (RL), adversarial attacks can trick an agent into unwanted states and disrupt training. We propose a system called Robust Student-DQN (RS-DQN), which permits online robustness training alongside Q networks, while preserving competitive performance. We show that RS-DQN can be combined with (i) state-of-the-art adversarial training and (ii) provably robust training to obtain an agent that is resilient to strong attacks during training and evaluation.
Many potential applications of reinforcement learning (RL) require guarantees that the agent will perform well in the face of disturbances to the dynamics or reward function. In this paper, we prove theoretically that maximum entropy (MaxEnt) RL maximizes a lower bound on a robust RL objective, and thus can be used to learn policies that are robust to some disturbances in the dynamics and the reward function. While this capability of MaxEnt RL has been observed empirically in prior work, to the best of our knowledge our work provides the first rigorous proof and theoretical characterization of…
ETH Zurich（苏黎世联邦理工学院）；University of Texas at Dallas（德克萨斯大学达拉斯分校）
Despite their success, policy gradient methods suffer from high variance of the gradient estimate, which can result in unsatisfactory sample complexity. Recently, numerous variance-reduced extensions of policy gradient methods with provably better sample complexity and competitive numerical performance have been proposed. After a compact survey on some of the main variance-reduced REINFORCE-type methods, we propose ProbAbilistic Gradient Estimation for Policy Gradient (PAGE-PG), a novel loopless variance-reduced policy gradient method based on a probabilistic switch between two types of update…
Randomized experiments have been critical tools of decision making for decades. However, subjects can show significant heterogeneity in response to treatments in many important applications. Therefore it is not enough to simply know which treatment is optimal for the entire population. What we need is a model that correctly customize treatment assignment base on subject characteristics. The problem of constructing such models from randomized experiments data is known as Uplift Modeling in the literature. Many algorithms have been proposed for uplift modeling and some have generated promising r…
Carnegie Mellon University（卡内基梅隆大学）；University of Pennsylvania（宾夕法尼亚大学）
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 reinfo…
ETH Zürich（苏黎世联邦理工学院）；California Institute of Technology（加州理工学院）
A core challenge in policy optimization in competitive Markov decision processes is the design of efficient optimization methods with desirable convergence and stability properties. To tackle this, we propose competitive policy optimization (CoPO), a novel policy gradient approach that exploits the game-theoretic nature of competitive games to derive policy updates. Motivated by the competitive gradient optimization method, we derive a bilinear approximation of the game objective. In contrast, off-the-shelf policy gradient methods utilize only linear approximations, and hence do not capture in…
We consider the problem of clustering in the presence of noise. That is, when on top of cluster structure, the data also contains a subset of \emph{unstructured} points. Our goal is to detect the clusters despite the presence of many unstructured points. Any algorithm that achieves this goal is noise-robust. We consider a regularisation method which converts any center-based clustering objective into a noise-robust one. We focus on the $k$-means objective and we prove that the regularised version of $k$-means is NP-Hard even for $k=1$. We consider two algorithms based on the convex (sdp and lp…
SUTD（新加坡科技设计大学(SUTD)（注：SUTD是Singapore University of Technology and Design的缩写，常见中文名新加坡科技设计大学））
Non-negative matrix factorization (NMF) is a fundamental non-convex optimization problem with numerous applications in Machine Learning (music analysis, document clustering, speech-source separation etc). Despite having received extensive study, it is poorly understood whether or not there exist natural algorithms that can provably converge to a local minimum. Part of the reason is because the objective is heavily symmetric and its gradient is not Lipschitz. In this paper we define a multiplicative weight update type dynamics (modification of the seminal Lee-Seung algorithm) that runs concurre…
Amazon Alexa（亚马逊Alexa）；Toyota Technological Institute at Chicago（芝加哥丰田技术研究所）
We study stochastic optimization of nonconvex loss functions, which are typical objectives for training neural networks. We propose stochastic approximation algorithms which optimize a series of regularized, nonlinearized losses on large minibatches of samples, using only first-order gradient information. Our algorithms provably converge to an approximate critical point of the expected objective with faster rates than minibatch stochastic gradient descent, and facilitate better parallelization by allowing larger minibatches.
Single-objective black box optimization (also known as zeroth-order optimization) is the process of minimizing a scalar objective $f(x)$, given evaluations at adaptively chosen inputs $x$. In this paper, we consider multi-objective optimization, where $f(x)$ outputs a vector of possibly competing objectives and the goal is to converge to the Pareto frontier. Quantitatively, we wish to maximize the standard hypervolume indicator metric, which measures the dominated hypervolume of the entire set of chosen inputs. In this paper, we introduce a novel scalarization function, which we term the hyper…
Tencent AI Lab（腾讯AI实验室）；Megvii Research Shanghai（上海旷视研究院）；Tsinghua University（清华大学）；Peking University（北京大学）；University of Texas at Arlington（德克萨斯大学阿灵顿分校）
Meta-learning for offline reinforcement learning (OMRL) is an understudied problem with tremendous potential impact by enabling RL algorithms in many real-world applications. A popular solution to the problem is to infer task identity as augmented state using a context-based encoder, for which efficient learning of robust task representations remains an open challenge. In this work, we provably improve upon one of the SOTA OMRL algorithms, FOCAL, by incorporating intra-task attention mechanism and inter-task contrastive learning objectives, to robustify task representation learning against spa…
Scaling Multi-Objective Security Games Provably via Space Discretization Based Evolutionary Search
East China Normal University（华东师范大学）；Shanghai Institute of AI for Education, East China Normal University（华东师范大学上海人工智能教育研究院）；Nanjing University（南京大学）；Polixir Technologies（Polixir科技）；Wenzhou University（温州大学）
Industrial Engineering and Operations Research, Columbia University（哥伦比亚大学工业工程与运筹学系）；School of Computing, National University of Singapore（新加坡国立大学计算机学院）
Machine learning algorithms are designed to make accurate predictions of the future based on existing data, while online algorithms seek to bound some performance measure (typically the competitive ratio) without knowledge of the future. Lykouris and Vassilvitskii demonstrated that augmenting online algorithms with a machine learned predictor can provably decrease the competitive ratio under as long as the predictor is suitably accurate. In this work we apply this idea to the Online Metrical Task System problem, which was put forth by Borodin, Linial, and Saks as a general model for dynamic sy…
In this paper, we present improved learning-augmented algorithms for the multi-option ski rental problem. Learning-augmented algorithms take ML predictions as an added part of the input and incorporates these predictions in solving the given problem. Due to their unique strength that combines the power of ML predictions with rigorous performance guarantees, they have been extensively studied in the context of online optimization problems. Even though ski rental problems are one of the canonical problems in the field of online optimization, only deterministic algorithms were previously known fo…
We present a Newton-type method that converges fast from any initialization and for arbitrary convex objectives with Lipschitz Hessians. We achieve this by merging the ideas of cubic regularization with a certain adaptive Levenberg--Marquardt penalty. In particular, we show that the iterates given by $x^{k+1}=x^k - \bigl(\nabla^2 f(x^k) + \sqrt{H\|\nabla f(x^k)\|} \mathbf{I}\bigr)^{-1}\nabla f(x^k)$, where $H>0$ is a constant, converge globally with a $\mathcal{O}(\frac{1}{k^2})$ rate. Our method is the first variant of Newton's method that has both cheap iterations and provably fast global co…
Provably Accelerated Decentralized Gradient Method Over Unbalanced Directed Graphs
Shanghai Center for Mathematical Sciences, Fudan University（复旦大学上海数学中心）；School of Mathematical Sciences, Fudan University（复旦大学数学科学学院）；Shanghai Key Laboratory for Contemporary Applied Mathematics（上海现代应用数学重点实验室）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）；School of Data Science, The Chinese University of Hong Kong, Shenzhen (CUHK-Shenzhen)（香港中文大学（深圳）数据科学学院）；Shenzhen Research Institute of Big Data（深圳大数据研究院）
We study infinite-horizon discounted two-player zero-sum Markov games, and develop a decentralized algorithm that provably converges to the set of Nash equilibria under self-play. Our algorithm is based on running an Optimistic Gradient Descent Ascent algorithm on each state to learn the policies, with a critic that slowly learns the value of each state. To the best of our knowledge, this is the first algorithm in this setting that is simultaneously rational (converging to the opponent's best response when it uses a stationary policy), convergent (converging to the set of Nash equilibria under…
In this paper, we consider efficient differentially private empirical risk minimization from the viewpoint of optimization algorithms. For strongly convex and smooth objectives, we prove that gradient descent with output perturbation not only achieves nearly optimal utility, but also significantly improves the running time of previous state-of-the-art private optimization algorithms, for both $ε$-DP and $(ε, δ)$-DP. For non-convex but smooth objectives, we propose an RRPSGD (Random Round Private Stochastic Gradient Descent) algorithm, which provably converges to a stationary point with privacy…
Univ. de Rouen（鲁昂大学）；Criteo AI Lab（Criteo人工智能实验室）；Univ Côte d’Azur（蔚蓝海岸大学）；CNRS（法国国家科学研究中心）；OCA Lagrange（拉格朗日蔚蓝海岸天文台）；INSA de Rouen（鲁昂国立应用科学学院）；IMAG（蒙彼利埃亚历山大·格罗滕迪克研究所）；Université de Montpellier（蒙彼利埃大学）
Owing to their statistical properties, non-convex sparse regularizers have attracted much interest for estimating a sparse linear model from high dimensional data. Given that the solution is sparse, for accelerating convergence, a working set strategy addresses the optimization problem through an iterative algorithm by incre-menting the number of variables to optimize until the identification of the solution support. While those methods have been well-studied and theoretically supported for convex regularizers, this paper proposes a working set algorithm for non-convex sparse regularizers with…
Sequential Monte Carlo (SMC) is an inference algorithm for state space models that approximates the posterior by sampling from a sequence of target distributions. The target distributions are often chosen to be the filtering distributions, but these ignore information from future observations, leading to practical and theoretical limitations in inference and model learning. We introduce SIXO, a method that instead learns targets that approximate the smoothing distributions, incorporating information from all observations. The key idea is to use density ratio estimation to fit functions that wa…
MGDA Converges under Generalized Smoothness, Provably
School of Electrical, Computer and Energy Engineering, Arizona State University（亚利桑那州立大学电气、计算机与能源工程学院）；Department of Computer Science and Engineering, University at Buffalo（纽约州立大学布法罗分校计算机科学与工程学院）
