We investigate the exploration of an unknown environment when no reward function is provided. Building on the incremental exploration setting introduced by Lim and Auer [1], we define the objective of learning the set of $ε$-optimal goal-conditioned policies attaining all states that are incrementally reachable within $L$ steps (in expectation) from a reference state $s_0$. In this paper, we introduce a novel model-based approach that interleaves discovering new states from $s_0$ and improving the accuracy of a model estimate that is used to compute goal-conditioned policies to reach newly discovered states. The resulting algorithm, DisCo, achieves a sample complexity scaling as $\tilde{O}(L^5 S_{L+ε} Γ_{L+ε} A ε^{-2})$, where $A$ is the number of actions, $S_{L+ε}$ is the number of states that are incrementally reachable from $s_0$ in $L+ε$ steps, and $Γ_{L+ε}$ is the branching factor of the dynamics over such states. This improves over the algorithm proposed in [1] in both $ε$ and $L$ at the cost of an extra $Γ_{L+ε}$ factor, which is small in most environments of interest. Furthermore, DisCo is the first algorithm that can return an $ε/c_{\min}$-optimal policy for any cost-sensitive shortest-path problem defined on the $L$-reachable states with minimum cost $c_{\min}$. Finally, we report preliminary empirical results confirming our theoretical findings.
We study the autonomous exploration (AX) problem proposed by Lim & Auer (2012). In this setting, the objective is to discover a set of $ε$-optimal policies reaching a set $\mathcal{S}_L^{\rightarrow}$ of incrementally $L$-controllable states. We introduce a novel layered decomposition of the set of incrementally $L$-controllable states that is based on the iterative application of a state-expansion operator. We leverage these results to design Layered Autonomous Exploration (LAE), a novel algorithm for AX that attains a sample complexity of $\tilde{\mathcal{O}}(LS^{\rightarrow}_{L(1+ε)}Γ_{L(1+…
Microsoft（微软）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Microsoft Research（微软研究院）；Google Research（谷歌研究院）
The low rank MDP has emerged as an important model for studying representation learning and exploration in reinforcement learning. With a known representation, several model-free exploration strategies exist. In contrast, all algorithms for the unknown representation setting are model-based, thereby requiring the ability to model the full dynamics. In this work, we present the first model-free representation learning algorithms for low rank MDPs. The key algorithmic contribution is a new minimax representation learning objective, for which we provide variants with differing tradeoffs in their …
Tsinghua University（清华大学）；Stanford University（斯坦福大学）；University of Washington（华盛顿大学）
We revisit the incremental autonomous exploration problem proposed by Lim & Auer (2012). In this setting, the agent aims to learn a set of near-optimal goal-conditioned policies to reach the $L$-controllable states: states that are incrementally reachable from an initial state $s_0$ within $L$ steps in expectation. We introduce a new algorithm with stronger sample complexity bounds than existing ones. Furthermore, we also prove the first lower bound for the autonomous exploration problem. In particular, the lower bound implies that our proposed algorithm, Value-Aware Autonomous Exploration, is…
Policy optimization is a widely-used method in reinforcement learning. Due to its local-search nature, however, theoretical guarantees on global optimality often rely on extra assumptions on the Markov Decision Processes (MDPs) that bypass the challenge of global exploration. To eliminate the need of such assumptions, in this work, we develop a general solution that adds dilated bonuses to the policy update to facilitate global exploration. To showcase the power and generality of this technique, we apply it to several episodic MDP settings with adversarial losses and bandit feedback, improving…
University of Copenhagen（哥本哈根大学）；Universitat Pompeu Fabra（庞培法布拉大学）；Univ. Lille（里尔大学）；Inria（法国国家信息与自动化研究所）；CNRS（法国国家科学研究中心）；Centrale Lille（里尔中央理工学院）；UMR 9189 – CRIStAL
We consider a regret minimization task under the average-reward criterion in an unknown Factored Markov Decision Process (FMDP). More specifically, we consider an FMDP where the state-action space $\mathcal X$ and the state-space $\mathcal S$ admit the respective factored forms of $\mathcal X = \otimes_{i=1}^n \mathcal X_i$ and $\mathcal S=\otimes_{i=1}^m \mathcal S_i$, and the transition and reward functions are factored over $\mathcal X$ and $\mathcal S$. Assuming known factorization structure, we introduce a novel regret minimization strategy inspired by the popular UCRL2 strategy, called D…
National Key Laboratory for Novel Software Technology, Nanjing University（南京大学新型软件技术国家重点实验室）；Shenzhen Research Institute of Big Data, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）深圳大数据研究院）
Despite massive empirical evaluations, one of the fundamental questions in imitation learning is still not fully settled: does AIL (adversarial imitation learning) provably generalize better than BC (behavioral cloning)? We study this open problem with tabular and episodic MDPs. For vanilla AIL that uses the direct maximum likelihood estimation, we provide both negative and positive answers under the known transition setting. For some MDPs, we show that vanilla AIL has a worse sample complexity than BC. The key insight is that the state-action distribution matching principle is weak so that AI…
We study the problem of episodic reinforcement learning in continuous state-action spaces with unknown rewards and transitions. Specifically, we consider the setting where the rewards and transitions are modeled using parametric bilinear exponential families. We propose an algorithm, BEF-RLSVI, that a) uses penalized maximum likelihood estimators to learn the unknown parameters, b) injects a calibrated Gaussian noise in the parameter of rewards to ensure exploration, and c) leverages linearity of the exponential family with respect to an underlying RKHS to perform tractable planning. We furthe…
Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Artificial Intelligence Research Institute FRC CSC RAS（俄罗斯科学院联邦研究中心计算机科学研究所人工智能研究院）
Exploration is an essential part of reinforcement learning, which restricts the quality of learned policy. Hard-exploration environments are defined by huge state space and sparse rewards. In such conditions, an exhaustive exploration of the environment is often impossible, and the successful training of an agent requires a lot of interaction steps. In this paper, we propose an exploration method called Rollback-Explore (RbExplore), which utilizes the concept of the persistent Markov decision process, in which agents during training can roll back to visited states. We test our algorithm in the…
Ecole Polytechnique（巴黎综合理工学院）；Facebook AI Research（Facebook人工智能研究院）；CREST, ENSAE（国立统计与经济行政学院经济研究与应用中心）
This paper studies privacy-preserving exploration in Markov Decision Processes (MDPs) with linear representation. We first consider the setting of linear-mixture MDPs (Ayoub et al., 2020) (a.k.a.\ model-based setting) and provide an unified framework for analyzing joint and local differential private (DP) exploration. Through this framework, we prove a $\widetilde{O}(K^{3/4}/\sqrtε)$ regret bound for $(ε,δ)$-local DP exploration and a $\widetilde{O}(\sqrt{K/ε})$ regret bound for $(ε,δ)$-joint DP. We further study privacy-preserving exploration in linear MDPs (Jin et al., 2020) (a.k.a.\ model-f…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；The University of Chicago（芝加哥大学）；Stanford University（斯坦福大学）；Google Research（谷歌研究院）
Although parallelism has been extensively used in reinforcement learning (RL), the quantitative effects of parallel exploration are not well understood theoretically. We study the benefits of simple parallel exploration for reward-free RL in linear Markov decision processes (MDPs) and two-player zero-sum Markov games (MGs). In contrast to the existing literature, which focuses on approaches that encourage agents to explore a diverse set of policies, we show that using a single policy to guide exploration across all agents is sufficient to obtain an almost-linear speedup in all cases compared t…
Recently, model-free reinforcement learning has attracted research attention due to its simplicity, memory and computation efficiency, and the flexibility to combine with function approximation. In this paper, we propose Exploration Enhanced Q-learning (EE-QL), a model-free algorithm for infinite-horizon average-reward Markov Decision Processes (MDPs) that achieves regret bound of $O(\sqrt{T})$ for the general class of weakly communicating MDPs, where $T$ is the number of interactions. EE-QL assumes that an online concentrating approximation of the optimal average reward is available. This is …
In order to deal with the curse of dimensionality in reinforcement learning (RL), it is common practice to make parametric assumptions where values or policies are functions of some low dimensional feature space. This work focuses on the representation learning question: how can we learn such features? Under the assumption that the underlying (unknown) dynamics correspond to a low rank transition matrix, we show how the representation learning question is related to a particular non-linear matrix decomposition problem. Structurally, we make precise connections between these low rank MDPs and l…
This work studies the question of Representation Learning in RL: how can we learn a compact low-dimensional representation such that on top of the representation we can perform RL procedures such as exploration and exploitation, in a sample efficient manner. We focus on the low-rank Markov Decision Processes (MDPs) where the transition dynamics correspond to a low-rank transition matrix. Unlike prior works that assume the representation is known (e.g., linear MDPs), here we need to learn the representation for the low-rank MDP. We study both the online RL and offline RL settings. For the onlin…
Peking University（北京大学）；University of California, Los Angeles（加州大学洛杉矶分校）
Although model-based reinforcement learning (RL) approaches are considered more sample efficient, existing algorithms are usually relying on sophisticated planning algorithm to couple tightly with the model-learning procedure. Hence the learned models may lack the ability of being re-used with more specialized planners. In this paper we address this issue and provide approaches to learn an RL model efficiently without the guidance of a reward signal. In particular, we take a plug-in solver approach, where we focus on learning a model in the exploration phase and demand that \emph{any planning …
Meta AI；UMPA, ENS Lyon（里昂高等师范学院纯数学与应用数学实验室）；Univ. Lille（里尔大学）；CNRS（法国国家科学研究中心）；Inria（法国国家信息与自动化研究所）；Centrale Lille（里尔中央理工学院）
In probably approximately correct (PAC) reinforcement learning (RL), an agent is required to identify an $ε$-optimal policy with probability $1-δ$. While minimax optimal algorithms exist for this problem, its instance-dependent complexity remains elusive in episodic Markov decision processes (MDPs). In this paper, we propose the first nearly matching (up to a horizon squared factor and logarithmic terms) upper and lower bounds on the sample complexity of PAC RL in deterministic episodic MDPs with finite state and action spaces. In particular, our bounds feature a new notion of sub-optimality g…
Is Pure Exploitation Sufficient in Exogenous MDPs with Linear Function Approximation?
Department of Informatics, King’s College London（伦敦国王学院信息学院）；Independent Researcher（独立研究者）；Department of Industrial Engineering and Management Sciences, Northwestern University（西北大学工业工程与管理科学系）；The Alan Turing Institute（艾伦·图灵研究所）
We present BRIEE (Block-structured Representation learning with Interleaved Explore Exploit), an algorithm for efficient reinforcement learning in Markov Decision Processes with block-structured dynamics (i.e., Block MDPs), where rich observations are generated from a set of unknown latent states. BRIEE interleaves latent states discovery, exploration, and exploitation together, and can provably learn a near-optimal policy with sample complexity scaling polynomially in the number of latent states, actions, and the time horizon, with no dependence on the size of the potentially infinite observa…
University of Science and Technology of China（中国科学技术大学）；The Pennsylvania State University（宾夕法尼亚州立大学）；The Ohio State University（俄亥俄州立大学）
In reward-free reinforcement learning (RL), an agent explores the environment first without any reward information, in order to achieve certain learning goals afterwards for any given reward. In this paper we focus on reward-free RL under low-rank MDP models, in which both the representation and linear weight vectors are unknown. Although various algorithms have been proposed for reward-free low-rank MDPs, the corresponding sample complexity is still far from being satisfactory. In this work, we first provide the first known sample complexity lower bound that holds for any algorithm under low-…
In many real-life reinforcement learning (RL) problems, deploying new policies is costly. In those scenarios, algorithms must solve exploration (which requires adaptivity) while switching the deployed policy sparsely (which limits adaptivity). In this paper, we go beyond the existing state-of-the-art on this problem that focused on linear Markov Decision Processes (MDPs) by considering linear Bellman-complete MDPs with low inherent Bellman error. We propose the ELEANOR-LowSwitching algorithm that achieves the near-optimal regret with a switching cost logarithmic in the number of episodes and l…
Reward-free reinforcement learning (RL) considers the setting where the agent does not have access to a reward function during exploration, but must propose a near-optimal policy for an arbitrary reward function revealed only after exploring. In the the tabular setting, it is well known that this is a more difficult problem than reward-aware (PAC) RL -- where the agent has access to the reward function during exploration -- with optimal sample complexities in the two settings differing by a factor of $|\mathcal{S}|$, the size of the state space. We show that this separation does not exist in t…
Indian Institute of Science（印度科学院）；Adobe Research（Adobe研究院）
We study Markov Decision Processes (MDP) wherein states correspond to causal graphs that stochastically generate rewards. In this setup, the learner's goal is to identify atomic interventions that lead to high rewards by intervening on variables at each state. Generalizing the recent causal-bandit framework, the current work develops (simple) regret minimization guarantees for two-stage causal MDPs, with parallel causal graph at each state. We propose an algorithm that achieves an instance dependent regret bound. A key feature of our algorithm is that it utilizes convex optimization to address…
HSE University（高等经济大学）；Artificial Intelligence Research Institute（人工智能研究院）；Duisburg-Essen University（杜伊斯堡-埃森大学）；Google DeepMind（谷歌DeepMind）；École Polytechnique（巴黎综合理工学院）；Mohamed Bin Zayed University of AI（穆罕默德·本·扎耶德人工智能大学）；IDEMIA（艾德米亚）；ENS Lyon（里昂高等师范学院）
Model-Based Exploration in Monitored Markov Decision Processes
Department of Computing Science, University of Alberta（阿尔伯塔大学计算机科学系）；Alberta Machine Intelligence Institute (Amii)（阿尔伯塔机器智能研究所）；Canada CIFAR AI Chair, Amii（加拿大CIFAR人工智能 chair，Amii）
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
This paper proposes a formal approach to online learning and planning for agents operating in a priori unknown, time-varying environments. The proposed method computes the maximally likely model of the environment, given the observations about the environment made by an agent earlier in the system run and assuming knowledge of a bound on the maximal rate of change of system dynamics. Such an approach generalizes the estimation method commonly used in learning algorithms for unknown Markov decision processes with time-invariant transition probabilities, but is also able to quickly and correctly…
Politecnico di Milano（米兰理工大学）；Facebook AI Research（脸书人工智能研究院）
In the contextual linear bandit setting, algorithms built on the optimism principle fail to exploit the structure of the problem and have been shown to be asymptotically suboptimal. In this paper, we follow recent approaches of deriving asymptotically optimal algorithms from problem-dependent regret lower bounds and we introduce a novel algorithm improving over the state-of-the-art along multiple dimensions. We build on a reformulation of the lower bound, where context distribution and exploration policy are decoupled, and we obtain an algorithm robust to unbalanced context distributions. Then…
Model-based RL in Contextual Decision Processes: PAC bounds and Exponential Improvements over Model-free Approaches
Carnegie Mellon University（卡内基梅隆大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Microsoft Research（微软研究院）
我们研究了样本复杂性的基于模型的强化学习（以下简称RL）在一般的上下文决策过程中，需要战略探索，以找到一个接近最优的政策。我们设计了一个通用的模型类RL的新算法，并分析其统计特性。我们的算法样本的复杂性由一个新的结构参数称为证人的排名，我们证明是小的几个设置的兴趣，包括因素的MDP。我们还表明，证人秩永远不会大于最近提出的Bellman秩参数，该参数控制无模型算法OLIVE的样本复杂度（Jiang et al.，2017年），唯一的其他可证明的样本有效的算法，在这个水平的一般性的全球探索。聚焦于因子化的MDP的特殊情况，我们证明了一般类无模型方法的指数下界，包括OLIVE，当与我们的算法结果相结合时，在一些丰富的观测设置中，基于模型的RL和无模型RL之间表现出指数分离。
Solving Partially Observable Markov Decision Processes (POMDPs) is hard. Learning optimal controllers for POMDPs when the model is unknown is harder. Online learning of optimal controllers for unknown POMDPs, which requires efficient learning using regret-minimizing algorithms that effectively tradeoff exploration and exploitation, is even harder, and no solution exists currently. In this paper, we consider infinite-horizon average-cost POMDPs with unknown transition model, though a known observation model. We propose a natural posterior sampling-based reinforcement learning algorithm (PSRL-PO…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We present a framework to address a class of sequential decision making problems. Our framework features learning the optimal control policy with robustness to noisy data, determining the unknown state and action parameters, and performing sensitivity analysis with respect to problem parameters. We consider two broad categories of sequential decision making problems modelled as infinite horizon Markov Decision Processes (MDPs) with (and without) an absorbing state. The central idea underlying our framework is to quantify exploration in terms of the Shannon Entropy of the trajectories under the…
Criteo AI Lab（Criteo人工智能实验室）；Facebook AI Research（Facebook人工智能研究院）
We study the exploration-exploitation dilemma in the linear quadratic regulator (LQR) setting. Inspired by the extended value iteration algorithm used in optimistic algorithms for finite MDPs, we propose to relax the optimistic optimization of \ofulq and cast it into a constrained \textit{extended} LQR problem, where an additional control variable implicitly selects the system dynamics within a confidence interval. We then move to the corresponding Lagrangian formulation for which we prove strong duality. As a result, we show that an $ε$-optimistic controller can be computed efficiently by sol…
