In many sequential decision-making problems, the goal is to optimize a utility function while satisfying a set of constraints on different utilities. This learning problem is formalized through Constrained Markov Decision Processes (CMDPs). In this paper, we investigate the exploration-exploitation dilemma in CMDPs. While learning in an unknown CMDP, an agent should trade-off exploration to discover new information about the MDP, and exploitation of the current knowledge to maximize the reward while satisfying the constraints. While the agent will eventually learn a good or optimal policy, we do not want the agent to violate the constraints too often during the learning process. In this work, we analyze two approaches for learning in CMDPs. The first approach leverages the linear formulation of CMDP to perform optimistic planning at each episode. The second approach leverages the dual formulation (or saddle-point formulation) of CMDP to perform incremental, optimistic updates of the primal and dual variables. We show that both achieves sublinear regret w.r.t.\ the main utility while having a sublinear regret on the constraint violations. That being said, we highlight a crucial difference between the two approaches; the linear programming approach results in stronger guarantees than in the dual formulation based approach.
While a large body of empirical results show that temporally-extended actions and options may significantly affect the learning performance of an agent, the theoretical understanding of how and when options can be beneficial in online reinforcement learning is relatively limited. In this paper, we derive an upper and lower bound on the regret of a variant of UCRL using options. While we first analyze the algorithm in the general case of semi-Markov decision processes (SMDPs), we show how these results can be translated to the specific case of MDPs with options and we illustrate simple scenario…
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）
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 …
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…
Sequel Team - Inria Lille（Inria Lille Sequel团队）；Facebook AI Research（Facebook人工智能研究）
While designing the state space of an MDP, it is common to include states that are transient or not reachable by any policy (e.g., in mountain car, the product space of speed and position contains configurations that are not physically reachable). This leads to defining weakly-communicating or multi-chain MDPs. In this paper, we introduce \tucrl, the first algorithm able to perform efficient exploration-exploitation in any finite Markov Decision Process (MDP) without requiring any form of prior knowledge. In particular, for any MDP with $S^{\texttt{C}}$ communicating states, $A$ actions and $Γ…
INRIA Lille（里尔法国国家信息与自动化研究所）；Facebook AI Research（脸书人工智能研究院）；Montanuniversität Leoben（莱奥本矿业大学）
We introduce SCAL, an algorithm designed to perform efficient exploration-exploitation in any unknown weakly-communicating Markov decision process (MDP) for which an upper bound $c$ on the span of the optimal bias function is known. For an MDP with $S$ states, $A$ actions and $Γ\leq S$ possible next states, we prove a regret bound of $\widetilde{O}(c\sqrt{ΓSAT})$, which significantly improves over existing algorithms (e.g., UCRL and PSRL), whose regret scales linearly with the MDP diameter $D$. In fact, the optimal bias span is finite and often much smaller than $D$ (e.g., $D=\infty$ in non-co…
We address reinforcement learning problems with finite state and action spaces where the underlying MDP has some known structure that could be potentially exploited to minimize the exploration rates of suboptimal (state, action) pairs. For any arbitrary structure, we derive problem-specific regret lower bounds satisfied by any learning algorithm. These lower bounds are made explicit for unstructured MDPs and for those whose transition probabilities and average reward functions are Lipschitz continuous w.r.t. the state and action. For Lipschitz MDPs, the bounds are shown not to scale with the s…
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…
Active Reinforcement Learning (ARL) is a twist on RL where the agent observes reward information only if it pays a cost. This subtle change makes exploration substantially more challenging. Powerful principles in RL like optimism, Thompson sampling, and random exploration do not help with ARL. We relate ARL in tabular environments to Bayes-Adaptive MDPs. We provide an ARL algorithm using Monte-Carlo Tree Search that is asymptotically Bayes optimal. Experimentally, this algorithm is near-optimal on small Bandit problems and MDPs. On larger MDPs it outperforms a Q-learner augmented with speciali…
University of Oxford（牛津大学）；Northeastern University（东北大学）
We study adaptive importance sampling (AIS) as an online learning problem and argue for the importance of the trade-off between exploration and exploitation in this adaptation. Borrowing ideas from the bandits literature, we propose Daisee, a partition-based AIS algorithm. We further introduce a notion of regret for AIS and show that Daisee has $\mathcal{O}(\sqrt{T}(\log T)^{\frac{3}{4}})$ cumulative pseudo-regret, where $T$ is the number of iterations. We then extend Daisee to adaptively learn a hierarchical partitioning of the sample space for more efficient sampling and confirm the performa…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
In this paper, we propose a novel neural exploration strategy in contextual bandits, EE-Net, distinct from the standard UCB-based and TS-based approaches. Contextual multi-armed bandits have been studied for decades with various applications. To solve the exploitation-exploration tradeoff in bandits, there are three main techniques: epsilon-greedy, Thompson Sampling (TS), and Upper Confidence Bound (UCB). In recent literature, linear contextual bandits have adopted ridge regression to estimate the reward function and combine it with TS or UCB strategies for exploration. However, this line of w…
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…
Facebook AI Research（Facebook人工智能研究（Facebook AI Research））
We introduce the active exploration problem in Markov decision processes (MDPs). Each state of the MDP is characterized by a random value and the learner should gather samples to estimate the mean value of each state as accurately as possible. Similarly to active exploration in multi-armed bandit (MAB), states may have different levels of noise, so that the higher the noise, the more samples are needed. As the noise level is initially unknown, we need to trade off the exploration of the environment to estimate the noise and the exploitation of these estimates to compute a policy maximizing the…
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…
The goal of meta-reinforcement learning (meta-RL) is to build agents that can quickly learn new tasks by leveraging prior experience on related tasks. Learning a new task often requires both exploring to gather task-relevant information and exploiting this information to solve the task. In principle, optimal exploration and exploitation can be learned end-to-end by simply maximizing task performance. However, such meta-RL approaches struggle with local optima due to a chicken-and-egg problem: learning to explore requires good exploitation to gauge the exploration's utility, but learning to exp…
Sparse reward is one of the biggest challenges in reinforcement learning (RL). In this paper, we propose a novel method called Generative Exploration and Exploitation (GENE) to overcome sparse reward. GENE automatically generates start states to encourage the agent to explore the environment and to exploit received reward signals. GENE can adaptively tradeoff between exploration and exploitation according to the varying distributions of states experienced by the agent as the learning progresses. GENE relies on no prior knowledge about the environment and can be combined with any RL algorithm, …
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…
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…
Twitter Inc.（推特公司）；University of California, Davis（加州大学戴维斯分校）
In this paper, we propose and study opportunistic bandits - a new variant of bandits where the regret of pulling a suboptimal arm varies under different environmental conditions, such as network load or produce price. When the load/price is low, so is the cost/regret of pulling a suboptimal arm (e.g., trying a suboptimal network configuration). Therefore, intuitively, we could explore more when the load/price is low and exploit more when the load/price is high. Inspired by this intuition, we propose an Adaptive Upper-Confidence-Bound (AdaUCB) algorithm to adaptively balance the exploration-exp…
We propose Deterministic Sequencing of Exploration and Exploitation (DSEE) algorithm with interleaving exploration and exploitation epochs for model-based RL problems that aim to simultaneously learn the system model, i.e., a Markov decision process (MDP), and the associated optimal policy. During exploration, DSEE explores the environment and updates the estimates for expected reward and transition probabilities. During exploitation, the latest estimates of the expected reward and transition probabilities are used to obtain a robust policy with high probability. We design the lengths of the e…
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…
Inria Lille（里尔法国国家信息与自动化研究所）；Facebook AI Research（脸书人工智能研究院）
We introduce and analyse two algorithms for exploration-exploitation in discrete and continuous Markov Decision Processes (MDPs) based on exploration bonuses. SCAL$^+$ is a variant of SCAL (Fruit et al., 2018) that performs efficient exploration-exploitation in any unknown weakly-communicating MDP for which an upper bound C on the span of the optimal bias function is known. For an MDP with $S$ states, $A$ actions and $Γ\leq S$ possible next states, we prove that SCAL$^+$ achieves the same theoretical guarantees as SCAL (i.e., a high probability regret bound of $\widetilde{O}(C\sqrt{ΓSAT})$), w…
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…
An agent learning through interactions should balance its action selection process between probing the environment to discover new rewards and using the information acquired in the past to adopt useful behaviour. This trade-off is usually obtained by perturbing either the agent's actions (e.g., e-greedy or Gibbs sampling) or the agent's parameters (e.g., NoisyNet), or by modifying the reward it receives (e.g., exploration bonus, intrinsic motivation, or hand-shaped rewards). Here, we adopt a disruptive but simple and generic perspective, where we explicitly disentangle exploration and exploita…
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 …
Despite the close connection between exploration and sample efficiency, most state of the art reinforcement learning algorithms include no considerations for exploration beyond maximizing the entropy of the policy. In this work we address this seeming missed opportunity. We observe that the most common formulation of directed exploration in deep RL, known as bonus-based exploration (BBE), suffers from bias and slow coverage in the few-sample regime. This causes BBE to be actively detrimental to policy learning in many control tasks. We show that by decoupling the task policy from the explorati…
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 Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Microsoft（微软）；Microsoft Research（微软研究院）；Google Research（谷歌研究院）
We study reward-free reinforcement learning (RL) under general non-linear function approximation, and establish sample efficiency and hardness results under various standard structural assumptions. On the positive side, we propose the RFOLIVE (Reward-Free OLIVE) algorithm for sample-efficient reward-free exploration under minimal structural assumptions, which covers the previously studied settings of linear MDPs (Jin et al., 2020b), linear completeness (Zanette et al., 2020b) and low-rank MDPs with unknown representation (Modi et al., 2021). Our analyses indicate that the explorability or reac…
Reinforcement learning studies how to balance exploration and exploitation in real-world systems, optimizing interactions with the world while simultaneously learning how the world operates. One general class of algorithms for such learning is the multi-armed bandit setting. Randomized probability matching, based upon the Thompson sampling approach introduced in the 1930s, has recently been shown to perform well and to enjoy provable optimality properties. It permits generative, interpretable modeling in a Bayesian setting, where prior knowledge is incorporated, and the computed posteriors nat…
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 Cambridge（剑桥大学）；Tencent RoboticsX（腾讯机器人X实验室）；Hong Kong University of Science and Technology（香港科技大学）；Tsinghua University（清华大学）；IDEA（粤港澳大湾区数字经济研究院）；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
In this work, we study the simple yet universally applicable case of reward shaping in value-based Deep Reinforcement Learning (DRL). We show that reward shifting in the form of the linear transformation is equivalent to changing the initialization of the $Q$-function in function approximation. Based on such an equivalence, we bring the key insight that a positive reward shifting leads to conservative exploitation, while a negative reward shifting leads to curiosity-driven exploration. Accordingly, conservative exploitation improves offline RL value estimation, and optimistic value estimation …
Balancing Exploration and Exploitation in Hierarchical Reinforcement Learning via Latent Landmark Graphs
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；School of Future Technology, University of Chinese Academy of Sciences（中国科学院大学未来技术学院）；School of Artificial Intelligence, University of Chinese Academy of Sciences（中国科学院大学人工智能学院）
Sorbonne Université（索邦大学）；CNRS（法国国家科学研究中心）；Institut des Systèmes Intelligents et de Robotique（智能系统与机器人研究所）
The exploration-exploitation trade-off is at the heart of reinforcement learning (RL). However, most continuous control benchmarks used in recent RL research only require local exploration. This led to the development of algorithms that have basic exploration capabilities, and behave poorly in benchmarks that require more versatile exploration. For instance, as demonstrated in our empirical study, state-of-the-art RL algorithms such as DDPG and TD3 are unable to steer a point mass in even small 2D mazes. In this paper, we propose a new algorithm called "Plan, Backplay, Chain Skills" (PBCS) tha…
Columbia University（哥伦比亚大学）；The University of Texas at Austin（得克萨斯大学奥斯汀分校）；University of Oxford（牛津大学）
We consider reinforcement learning (RL) in continuous time and study the problem of achieving the best trade-off between exploration of a black box environment and exploitation of current knowledge. We propose an entropy-regularized reward function involving the differential entropy of the distributions of actions, and motivate and devise an exploratory formulation for the feature dynamics that captures repetitive learning under exploration. The resulting optimization problem is a revitalization of the classical relaxed stochastic control. We carry out a complete analysis of the problem in the…
We integrate information-theoretic concepts into the design and analysis of optimistic algorithms and Thompson sampling. By making a connection between information-theoretic quantities and confidence bounds, we obtain results that relate the per-period performance of the agent with its information gain about the environment, thus explicitly characterizing the exploration-exploitation tradeoff. The resulting cumulative regret bound depends on the agent's uncertainty over the environment and quantifies the value of prior information. We show applicability of this approach to several environments…
In continuous action domains, standard deep reinforcement learning algorithms like DDPG suffer from inefficient exploration when facing sparse or deceptive reward problems. Conversely, evolutionary and developmental methods focusing on exploration like Novelty Search, Quality-Diversity or Goal Exploration Processes explore more robustly but are less efficient at fine-tuning policies using gradient descent. In this paper, we present the GEP-PG approach, taking the best of both worlds by sequentially combining a Goal Exploration Process and two variants of DDPG. We study the learning performance…
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…
University of Science and Technology of China（中国科学技术大学）；The University of Birmingham（伯明翰大学）
Exploration has been a crucial part of reinforcement learning, yet several important questions concerning exploration efficiency are still not answered satisfactorily by existing analytical frameworks. These questions include exploration parameter setting, situation analysis, and hardness of MDPs, all of which are unavoidable for practitioners. To bridge the gap between the theory and practice, we propose a new analytical framework called the success probability of exploration. We show that those important questions of exploration above can all be answered under our framework, and the answers …
University of Michigan（密歇根大学）；ShanghaiTech University（上海科技大学）
Multi-armed bandit (MAB) is a classic model for understanding the exploration-exploitation trade-off. The traditional MAB model for recommendation systems assumes the user stays in the system for the entire learning horizon. In new online education platforms such as ALEKS or new video recommendation systems such as TikTok and YouTube Shorts, the amount of time a user spends on the app depends on how engaging the recommended contents are. Users may temporarily leave the system if the recommended items cannot engage the users. To understand the exploration, exploitation, and engagement in these …
While in general trading off exploration and exploitation in reinforcement learning is hard, under some formulations relatively simple solutions exist. In this paper, we first derive upper bounds for the utility of selecting different actions in the multi-armed bandit setting. Unlike the common statistical upper confidence bounds, these explicitly link the planning horizon, uncertainty and the need for exploration explicit. The resulting algorithm can be seen as a generalisation of the classical Thompson sampling algorithm. We experimentally test these algorithms, as well as $ε$-greedy and the…
We consider an agent who is involved in a Markov decision process and receives a vector of outcomes every round. Her objective is to maximize a global concave reward function on the average vectorial outcome. The problem models applications such as multi-objective optimization, maximum entropy exploration, and constrained optimization in Markovian environments. In our general setting where a stationary policy could have multiple recurrent classes, the agent faces a subtle yet consequential trade-off in alternating among different actions for balancing the vectorial outcomes. In particular, sta…
