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-communicating MDPs). A similar result was originally derived by Bartlett and Tewari (2009) for REGAL.C, for which no tractable algorithm is available. In this paper, we relax the optimization problem at the core of REGAL.C, we carefully analyze its properties, and we provide the first computationally efficient algorithm to solve it. Finally, we report numerical simulations supporting our theoretical findings and showing how SCAL significantly outperforms UCRL in MDPs with large diameter and small span.
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…
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, …
Technion（以色列理工学院）；Facebook AI Research（Facebook人工智能研究院）
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 …
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…
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…
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…
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…
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…
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 …
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…
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…
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…
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…
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…
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…
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 …
University of California San Diego（加州大学圣地亚哥分校）；The Abdus Salam International Centre for Theoretical Physics (ICTP)（阿卜杜勒·萨拉姆国际理论物理中心（ICTP））
Proper balance between exploitation and exploration is what makes good decisions, which achieve high rewards like payoff or evolutionary fitness. The Infomax principle postulates that maximization of information directs the function of diverse systems, from living systems to artificial neural networks. While specific applications are successful, the validity of information as a proxy for reward remains unclear. Here, we consider the multi-armed bandit decision problem, which features arms (slot-machines) of unknown probabilities of success and a player trying to maximize cumulative payoff by c…
Tsinghua University（清华大学）；Tencent AI Lab（腾讯人工智能实验室）
Model-based deep reinforcement learning has achieved success in various domains that require high sample efficiencies, such as Go and robotics. However, there are some remaining issues, such as planning efficient explorations to learn more accurate dynamic models, evaluating the uncertainty of the learned models, and more rational utilization of models. To mitigate these issues, we present MEEE, a model-ensemble method that consists of optimistic exploration and weighted exploitation. During exploration, unlike prior methods directly selecting the optimal action that maximizes the expected acc…
Intrinsic motivation enables reinforcement learning (RL) agents to explore when rewards are very sparse, where traditional exploration heuristics such as Boltzmann or e-greedy would typically fail. However, intrinsic exploration is generally handled in an ad-hoc manner, where exploration is not treated as a core objective of the learning process; this weak formulation leads to sub-optimal exploration performance. To overcome this problem, we propose a framework based on multi-objective RL where both exploration and exploitation are being optimized as separate objectives. This formulation bring…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We present blind exploration and exploitation (BEE) algorithms for identifying the most reliable stochastic expert based on formulations that employ posterior sampling, upper-confidence bounds, empirical Kullback-Leibler divergence, and minmax methods for the stochastic multi-armed bandit problem. Joint sampling and consultation of experts whose opinions depend on the hidden and random state of the world becomes challenging in the unsupervised, or blind, framework as feedback from the true state is not available. We propose an empirically realizable measure of expert competence that can be inf…
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…
College of Software, Nankai University（南开大学软件学院）；Zhongguancun Academy（中关村学院）；School of Automation , Beijing Institute of Technology（北京理工大学自动化学院）；College of Computer Science（计算机科学学院）；Technology, Zhejiang University（浙江大学技术学院）
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）；LRI（计算机研究实验室）；Université Paris Sud（巴黎第十一大学）
Motivated by applications in energy management, this paper presents the Multi-Armed Risk-Aware Bandit (MARAB) algorithm. With the goal of limiting the exploration of risky arms, MARAB takes as arm quality its conditional value at risk. When the user-supplied risk level goes to 0, the arm quality tends toward the essential infimum of the arm distribution density, and MARAB tends toward the MIN multi-armed bandit algorithm, aimed at the arm with maximal minimal value. As a first contribution, this paper presents a theoretical analysis of the MIN algorithm under mild assumptions, establishing its…
Federal Center for Technological Education Celso Suckow da Fonseca (CEFET-RJ)（塞尔索·苏科·达·丰塞卡联邦技术教育中心（里约热内卢联邦技术教育中心））
A popular computer puzzle, the game of Minesweeper requires its human players to have a mix of both luck and strategy to succeed. Analyzing these aspects more formally, in our research we assessed the feasibility of a novel methodology based on Reinforcement Learning as an adequate approach to tackle the problem presented by this game. For this purpose we employed Multi-Armed Bandit algorithms which were carefully adapted in order to enable their use to define autonomous computational players, targeting to make the best use of some game peculiarities. After experimental evaluation, results sho…
Online learning algorithms, widely used to power search and content optimization on the web, must balance exploration and exploitation, potentially sacrificing the experience of current users for information that will lead to better decisions in the future. Recently, concerns have been raised about whether the process of exploration could be viewed as unfair, placing too much burden on certain individuals or groups. Motivated by these concerns, we initiate the study of the externalities of exploration - the undesirable side effects that the presence of one party may impose on another - under t…
Singapore University of Technology and Design（新加坡科技设计大学）；University of Oxford（牛津大学）
The interplay between exploration and exploitation in competitive multi-agent learning is still far from being well understood. Motivated by this, we study smooth Q-learning, a prototypical learning model that explicitly captures the balance between game rewards and exploration costs. We show that Q-learning always converges to the unique quantal-response equilibrium (QRE), the standard solution concept for games under bounded rationality, in weighted zero-sum polymatrix games with heterogeneous learning agents using positive exploration rates. Complementing recent results about convergence in…
School of Mathematics, University of Edinburgh（爱丁堡大学数学学院）；Alan Turing Institute（艾伦·图灵研究所）；Department of Statistics, London School of Economics and Political Science（伦敦政治经济学院统计系）
We develop a probabilistic framework for analysing model-based reinforcement learning in the episodic setting. We then apply it to study finite-time horizon stochastic control problems with linear dynamics but unknown coefficients and convex, but possibly irregular, objective function. Using probabilistic representations, we study regularity of the associated cost functions and establish precise estimates for the performance gap between applying optimal feedback control derived from estimated and true model parameters. We identify conditions under which this performance gap is quadratic, impro…
Exploration-Exploitation Tradeoff in Universal Lossy Compression
Viterbi Faculty of Electrical and Computer Engineering, Technion – Israel Institute of Technology（维特比电气工程与计算机科学学院，技术学院–以色列理工学院）；Department of Electrical Engineering-Systems, Tel Aviv University（电气工程-系统系，特拉维夫大学）
Technion（以色列理工学院）；Microsoft Research New England（微软新英格兰研究院）
We consider a multi-armed bandit problem where the decision maker can explore and exploit different arms at every round. The exploited arm adds to the decision maker's cumulative reward (without necessarily observing the reward) while the explored arm reveals its value. We devise algorithms for this setup and show that the dependence on the number of arms, k, can be much better than the standard square root of k dependence, depending on the behavior of the arms' reward sequences. For the important case of piecewise stationary stochastic bandits, we show a significant improvement over existing …
Columbia University（哥伦比亚大学）；Stanford University（斯坦福大学）
In a multi-armed bandit (MAB) problem a gambler needs to choose at each round of play one of K arms, each characterized by an unknown reward distribution. Reward realizations are only observed when an arm is selected, and the gambler's objective is to maximize his cumulative expected earnings over some given horizon of play T. To do this, the gambler needs to acquire information about arms (exploration) while simultaneously optimizing immediate rewards (exploitation); the price paid due to this trade off is often referred to as the regret, and the main question is how small can this price be a…
The exploration/exploitation (E/E) dilemma arises naturally in many subfields of Science. Multi-armed bandit problems formalize this dilemma in its canonical form. Most current research in this field focuses on generic solutions that can be applied to a wide range of problems. However, in practice, it is often the case that a form of prior information is available about the specific class of target problems. Prior knowledge is rarely used in current solutions due to the lack of a systematic approach to incorporate it into the E/E strategy. To address a specific class of E/E problems, we propos…
Exploration bonus derived from the novelty of the states in an environment has become a popular approach to motivate exploration for deep reinforcement learning agents in the past few years. Recent methods such as curiosity-driven exploration usually estimate the novelty of new observations by the prediction errors of their system dynamics models. Due to the capacity limitation of the models and difficulty of performing next-frame prediction, however, these methods typically fail to balance between exploration and exploitation in high-dimensional observation tasks, resulting in the agents forg…
Department of Electrical-Engineering, Technion Institute of Technology, Israel（电气工程系，技术学院技术研究所，以色列）；Nvidia Research（Nvidia研究）；Technion (currently at Google Research)（技术学院（目前在谷歌研究））
Semantic-Space Exploration and Exploitation in RLVR for LLM Reasoning
Tsinghua Shenzhen International Graduate School, Tsinghua University（清华大学深圳国际研究生院，清华大学）；University of California, Los Angeles（加州大学洛杉矶分校）；Shenzhen Technology University（深圳技术大学）
HTPO: Towards Exploration-Exploitation Balanced Policy Optimization via Hierarchical Token-level Objective Control
School of Information Science and Electronic Engineering, Shanghai Jiao Tong University（上海交通大学信息科学与电子工程学院）；Xiaohongshu Inc.（小红书公司）；MoE Key Lab of Artificial Intelligence, AI Institute, Shanghai Jiao Tong University（上海交通大学人工智能研究院）
From Exploration to Exploitation: A Two-Stage Entropy RLVR Approach for Noise-Tolerant MLLM Training
Independent Researcher（独立研究者）；The Chinese University of Hong Kong（香港中文大学）；City University of Hong Kong（香港城市大学）；Hong Kong University of Science and Technology（香港科技大学）；University of Hong Kong（香港大学）
