Ensemble Value Functions for Efficient Exploration in Multi-Agent Reinforcement Learning
University of Edinburgh（爱丁堡大学）；University College London（伦敦大学学院）；Carnegie Mellon University（卡内基梅隆大学）；King’s College London（伦敦国王学院）；Queen Mary University London（伦敦玛丽女王大学）；Microsoft Research Cambridge（微软研究院剑桥分部）
Lukas Schäfer, Oliver Slumbers, Stephen McAleer, Yali Du, Stefano V. Albrecht, David Mguni
备注：
Published at 24th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2025)
Multi-agent reinforcement learning (MARL) requires agents to explore within a vast joint action space to find joint actions that lead to coordination. Existing value-based MARL algorithms commonly rely on random exploration, such as $ε$-greedy, to explore the environment which is not systematic and inefficient at identifying effective actions in multi-agent problems. Additionally, the concurrent training of the policies of multiple agents during training can render the optimisation non-stationary. This can lead to unstable value estimates, highly variant gradients, and ultimately hinder coordination between agents. To address these challenges, we propose ensemble value functions for multi-agent exploration (EMAX). EMAX is a framework to seamlessly extend value-based MARL algorithms. EMAX leverages an ensemble of value functions for each agent to guide their exploration, reduce the variance of their optimisation, and makes their policies more robust to miscoordination. EMAX achieves these benefits by (1) systematically guiding the exploration of agents with a UCB policy towards parts of the environment that require multiple agents to coordinate. (2) EMAX computes average value estimates across the ensemble as target values to reduce the variance of gradients and make optimisation more stable. (3) During evaluation, EMAX selects actions following a majority vote across the ensemble to reduce the likelihood of miscoordination. We first instantiate independent DQN with EMAX and evaluate it in 11 general-sum tasks with sparse rewards. We show that EMAX improves final evaluation returns by 185% across all tasks. We then evaluate EMAX on top of IDQN, VDN and QMIX in 21 common-reward tasks, and show that EMAX improves sample efficiency and final evaluation returns across all tasks over all three vanilla algorithms by 60%, 47%, and 538%, respectively.
The multi-agent setting is intricate and unpredictable since the behaviors of multiple agents influence one another. To address this environmental uncertainty, distributional reinforcement learning algorithms that incorporate uncertainty via distributional output have been integrated with multi-agent reinforcement learning (MARL) methods, achieving state-of-the-art performance. However, distributional MARL algorithms still rely on the traditional $ε$-greedy, which does not take cooperative strategy into account. In this paper, we present a risk-based exploration that leads to collaboratively o…
Optimistic ε-Greedy Exploration for Cooperative Multi-Agent Reinforcement Learning
University of Electronic Science and Technology of China（电子科技大学）；Southwest Minzu University（西南民族大学）；Chengdu University of Technology（成都理工大学）；Nanyang Technological University（南洋理工大学）
McGill University（麦吉尔大学）；University of Amsterdam（阿姆斯特丹大学）
Exploration is an essential component of reinforcement learning algorithms, where agents need to learn how to predict and control unknown and often stochastic environments. Reinforcement learning agents depend crucially on exploration to obtain informative data for the learning process as the lack of enough information could hinder effective learning. In this article, we provide a survey of modern exploration methods in (Sequential) reinforcement learning, as well as a taxonomy of exploration methods.
OpenAI；University of California, Berkeley（加州大学伯克利分校）
We show how an ensemble of $Q^*$-functions can be leveraged for more effective exploration in deep reinforcement learning. We build on well established algorithms from the bandit setting, and adapt them to the $Q$-learning setting. We propose an exploration strategy based on upper-confidence bounds (UCB). Our experiments show significant gains on the Atari benchmark.
We propose a framework based on distributional reinforcement learning and recent attempts to combine Bayesian parameter updates with deep reinforcement learning. We show that our proposed framework conceptually unifies multiple previous methods in exploration. We also derive a practical algorithm that achieves efficient exploration on challenging control tasks.
Ulsan National Institute of Science and Technology（蔚山国立科学技术院）；OpenAI LP（OpenAI有限合伙公司）
This paper reviews exploration techniques in deep reinforcement learning. Exploration techniques are of primary importance when solving sparse reward problems. In sparse reward problems, the reward is rare, which means that the agent will not find the reward often by acting randomly. In such a scenario, it is challenging for reinforcement learning to learn rewards and actions association. Thus more sophisticated exploration methods need to be devised. This review provides a comprehensive overview of existing exploration approaches, which are categorized based on the key contributions as follow…
Sufficient exploration is paramount for the success of a reinforcement learning agent. Yet, exploration is rarely assessed in an algorithm-independent way. We compare the behavior of three data-based, offline exploration metrics described in the literature on intuitive simple distributions and highlight problems to be aware of when using them. We propose a fourth metric,uniform relative entropy, and implement it using either a k-nearest-neighbor or a nearest-neighbor-ratio estimator, highlighting that the implementation choices have a profound impact on these measures.
Department of Mathematics, Linn us University, 351 95 Växjö, Sweden
It is well known that ensemble methods often provide enhanced performance in reinforcement learning. In this paper, we explore this concept further by using group-aided training within the distributional reinforcement learning paradigm. Specifically, we propose an extension to categorical reinforcement learning, where distributional learning targets are implicitly based on the total information gathered by an ensemble. We empirically show that this may lead to much more robust initial learning, a stronger individual performance level, and good efficiency on a per-sample basis.
Multi-agent reinforcement learning (MARL) can model many real world applications. However, many MARL approaches rely on epsilon greedy for exploration, which may discourage visiting advantageous states in hard scenarios. In this paper, we propose a new approach QMIX(SEG) for tackling MARL. It makes use of the value function factorization method QMIX to train per-agent policies and a novel Semantic Epsilon Greedy (SEG) exploration strategy. SEG is a simple extension to the conventional epsilon greedy exploration strategy, yet it is experimentally shown to greatly improve the performance of MARL…
Korea University of Technology and Education（韩国技术教育大学）
Efficient exploration strategy is one of essential issues in cooperative multi-agent reinforcement learning (MARL) algorithms requiring complex coordination. In this study, we introduce a new exploration method with the strangeness that can be easily incorporated into any centralized training and decentralized execution (CTDE)-based MARL algorithms. The strangeness refers to the degree of unfamiliarity of the observations that an agent visits. In order to give the observation strangeness a global perspective, it is also augmented with the the degree of unfamiliarity of the visited entire state…
TU Delft（代尔夫特理工大学）；Microsoft Research NYC（微软研究院纽约）；Microsoft Research Cambridge（微软研究院剑桥）
High sample complexity remains a barrier to the application of reinforcement learning (RL), particularly in multi-agent systems. A large body of work has demonstrated that exploration mechanisms based on the principle of optimism under uncertainty can significantly improve the sample efficiency of RL in single agent tasks. This work seeks to understand the role of optimistic exploration in non-cooperative multi-agent settings. We will show that, in zero-sum games, optimistic exploration can cause the learner to waste time sampling parts of the state space that are irrelevant to strategic play,…
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…
KAIST（韩国科学技术院）；Kim Jaechul Graduate School of Artificial Intelligence（金在澈人工智能研究生院）
Distributional reinforcement learning demonstrates state-of-the-art performance in continuous and discrete control settings with the features of variance and risk, which can be used to explore. However, the exploration method employing the risk property is hard to find, although numerous exploration methods in Distributional RL employ the variance of return distribution per action. In this paper, we present risk scheduling approaches that explore risk levels and optimistic behaviors from a risk perspective. We demonstrate the performance enhancement of the DMIX algorithm using risk scheduling …
Exploration in environments with continuous control and sparse rewards remains a key challenge in reinforcement learning (RL). Recently, surprise has been used as an intrinsic reward that encourages systematic and efficient exploration. We introduce a new definition of surprise and its RL implementation named Variational Assorted Surprise Exploration (VASE). VASE uses a Bayesian neural network as a model of the environment dynamics and is trained using variational inference, alternately updating the accuracy of the agent's model and policy. Our experiments show that in continuous control spars…
Stanford University（斯坦福大学）；University of Pennsylvania（宾夕法尼亚大学）
A key challenge to deploying reinforcement learning in practice is avoiding excessive (harmful) exploration in individual episodes. We propose a natural constraint on exploration -- \textit{uniformly} outperforming a conservative policy (adaptively estimated from all data observed thus far), up to a per-episode exploration budget. We design a novel algorithm that uses a UCB reinforcement learning policy for exploration, but overrides it as needed to satisfy our exploration constraint with high probability. Importantly, to ensure unbiased exploration across the state space, our algorithm adapti…
Sparse-reward domains are challenging for reinforcement learning algorithms since significant exploration is needed before encountering reward for the first time. Hierarchical reinforcement learning can facilitate exploration by reducing the number of decisions necessary before obtaining a reward. In this paper, we present a novel hierarchical reinforcement learning framework based on the compression of an invariant state space that is common to a range of tasks. The algorithm introduces subtasks which consist of moving between the state partitions induced by the compression. Results indicate …
Recently deep reinforcement learning (DRL) has achieved outstanding success on solving many difficult and large-scale RL problems. However the high sample cost required for effective learning often makes DRL unaffordable in resource-limited applications. With the aim of improving sample efficiency and learning performance, we will develop a new DRL algorithm in this paper that seamless integrates entropy-induced and bootstrap-induced techniques for efficient and deep exploration of the learning environment. Specifically, a general form of Tsallis entropy regularizer will be utilized to drive e…
Equipping artificial agents with useful exploration mechanisms remains a challenge to this day. Humans, on the other hand, seem to manage the trade-off between exploration and exploitation effortlessly. In the present article, we put forward the hypothesis that they accomplish this by making optimal use of limited computational resources. We study this hypothesis by meta-learning reinforcement learning algorithms that sacrifice performance for a shorter description length (defined as the number of bits required to implement the given algorithm). The emerging class of models captures human expl…
We study an exploration method for model-free RL that generalizes the counter-based exploration bonus methods and takes into account long term exploratory value of actions rather than a single step look-ahead. We propose a model-free RL method that modifies Delayed Q-learning and utilizes the long-term exploration bonus with provable efficiency. We show that our proposed method finds a near-optimal policy in polynomial time (PAC-MDP), and also provide experimental evidence that our proposed algorithm is an efficient exploration method.
Tianjin University（天津大学）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）；Harbin Institute of Technology（哈尔滨工业大学）；Northwestern Polytechnical University（西北工业大学）
Deep Reinforcement Learning (DRL) and Deep Multi-agent Reinforcement Learning (MARL) have achieved significant successes across a wide range of domains, including game AI, autonomous vehicles, robotics, and so on. However, DRL and deep MARL agents are widely known to be sample inefficient that millions of interactions are usually needed even for relatively simple problem settings, thus preventing the wide application and deployment in real-industry scenarios. One bottleneck challenge behind is the well-known exploration problem, i.e., how efficiently exploring the environment and collecting in…
MIT（麻省理工学院）；UC Berkeley（加州大学伯克利分校）；Microsoft Research NYC（微软研究院纽约分院）
How do you incentivize self-interested agents to $\textit{explore}$ when they prefer to $\textit{exploit}$? We consider complex exploration problems, where each agent faces the same (but unknown) MDP. In contrast with traditional formulations of reinforcement learning, agents control the choice of policies, whereas an algorithm can only issue recommendations. However, the algorithm controls the flow of information, and can incentivize the agents to explore via information asymmetry. We design an algorithm which explores all reachable states in the MDP. We achieve provable guarantees similar to…
Exploration efficiency is a challenging problem in multi-agent reinforcement learning (MARL), as the policy learned by confederate MARL depends on the collaborative approach among multiple agents. Another important problem is the less informative reward restricts the learning speed of MARL compared with the informative label in supervised learning. In this work, we leverage on a novel communication method to guide MARL to accelerate exploration and propose a predictive network to forecast the reward of current state-action pair and use the guidance learned by the predictive network to modify t…
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…
The exploration--exploitation trade-off in reinforcement learning (RL) is a well-known and much-studied problem that balances greedy action selection with novel experience, and the study of exploration methods is usually only considered in the context of learning the optimal policy for a single learning task. However, in the context of online task transfer, where there is a change to the task during online operation, we hypothesize that exploration strategies that anticipate the need to adapt to future tasks can have a pronounced impact on the efficiency of transfer. As such, we re-examine the…
Imperial College London（伦敦帝国理工学院）；ETH Zurich（苏黎世联邦理工学院）
Efficient exploration remains a major challenge for reinforcement learning. One reason is that the variability of the returns often depends on the current state and action, and is therefore heteroscedastic. Classical exploration strategies such as upper confidence bound algorithms and Thompson sampling fail to appropriately account for heteroscedasticity, even in the bandit setting. Motivated by recent findings that address this issue in bandits, we propose to use Information-Directed Sampling (IDS) for exploration in reinforcement learning. As our main contribution, we build on recent advance…
Efficient exploration is a crucial challenge in deep reinforcement learning. Several methods, such as behavioral priors, are able to leverage offline data in order to efficiently accelerate reinforcement learning on complex tasks. However, if the task at hand deviates excessively from the demonstrated task, the effectiveness of such methods is limited. In our work, we propose to learn features from offline data that are shared by a more diverse range of tasks, such as correlation between actions and directedness. Therefore, we introduce state-free priors, which directly model temporal consiste…
Heterogeneous ensembles that can aggregate an unrestricted number and variety of base predictors can effectively address challenging prediction problems. In particular, accurate ensembles that are also parsimonious, i.e., consist of as few base predictors as possible, can help reveal potentially useful knowledge about the target problem domain. Although ensemble selection offers a potential approach to achieving these goals, the currently available algorithms are limited in their abilities. In this paper, we present several algorithms that incorporate ensemble diversity into a reinforcement le…
The Exploration-Exploitation tradeoff arises in Reinforcement Learning when one cannot tell if a policy is optimal. Then, there is a constant need to explore new actions instead of exploiting past experience. In practice, it is common to resolve the tradeoff by using a fixed exploration mechanism, such as $ε$-greedy exploration or by adding Gaussian noise, while still trying to learn an optimal policy. In this work, we take a different approach and study exploration-conscious criteria, that result in optimal policies with respect to the exploration mechanism. Solving these criteria, as we esta…
Model-based Reinforcement Learning (RL) is a popular learning paradigm due to its potential sample efficiency compared to model-free RL. However, existing empirical model-based RL approaches lack the ability to explore. This work studies a computationally and statistically efficient model-based algorithm for both Kernelized Nonlinear Regulators (KNR) and linear Markov Decision Processes (MDPs). For both models, our algorithm guarantees polynomial sample complexity and only uses access to a planning oracle. Experimentally, we first demonstrate the flexibility and efficacy of our algorithm on a …
Indian Institute of Technology Madras（印度理工学院马德拉斯分校）
Exploration in multi-task reinforcement learning is critical in training agents to deduce the underlying MDP. Many of the existing exploration frameworks such as $E^3$, $R_{max}$, Thompson sampling assume a single stationary MDP and are not suitable for system identification in the multi-task setting. We present a novel method to facilitate exploration in multi-task reinforcement learning using deep generative models. We supplement our method with a low dimensional energy model to learn the underlying MDP distribution and provide a resilient and adaptive exploration signal to the agent. We eva…
We propose a model-based lifelong reinforcement-learning approach that estimates a hierarchical Bayesian posterior distilling the common structure shared across different tasks. The learned posterior combined with a sample-based Bayesian exploration procedure increases the sample efficiency of learning across a family of related tasks. We first derive an analysis of the relationship between the sample complexity and the initialization quality of the posterior in the finite MDP setting. We next scale the approach to continuous-state domains by introducing a Variational Bayesian Lifelong Reinfor…
The Hong Kong Polytechnic University（香港理工大学）；Eastern Institute for Advanced Study（东方高等研究院）
Exploration is critical for deep reinforcement learning in complex environments with high-dimensional observations and sparse rewards. To address this problem, recent approaches proposed to leverage intrinsic rewards to improve exploration, such as novelty-based exploration and prediction-based exploration. However, many intrinsic reward modules require sophisticated structures and representation learning, resulting in prohibitive computational complexity and unstable performance. In this paper, we propose Rewarding Episodic Visitation Discrepancy (REVD), a computation-efficient and quantified…
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…
University of Geneva（日内瓦大学）；Google Research（谷歌研究院）；Univ. Lorraine（洛林大学）；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）；Univ. Lille（里尔大学）
Offline Reinforcement Learning (RL) aims at learning an optimal control from a fixed dataset, without interactions with the system. An agent in this setting should avoid selecting actions whose consequences cannot be predicted from the data. This is the converse of exploration in RL, which favors such actions. We thus take inspiration from the literature on bonus-based exploration to design a new offline RL agent. The core idea is to subtract a prediction-based exploration bonus from the reward, instead of adding it for exploration. This allows the policy to stay close to the support of the da…
College of Information and Computer Sciences（信息与计算机科学学院）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）
In this paper we consider the problem of how a reinforcement learning agent that is tasked with solving a sequence of reinforcement learning problems (a sequence of Markov decision processes) can use knowledge acquired early in its lifetime to improve its ability to solve new problems. We argue that previous experience with similar problems can provide an agent with information about how it should explore when facing a new but related problem. We show that the search for an optimal exploration strategy can be formulated as a reinforcement learning problem itself and demonstrate that such strat…
Improving sample efficiency is a key challenge in reinforcement learning, especially in environments with large state spaces and sparse rewards. In literature, this is resolved either through the use of auxiliary tasks (subgoals) or through clever exploration strategies. Exploration methods have been used to sample better trajectories in large environments while auxiliary tasks have been incorporated where the reward is sparse. However, few studies have attempted to tackle both large scale and reward sparsity at the same time. This paper explores the idea of combining exploration with auxiliar…
Recent advances of gradient temporal-difference methods allow to learn off-policy multiple value functions in parallel with- out sacrificing convergence guarantees or computational efficiency. This opens up new possibilities for sound ensemble techniques in reinforcement learning. In this work we propose learning an ensemble of policies related through potential-based shaping rewards. The ensemble induces a combination policy by using a voting mechanism on its components. Learning happens in real time, and we empirically show the combination policy to outperform the individual policies of the …
Efficient exploration for automatic subgoal discovery is a challenging problem in Hierarchical Reinforcement Learning (HRL). In this paper, we show that intrinsic motivation learning increases the efficiency of exploration, leading to successful subgoal discovery. We introduce a model-free subgoal discovery method based on unsupervised learning over a limited memory of agent's experiences during intrinsic motivation. Additionally, we offer a unified approach to learning representations in model-free HRL.
Rutgers University（罗格斯大学）；Massachusetts Institute of Technology（麻省理工学院）
We present a modular approach to reinforcement learning that uses a Bayesian representation of the uncertainty over models. The approach, BOSS (Best of Sampled Set), drives exploration by sampling multiple models from the posterior and selecting actions optimistically. It extends previous work by providing a rule for deciding when to resample and how to combine the models. We show that our algorithm achieves nearoptimal reward with high probability with a sample complexity that is low relative to the speed at which the posterior distribution converges during learning. We demonstrate that BOSS …
We propose to use boosted regression trees as a way to compute human-interpretable solutions to reinforcement learning problems. Boosting combines several regression trees to improve their accuracy without significantly reducing their inherent interpretability. Prior work has focused independently on reinforcement learning and on interpretable machine learning, but there has been little progress in interpretable reinforcement learning. Our experimental results show that boosted regression trees compute solutions that are both interpretable and match the quality of leading reinforcement learnin…
Deep reinforcement learning algorithms have been shown to learn complex tasks using highly general policy classes. However, sparse reward problems remain a significant challenge. Exploration methods based on novelty detection have been particularly successful in such settings but typically require generative or predictive models of the observations, which can be difficult to train when the observations are very high-dimensional and complex, as in the case of raw images. We propose a novelty detection algorithm for exploration that is based entirely on discriminatively trained exemplar models, …
Balancing exploration and exploitation remains a key challenge in reinforcement learning (RL). State-of-the-art RL algorithms suffer from high sample complexity, particularly in the sparse reward case, where they can do no better than to explore in all directions until the first positive rewards are found. To mitigate this, we propose Rapidly Randomly-exploring Reinforcement Learning (R3L). We formulate exploration as a search problem and leverage widely-used planning algorithms such as Rapidly-exploring Random Tree (RRT) to find initial solutions. These solutions are used as demonstrations to…
Constrained Ensemble Exploration for Unsupervised Skill Discovery
Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）；Shenzhen Research Institute of Northwestern Polytechnical University（西北工业大学深圳研究院）；Hong Kong University of Science and Technology（香港科技大学）；Tencent（腾讯）；East China University of Science and Technology（华东理工大学）；The Institute of Artificial Intelligence (TeleAI), China Telecom（中国电信人工智能研究院（TeleAI））
Institute of Intelligent Systems and Robotics（智能系统与机器人研究所）；Sorbonne Universités（索邦大学）；UPMC Univ Paris 06（巴黎第六大学）；CNRS（法国国家科学研究中心）；National Technical University of Athens（雅典国家技术大学）
Online model-free reinforcement learning (RL) methods with continuous actions are playing a prominent role when dealing with real-world applications such as Robotics. However, when confronted to non-stationary environments, these methods crucially rely on an exploration-exploitation trade-off which is rarely dynamically and automatically adjusted to changes in the environment. Here we propose an active exploration algorithm for RL in structured (parameterized) continuous action space. This framework deals with a set of discrete actions, each of which is parameterized with continuous variables.…
University of Cambridge（剑桥大学）；Alan Turing Institute（艾伦·图灵研究所）；University College London（伦敦大学学院）
The use of ensembles of neural networks (NNs) for the quantification of predictive uncertainty is widespread. However, the current justification is intuitive rather than analytical. This work proposes one minor modification to the normal ensembling methodology, which we prove allows the ensemble to perform Bayesian inference, hence converging to the corresponding Gaussian Process as both the total number of NNs, and the size of each, tend to infinity. This working paper provides early-stage results in a reinforcement learning setting, analysing the practicality of the technique for an ensemble…
