We show that in a cooperative $N$-agent network, one can design locally executable policies for the agents such that the resulting discounted sum of average rewards (value) well approximates the optimal value computed over all (including non-local) policies. Specifically, we prove that, if $|\mathcal{X}|, |\mathcal{U}|$ denote the size of state, and action spaces of individual agents, then for sufficiently small discount factor, the approximation error is given by $\mathcal{O}(e)$ where $e\triangleq \frac{1}{\sqrt{N}}\left[\sqrt{|\mathcal{X}|}+\sqrt{|\mathcal{U}|}\right]$. Moreover, in a special case where the reward and state transition functions are independent of the action distribution of the population, the error improves to $\mathcal{O}(e)$ where $e\triangleq \frac{1}{\sqrt{N}}\sqrt{|\mathcal{X}|}$. Finally, we also devise an algorithm to explicitly construct a local policy. With the help of our approximation results, we further establish that the constructed local policy is within $\mathcal{O}(\max\{e,ε\})$ distance of the optimal policy, and the sample complexity to achieve such a local policy is $\mathcal{O}(ε^{-3})$, for any $ε>0$.
Queensland University of Technology (QUT)（昆士兰科技大学）
This paper proposes the Cooperative Soft Actor Critic (CSAC) method of enabling consecutive reinforcement learning agents to cooperatively solve a long time horizon multi-stage task. This method is achieved by modifying the policy of each agent to maximise both the current and next agent's critic. Cooperatively maximising each agent's critic allows each agent to take actions that are beneficial for its task as well as subsequent tasks. Using this method in a multi-room maze domain, the cooperative policies were able to outperform both uncooperative policies as well as a single agent trained ac…
Queensland University of Technology（昆士兰科技大学）；Queensland Centre of Robotics（昆士兰机器人中心）
Many hierarchical reinforcement learning algorithms utilise a series of independent skills as a basis to solve tasks at a higher level of reasoning. These algorithms don't consider the value of using skills that are cooperative instead of independent. This paper proposes the Cooperative Consecutive Policies (CCP) method of enabling consecutive agents to cooperatively solve long time horizon multi-stage tasks. This method is achieved by modifying the policy of each agent to maximise both the current and next agent's critic. Cooperatively maximising critics allows each agent to take actions that…
School of Computer Science and Engineering, Nanyang Technological University（南洋理工大学计算机科学与工程学院）；Department of Computer Science and Engineering, Hong Kong University of Science and Technology（香港科技大学计算机科学与工程学系）
Current value-based multi-agent reinforcement learning methods optimize individual Q values to guide individuals' behaviours via centralized training with decentralized execution (CTDE). However, such expected, i.e., risk-neutral, Q value is not sufficient even with CTDE due to the randomness of rewards and the uncertainty in environments, which causes the failure of these methods to train coordinating agents in complex environments. To address these issues, we propose RMIX, a novel cooperative MARL method with the Conditional Value at Risk (CVaR) measure over the learned distributions of indi…
Towards Global Optimality in Cooperative MARL with the Transformation And Distillation Framework
Washington University in St. Louis（华盛顿大学圣路易斯分校）；Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院）；Department of Computer Science and Technology, Tsinghua University（清华大学计算机科学与技术系）
Helsinki Institute for Information Technology HIIT（赫尔辛基信息技术研究所（HIIT））；Aalto University（阿尔托大学）；Bitville Oy（比特维尔公司）；University of Manchester（曼彻斯特大学）
The cooperation among AI systems, and between AI systems and humans is becoming increasingly important. In various real-world tasks, an agent needs to cooperate with unknown partner agent types. This requires the agent to assess the behaviour of the partner agent during a cooperative task and to adjust its own policy to support the cooperation. Deep reinforcement learning models can be trained to deliver the required functionality but are known to suffer from sample inefficiency and slow learning. However, adapting to a partner agent behaviour during the ongoing task requires ability to assess…
École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
We address the challenge of learning factored policies in cooperative MARL scenarios. In particular, we consider the situation in which a team of agents collaborates to optimize a common cost. The goal is to obtain factored policies that determine the individual behavior of each agent so that the resulting joint policy is optimal. The main contribution of this work is the introduction of Logical Team Q-learning (LTQL). LTQL does not rely on assumptions about the environment and hence is generally applicable to any collaborative MARL scenario. We derive LTQL as a stochastic approximation to a d…
UM-SJTU Joint Institute, Shanghai Jiao Tong University（上海交通大学密西根学院）；Shanghai Jiao Tong University（上海交通大学）
We consider the problem of learning fair policies in (deep) cooperative multi-agent reinforcement learning (MARL). We formalize it in a principled way as the problem of optimizing a welfare function that explicitly encodes two important aspects of fairness: efficiency and equity. As a solution method, we propose a novel neural network architecture, which is composed of two sub-networks specifically designed for taking into account the two aspects of fairness. In experiments, we demonstrate the importance of the two sub-networks for fair optimization. Our overall approach is general as it can a…
We explore a collaborative and cooperative multi-agent reinforcement learning setting where a team of reinforcement learning agents attempt to solve a single cooperative task in a multi-scenario setting. We propose a novel multi-agent reinforcement learning algorithm inspired by universal value function approximators that not only generalizes over state space but also over a set of different scenarios. Additionally, to prove our claim, we are introducing a challenging 2D multi-agent urban security environment where the learning agents are trying to protect a person from nearby bystanders in a …
Finding different solutions to the same problem is a key aspect of intelligence associated with creativity and adaptation to novel situations. In reinforcement learning, a set of diverse policies can be useful for exploration, transfer, hierarchy, and robustness. We propose DOMiNO, a method for Diversity Optimization Maintaining Near Optimality. We formalize the problem as a Constrained Markov Decision Process where the objective is to find diverse policies, measured by the distance between the state occupancies of the policies in the set, while remaining near-optimal with respect to the extri…
Smart modular freight containers -- as propagated in the Physical Internet paradigm -- are equipped with sensors, data storage capability and intelligence that enable them to route themselves from origin to destination without manual intervention or central governance. In this self-organizing setting, containers can autonomously place bids on transport services in a spot market setting. However, for individual containers it may be difficult to learn good bidding policies due to limited observations. By sharing information and costs between one another, smart containers can jointly learn biddin…
We explore deep reinforcement learning methods for multi-agent domains. We begin by analyzing the difficulty of traditional algorithms in the multi-agent case: Q-learning is challenged by an inherent non-stationarity of the environment, while policy gradient suffers from a variance that increases as the number of agents grows. We then present an adaptation of actor-critic methods that considers action policies of other agents and is able to successfully learn policies that require complex multi-agent coordination. Additionally, we introduce a training regimen utilizing an ensemble of policies …
Restless bandits are an important class of problems with applications in recommender systems, active learning, revenue management and other areas. We consider infinite-horizon discounted restless bandits with many arms where a fixed proportion of arms may be pulled in each period and where arms share a finite state space. Although an average-case-optimal policy can be computed via stochastic dynamic programming, the computation required grows exponentially with the number of arms $N$. Thus, it is important to find scalable policies that can be computed efficiently for large $N$ and that are ne…
University of Michigan（密歇根大学）；Queen’s University（女王大学）
In this paper, for POMDPs, we provide the convergence of a Q learning algorithm for control policies using a finite history of past observations and control actions, and, consequentially, we establish near optimality of such limit Q functions under explicit filter stability conditions. We present explicit error bounds relating the approximation error to the length of the finite history window. We establish the convergence of such Q-learning iterations under mild ergodicity assumptions on the state process during the exploration phase. We further show that the limit fixed point equation gives a…
One of the preeminent obstacles to scaling multi-agent reinforcement learning to large numbers of agents is assigning credit to individual agents' actions. In this paper, we address this credit assignment problem with an approach that we call \textit{partial reward decoupling} (PRD), which attempts to decompose large cooperative multi-agent RL problems into decoupled subproblems involving subsets of agents, thereby simplifying credit assignment. We empirically demonstrate that decomposing the RL problem using PRD in an actor-critic algorithm results in lower variance policy gradient estimates,…
Enhancing Cooperative Multi-Agent Reinforcement Learning with State Modelling and Adversarial Exploration
School of Electrical；Archimedes, Athena Research Center, Greece；Department of Mathematics, ETH Zurich；Dept. of Mechanical Engineering \& Materials Science, Duke University；Dept. of Digital Systems, University of Piraeus, Greece
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；University of Tubingen（蒂宾根大学）
The deep reinforcement learning (DRL) algorithm works brilliantly on solving various complex control tasks. This phenomenal success can be partly attributed to DRL encouraging intelligent agents to sufficiently explore the environment and collect diverse experiences during the agent training process. Therefore, exploration plays a significant role in accessing an optimal policy for DRL. Despite recent works making great progress in continuous control tasks, exploration in these tasks has remained insufficiently investigated. To explicitly encourage exploration in continuous control tasks, we p…
We consider finite-horizon restless bandits with multiple pulls per period, which play an important role in recommender systems, active learning, revenue management, and many other areas. While an optimal policy can be computed, in principle, using dynamic programming, the computation required scales exponentially in the number of arms $N$. Thus, there is substantial value in understanding the performance of index policies and other policies that can be computed efficiently for large $N$. We study the growth of the optimality gap, i.e., the loss in expected performance compared to an optimal p…
In the theory of Partially Observed Markov Decision Processes (POMDPs), existence of optimal policies have in general been established via converting the original partially observed stochastic control problem to a fully observed one on the belief space, leading to a belief-MDP. However, computing an optimal policy for this fully observed model, and so for the original POMDP, using classical dynamic or linear programming methods is challenging even if the original system has finite state and action spaces, since the state space of the fully observed belief-MDP model is always uncountable. Furth…
N-discount optimality was introduced as a hierarchical form of policy- and value-function optimality, with Blackwell optimality lying at the top level of the hierarchy Veinott (1969); Blackwell (1962). We formalize notions of myopic discount factors, value functions and policies in terms of Blackwell optimality in MDPs, and we provide a novel concept of regret, called Blackwell regret, which measures the regret compared to a Blackwell optimal policy. Our main analysis focuses on long horizon MDPs with sparse rewards. We show that selecting the discount factor under which zero Blackwell regret …
Artificial and Natural Intelligence Toulouse Institute (ANITI)（图卢兹人工与自然智能研究所）；University of Toulouse（图卢兹大学）；ISAE-Supaero（法国高等航空航天学院）；Andalusian Research Institute in Data Science and Computational Intelligence (DaSCI)（安达卢西亚数据科学与计算智能研究所）；Research Center for Information and Communications Technologies of the University of Granada (CITIC-UGR)（格拉纳达大学信息与通信技术研究中心）；University of Granada（格拉纳达大学）
A quantitative assessment of the global importance of an agent in a team is as valuable as gold for strategists, decision-makers, and sports coaches. Yet, retrieving this information is not trivial since in a cooperative task it is hard to isolate the performance of an individual from the one of the whole team. Moreover, it is not always clear the relationship between the role of an agent and his personal attributes. In this work we conceive an application of the Shapley analysis for studying the contribution of both agent policies and attributes, putting them on equal footing. Since the compu…
Benchmarking Reinforcement Learning via Stochastic Converse Optimality: Generating Systems with Known Optimal Policies
Skolkovo Institute of Science and Technology（斯克尔科沃科学与技术研究所）；Innopolis University（因纳波利斯大学）；Technische Universität Chemnitz（化学工业大学）；Central University（中央大学）；Sirius University of Science and Technology（西里乌斯科学与技术大学）
Nara Institute of Science and Technology（奈良先端科学技术大学院大学）
In this paper, we explore a multi-agent reinforcement learning approach to address the design problem of communication and control strategies for multi-agent cooperative transport. Typical end-to-end deep neural network policies may be insufficient for covering communication and control; these methods cannot decide the timing of communication and can only work with fixed-rate communications. Therefore, our framework exploits event-triggered architecture, namely, a feedback controller that computes the communication input and a triggering mechanism that determines when the input has to be updat…
Achieving and maintaining cooperation between agents to accomplish a common objective is one of the central goals of Multi-Agent Reinforcement Learning (MARL). Nevertheless in many real-world scenarios, separately trained and specialized agents are deployed into a shared environment, or the environment requires multiple objectives to be achieved by different coexisting parties. These variations among specialties and objectives are likely to cause mixed motives that eventually result in a social dilemma where all the parties are at a loss. In order to resolve this issue, we propose the Incentiv…
Southeast University（东南大学）；Purple Mountain Laboratories（紫金山实验室）；Georgia Institute of Technology（佐治亚理工学院）
For ultra-dense networks with wireless backhaul, caching strategy at small base stations (SBSs), usually with limited storage, is critical to meet massive high data rate requests. Since the content popularity profile varies with time in an unknown way, we exploit reinforcement learning (RL) to design a cooperative caching strategy with maximum-distance separable (MDS) coding. We model the MDS coding based cooperative caching as a Markov decision process to capture the popularity dynamics and maximize the long-term expected cumulative traffic load served directly by the SBSs without accessing t…
Investigating cooperativity of interlocutors is central in studying pragmatics of dialogue. Models of conversation that only assume cooperative agents fail to explain the dynamics of strategic conversations. Thus, we investigate the ability of agents to identify non-cooperative interlocutors while completing a concurrent visual-dialogue task. Within this novel setting, we study the optimality of communication strategies for achieving this multi-task objective. We use the tools of learning theory to develop a theoretical model for identifying non-cooperative interlocutors and apply this theory …
University of Oxford（牛津大学）；Google Research（谷歌研究院）；Harvard University（哈佛大学）
We study the problem of planning restless multi-armed bandits (RMABs) with multiple actions. This is a popular model for multi-agent systems with applications like multi-channel communication, monitoring and machine maintenance tasks, and healthcare. Whittle index policies, which are based on Lagrangian relaxations, are widely used in these settings due to their simplicity and near-optimality under certain conditions. In this work, we first show that Whittle index policies can fail in simple and practically relevant RMAB settings, even when the RMABs are indexable. We discuss why the optimalit…
The growing demand on high-quality and low-latency multimedia services has led to much interest in edge caching techniques. Motivated by this, we in this paper consider edge caching at the base stations with unknown content popularity distributions. To solve the dynamic control problem of making caching decisions, we propose a deep actor-critic reinforcement learning based multi-agent framework with the aim to minimize the overall average transmission delay. To evaluate the proposed framework, we compare the learning-based performance with three other caching policies, namely least recently us…
Most previous studies on multi-agent reinforcement learning focus on deriving decentralized and cooperative policies to maximize a common reward and rarely consider the transferability of trained policies to new tasks. This prevents such policies from being applied to more complex multi-agent tasks. To resolve these limitations, we propose a model that conducts both representation learning for multiple agents using hierarchical graph attention network and policy learning using multi-agent actor-critic. The hierarchical graph attention network is specially designed to model the hierarchical rel…
Robustifying a Policy in Multi-Agent RL with Diverse Cooperative Behaviors and Adversarial Style Sampling for Assistive Tasks
Graduate School of Information Science and Technology, the University of Tokyo（东京大学信息科学与技术研究生院）；RIKEN Center for Advanced Intelligence Project (AIP)（理化学研究所先进智能项目中心）
We consider a new form of reinforcement learning (RL) that is based on opportunities to directly learn the optimal control policy and a general Markov decision process (MDP) framework devised to support these opportunities. Derivations of general classes of our control-based RL methods are presented, together with forms of exploration and exploitation in learning and applying the optimal control policy over time. Our general MDP framework extends the classical Bellman operator and optimality criteria by generalizing the definition and scope of a policy for any given state. We establish the con…
We study fairness through the lens of cooperative multi-agent learning. Our work is motivated by empirical evidence that naive maximization of team reward yields unfair outcomes for individual team members. To address fairness in multi-agent contexts, we introduce team fairness, a group-based fairness measure for multi-agent learning. We then prove that it is possible to enforce team fairness during policy optimization by transforming the team's joint policy into an equivariant map. We refer to our multi-agent learning strategy as Fairness through Equivariance (Fair-E) and demonstrate its effe…
MIT-LIDS（麻省理工学院信息与决策系统实验室）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）；IBM Research（IBM研究院）
Collective learning can be greatly enhanced when agents effectively exchange knowledge with their peers. In particular, recent work studying agents that learn to teach other teammates has demonstrated that action advising accelerates team-wide learning. However, the prior work has simplified the learning of advising policies by using simple function approximations and only considered advising with primitive (low-level) actions, limiting the scalability of learning and teaching to complex domains. This paper introduces a novel learning-to-teach framework, called hierarchical multiagent teaching…
University of Tuebingen（图宾根大学）；Center on Long-Term Risk（长期风险中心）；New York University（纽约大学）；Vector Institute（矢量研究所）；University of Toronto（多伦多大学）；DeepMind
Cooperation in settings where agents have both common and conflicting interests (mixed-motive environments) has recently received considerable attention in multi-agent learning. However, the mixed-motive environments typically studied have a single cooperative outcome on which all agents can agree. Many real-world multi-agent environments are instead bargaining problems (BPs): they have several Pareto-optimal payoff profiles over which agents have conflicting preferences. We argue that typical cooperation-inducing learning algorithms fail to cooperate in BPs when there is room for normative di…
Self-play is a common paradigm for constructing solutions in Markov games that can yield optimal policies in collaborative settings. However, these policies often adopt highly-specialized conventions that make playing with a novel partner difficult. To address this, recent approaches rely on encoding symmetry and convention-awareness into policy training, but these require strong environmental assumptions and can complicate policy training. We therefore propose moving the learning of conventions to the belief space. Specifically, we propose a belief learning model that can maintain beliefs ove…
Learning to play optimally against any mixture over a diverse set of strategies is of important practical interests in competitive games. In this paper, we propose simplex-NeuPL that satisfies two desiderata simultaneously: i) learning a population of strategically diverse basis policies, represented by a single conditional network; ii) using the same network, learn best-responses to any mixture over the simplex of basis policies. We show that the resulting conditional policies incorporate prior information about their opponents effectively, enabling near optimal returns against arbitrary mixt…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Georgia Institute of Technology（佐治亚理工学院）；University of Nevada, Reno（内华达大学雷诺分校）
A distributed stochastic optimal control solution is presented for cooperative multi-agent systems. The network of agents is partitioned into multiple factorial subsystems, each of which consists of a central agent and neighboring agents. Local control actions that rely only on agents' local observations are designed to optimize the joint cost functions of subsystems. When solving for the local control actions, the joint optimality equation for each subsystem is cast as a linear partial differential equation and solved using the Feynman-Kac formula. The solution and the optimal control action …
