QMIX is a popular $Q$-learning algorithm for cooperative MARL in the centralised training and decentralised execution paradigm. In order to enable easy decentralisation, QMIX restricts the joint action $Q$-values it can represent to be a monotonic mixing of each agent's utilities. However, this restriction prevents it from representing value functions in which an agent's ordering over its actions can depend on other agents' actions. To analyse this representational limitation, we first formalise the objective QMIX optimises, which allows us to view QMIX as an operator that first computes the $Q$-learning targets and then projects them into the space representable by QMIX. This projection returns a representable $Q$-value that minimises the unweighted squared error across all joint actions. We show in particular that this projection can fail to recover the optimal policy even with access to $Q^*$, which primarily stems from the equal weighting placed on each joint action. We rectify this by introducing a weighting into the projection, in order to place more importance on the better joint actions. We propose two weighting schemes and prove that they recover the correct maximal action for any joint action $Q$-values, and therefore for $Q^*$ as well. Based on our analysis and results in the tabular setting we introduce two scalable versions of our algorithm, Centrally-Weighted (CW) QMIX and Optimistically-Weighted (OW) QMIX and demonstrate improved performance on both predator-prey and challenging multi-agent StarCraft benchmark tasks (Samvelyan et al., 2019).

Learning communication via deep reinforcement learning has recently been shown to be an effective way to solve cooperative multi-agent tasks. However, learning which communicated information is beneficial for each agent's decision-making process remains a challenging task. In order to address this problem, we explore relational reinforcement learning which leverages attention-based networks to learn efficient and interpretable relations between entities. On the foundation of relations, we introduce a novel communication architecture that exploits a memory-based attention network that selectively reasons about the value of information received from other agents while considering its past experiences. Specifically, the model communicates by first computing the relevance of messages received from other agents and then extracts task-relevant information from memories given the newly received information. We empirically demonstrate the strength of our model in cooperative and competitive multi-agent tasks, where inter-agent communication and reasoning over prior information substantially improves performance compared to baselines. We further show in the accompanying videos and experimental results that the agents learn a sophisticated and diverse set of cooperative behaviors to solve challenging tasks, both for discrete and continuous action spaces using on-policy and off-policy gradient methods. By developing an explicit architecture that is targeted towards communication, our work aims to open new directions to overcome important challenges in multi-agent cooperation through learned communication.

Multi-agent reinforcement learning has recently shown great promise as an approach to networked system control. Arguably, one of the most difficult and important tasks for which large scale networked system control is applicable is common-pool resource management. Crucial common-pool resources include arable land, fresh water, wetlands, wildlife, fish stock, forests and the atmosphere, of which proper management is related to some of society's greatest challenges such as food security, inequality and climate change. Here we take inspiration from a recent research program investigating the game-theoretic incentives of humans in social dilemma situations such as the well-known \textit{tragedy of the commons}. However, instead of focusing on biologically evolved human-like agents, our concern is rather to better understand the learning and operating behaviour of engineered networked systems comprising general-purpose reinforcement learning agents, subject only to nonbiological constraints such as memory, computation and communication bandwidth. Harnessing tools from empirical game-theoretic analysis, we analyse the differences in resulting solution concepts that stem from employing different information structures in the design of networked multi-agent systems. These information structures pertain to the type of information shared between agents as well as the employed communication protocol and network topology. Our analysis contributes new insights into the consequences associated with certain design choices and provides an additional dimension of comparison between systems beyond efficiency, robustness, scalability and mean control performance.

This paper considers offline multi-agent reinforcement learning. We propose the strategy-wise concentration principle which directly builds a confidence interval for the joint strategy, in contrast to the point-wise concentration principle which builds a confidence interval for each point in the joint action space. For two-player zero-sum Markov games, by exploiting the convexity of the strategy-wise bonus, we propose a computationally efficient algorithm whose sample complexity enjoys a better dependency on the number of actions than the prior methods based on the point-wise bonus. Furthermore, for offline multi-agent general-sum Markov games, based on the strategy-wise bonus and a novel surrogate function, we give the first algorithm whose sample complexity only scales $\sum_{i=1}^m A_i$ where $A_i$ is the action size of the $i$-th player and $m$ is the number of players. In sharp contrast, the sample complexity of methods based on the point-wise bonus would scale with the size of the joint action space $\Pi_{i=1}^m A_i$ due to the curse of multiagents. Lastly, all of our algorithms can naturally take a pre-specified strategy class $\Pi$ as input and output a strategy that is close to the best strategy in $\Pi$.

Self-Driven Particles (SDP) describe a category of multi-agent systems common in everyday life, such as flocking birds and traffic flows. In a SDP system, each agent pursues its own goal and constantly changes its cooperative or competitive behaviors with its nearby agents. Manually designing the controllers for such SDP system is time-consuming, while the resulting emergent behaviors are often not realistic nor generalizable. Thus the realistic simulation of SDP systems remains challenging. Reinforcement learning provides an appealing alternative for automating the development of the controller for SDP.

Recently, model-based agents have achieved better performance than model-free ones using the same computational budget and training time in single-agent environments. However, due to the complexity of multi-agent systems, it is tough to learn the model of the environment. The significant compounding error may hinder the learning process when model-based methods are applied to multi-agent tasks. This paper proposes an implicit model-based multi-agent reinforcement learning method based on value decomposition methods. Under this method, agents can interact with the learned virtual environment and evaluate the current state value according to imagined future states in the latent space, making agents have the foresight. Our approach can be applied to any multi-agent value decomposition method. The experimental results show that our method improves the sample efficiency in different partially observable Markov decision process domains.

Neural agents trained in reinforcement learning settings can learn to communicate among themselves via discrete tokens, accomplishing as a team what agents would be unable to do alone. However, the current standard of using one-hot vectors as discrete communication tokens prevents agents from acquiring more desirable aspects of communication such as zero-shot understanding. Inspired by word embedding techniques from natural language processing, we propose neural agent architectures that enables them to communicate via discrete tokens derived from a learned, continuous space. We show in a decision theoretic framework that our technique optimizes communication over a wide range of scenarios, whereas one-hot tokens are only optimal under restrictive assumptions. In self-play experiments, we validate that our trained agents learn to cluster tokens in semantically-meaningful ways, allowing them communicate in noisy environments where other techniques fail. Lastly, we demonstrate both that agents using our method can effectively respond to novel human communication and that humans can understand unlabeled emergent agent communication, outperforming the use of one-hot communication.

Learning from datasets without interaction with environments (Offline Learning) is an essential step to apply Reinforcement Learning (RL) algorithms in real-world scenarios.However, compared with the single-agent counterpart, offline multi-agent RL introduces more agents with the larger state and action space, which is more challenging but attracts little attention. We demonstrate current offline RL algorithms are ineffective in multi-agent systems due to the accumulated extrapolation error. In this paper, we propose a novel offline RL algorithm, named Implicit Constraint Q-learning (ICQ), which effectively alleviates the extrapolation error by only trusting the state-action pairs given in the dataset for value estimation. Moreover, we extend ICQ to multi-agent tasks by decomposing the joint-policy under the implicit constraint. Experimental results demonstrate that the extrapolation error is successfully controlled within a reasonable range and insensitive to the number of agents. We further show that ICQ achieves the state-of-the-art performance in the challenging multi-agent offline tasks (StarCraft II). Our code is public online at https://github.com/YiqinYang/ICQ.

We introduce an automatic curriculum algorithm, Variational Automatic Curriculum Learning (VACL), for solving challenging goal-conditioned cooperative multi-agent reinforcement learning problems. We motivate our curriculum learning paradigm through a variational perspective, where the learning objective can be decomposed into two terms: task learning on the current curriculum, and curriculum update to a new task distribution. Local optimization over the second term suggests that the curriculum should gradually expand the training tasks from easy to hard. Our VACL algorithm implements this variational paradigm with two practical components, task expansion and entity curriculum, which produces a series of training tasks over both the task configurations as well as the number of entities in the task. Experiment results show that VACL solves a collection of sparse-reward problems with a large number of agents. Particularly, using a single desktop machine, VACL achieves 98% coverage rate with 100 agents in the simple-spread benchmark and reproduces the ramp-use behavior originally shown in OpenAI's hide-and-seek project.

Promoting behavioural diversity is of critical importance in multi-agent reinforcement learning, since it helps the agent population maintain robust performance when encountering unfamiliar opponents at test time, or, when the game is highly non-transitive in the strategy space (e.g., Rock-Paper-Scissor). While a myriad of diversity metrics have been proposed, there are no widely accepted or unified definitions in the literature, making the consequent diversity-aware learning algorithms difficult to evaluate and the insights elusive. In this work, we propose a novel metric called the Unified Diversity Measure (UDM) that offers a unified view for existing diversity metrics. Based on UDM, we design the UDM-Fictitious Play (UDM-FP) and UDM-Policy Space Response Oracle (UDM-PSRO) algorithms as efficient solvers for normal-form games and open-ended games. In theory, we prove that UDM-based methods can enlarge the gamescape by increasing the response capacity of the strategy pool, and have convergence guarantee to two-player Nash equilibrium. We validate our algorithms on games that show strong non-transitivity, and empirical results show that our algorithms achieve better performances than strong PSRO baselines in terms of the exploitability and population effectivity.