In this paper, we introduce a probabilistic recursive reasoning (PR2) framework for multi-agent reinforcement learning. Our hypothesis is that it is beneficial for each agent to account for how the opponents would react to its future behaviors. Under the PR2 framework, we adopt variational Bayes methods to approximate the opponents’ conditional policy, to which each agent finds the best response and then improve their own policy. We develop decentralized-training-decentralized-execution algorithms, PR2-Q and PR2-Actor-Critic, that are proved to converge in the self-play scenario when there is one Nash equilibrium. Our methods are tested on both the matrix game and the differential game, which have a non-trivial equilibrium where common gradient-based methods fail to converge. Our experiments show that it is critical to reason about how the opponents believe about what the agent believes. We expect our work to contribute a new idea of modeling the opponents to the multi-agent reinforcement learning community.
Many artificial intelligence (AI) applications often require multiple intelligent agents to work in a collaborative effort. Efficient learning for intra-agent communication and coordination is an indispensable step towards general AI. In this paper, we take StarCraft combat game as a case study, where the task is to coordinate multiple agents as a team to defeat their enemies. To maintain a scalable yet effective communication protocol, we introduce a Multiagent Bidirectionally-Coordinated Network (BiCNet [‘bIknet]) with a vectorised extension of actor-critic formulation. We show that BiCNet can handle different types of combats with arbitrary numbers of AI agents for both sides. Our analysis demonstrates that without any supervisions such as human demonstrations or labelled data, BiCNet could learn various types of advanced coordination strategies that have been commonly used by experienced game players. In our experiments, we evaluate our approach against multiple baselines under different scenarios; it shows state-of-the-art performance, and possesses potential values for large-scale real-world applications.