DM$^2$: Decentralized Multi-Agent Reinforcement Learning for Distribution Matching

Current approaches to multi-agent cooperation rely heavily on centralized mechanisms or explicit communication protocols to ensure convergence. This paper studies the problem of distributed multi-agent learning without resorting to centralized components or explicit communication. It examines the use of distribution matching to facilitate the coordination of independent agents. In the proposed scheme, each agent independently minimizes the distribution mismatch to the corresponding component of a target visitation distribution. The theoretical analysis shows that under certain conditions, each agent minimizing its individual distribution mismatch allows the convergence to the joint policy that generated the target distribution. Further, if the target distribution is from a joint policy that optimizes a cooperative task, the optimal policy for a combination of this task reward and the distribution matching reward is the same joint policy. This insight is used to formulate a practical algorithm (DM$^2$), in which each individual agent matches a target distribution derived from concurrently sampled trajectories from a joint expert policy. Experimental validation on the StarCraft domain shows that combining (1) a task reward, and (2) a distribution matching reward for expert demonstrations for the same task, allows agents to outperform a naive distributed baseline. Additional experiments probe the conditions under which expert demonstrations need to be sampled to obtain the learning benefits.