Learning to best reply: On the consistency of multi-agent reinforcement learning

Abstract

This paper provides asymptotic results for a class of model-free actor-critic batch - reinforcement learning algorithms in the multi-agent setting. At each period, each agent faces an estimation problem (the critic, e.g. a value function), and a policy updating problem. The estimation step is done by parametric function estimation based on a bath of past observations. Agents have no knowledge of each others incentives and policies. I provide sufficient conditions for each agent's parametric function estimator to be consistent in the multi-agent environment, which enables agents to learn to best respond despite the non-stationarity inherent in multi-agent systems. The conditions depend on the environment, batch size, and policy step size.

These sufficient conditions are useful in the asymptotic analysis of multi-agent learning, e.g. in the application of long-run characterisations using stochastic approximation techniques.