Oracle-free Reinforcement Learning in Mean-Field Games along a Single Sample Path

TL;DR

This paper introduces Sandbox Learning, an oracle-free reinforcement learning algorithm for mean-field games that uses a single sample path to approximate the equilibrium, providing convergence guarantees and practical effectiveness.

Contribution

It develops a novel two-time-scale algorithm for MFGs that avoids the need for a mean-field oracle, with proven finite-sample convergence and broad applicability.

Findings

Finite sample convergence guarantees for the algorithm.

Sample complexity of 4(\u03b5^{-4}) for MFE approximation.

Empirical validation in diverse scenarios, including non-communicating MDPs.

Abstract

We consider online reinforcement learning in Mean-Field Games (MFGs). Unlike traditional approaches, we alleviate the need for a mean-field oracle by developing an algorithm that approximates the Mean-Field Equilibrium (MFE) using the single sample path of the generic agent. We call this {\it Sandbox Learning}, as it can be used as a warm-start for any agent learning in a multi-agent non-cooperative setting. We adopt a two time-scale approach in which an online fixed-point recursion for the mean-field operates on a slower time-scale, in tandem with a control policy update on a faster time-scale for the generic agent. Given that the underlying Markov Decision Process (MDP) of the agent is communicating, we provide finite sample convergence guarantees in terms of convergence of the mean-field and control policy to the mean-field equilibrium. The sample complexity of the Sandbox learning algorithm is $\tilde{\mathcal{O}}(\epsilon^{-4})$ where $\epsilon$ is the MFE approximation error. This is similar to works which assume access to oracle. Finally, we empirically demonstrate the effectiveness of the sandbox learning algorithm in diverse scenarios, including those where the MDP does not necessarily have a single communicating class.