Population-Aware Imitation Learning in Mean-field Games with Common Noise

TL;DR

This paper develops methods for imitation learning in mean-field games with common noise, emphasizing population-aware policies to handle stochastic population dynamics and improve equilibrium approximation.

Contribution

It introduces population-aware imitation learning objectives, analyzes error bounds, and proposes a deep learning framework for computing such policies in stochastic mean-field games.

Findings

Population-aware policies outperform population-unaware ones in stochastic environments.

Minimizing imitation proxies reduces exploitability and improves performance.

Standard policies fail to capture equilibrium dynamics under common noise.

Abstract

Mean Field Games (MFGs) provide a powerful framework for modeling the collective behavior of large populations of interacting agents. In this paper, we address the problem of Imitation Learning (IL) in MFGs subject to common noise, where the population distribution evolves stochastically. This stochasticity compels agents to adopt population-aware policies to respond to aggregate shocks. We formulate two distinct learning objectives: recovering a Nash equilibrium and maximizing performance against an expert population. We investigate two imitation proxies: Behavioral Cloning (BC) and Adversarial (ADV) divergence. We then establish finite-sample error bounds showing that minimizing these proxies effectively controls both the policy's exploitability and its performance gap relative to the expert. Furthermore, we propose a numerical framework using generalized Fictitious Play and Deep Learning to compute expert population-aware policies. Through experiments on three environments we demonstrate that standard population-unaware policies fail to capture the equilibrium dynamics. Our results highlight that learning population-aware policies is crucial to avoid being misled by the randomness inherent in common noise.