On Imitation in Mean-field Games

TL;DR

This paper investigates imitation learning in mean-field games, introduces a new solution concept, and proposes an adversarial approach linking mean-field control to improve imitation in complex population-dependent settings.

Contribution

It introduces the Nash imitation gap, analyzes IL challenges in population-dependent dynamics, and proposes an adversarial MFC-based method for better imitation in mean-field games.

Findings

IL reduces to single-agent IL when only rewards depend on population.

Population-dependent dynamics make IL significantly harder.

Adversarial MFC approach offers a promising direction for complex IL in MFGs.

Abstract

We explore the problem of imitation learning (IL) in the context of mean-field games (MFGs), where the goal is to imitate the behavior of a population of agents following a Nash equilibrium policy according to some unknown payoff function. IL in MFGs presents new challenges compared to single-agent IL, particularly when both the reward function and the transition kernel depend on the population distribution. In this paper, departing from the existing literature on IL for MFGs, we introduce a new solution concept called the Nash imitation gap. Then we show that when only the reward depends on the population distribution, IL in MFGs can be reduced to single-agent IL with similar guarantees. However, when the dynamics is population-dependent, we provide a novel upper-bound that suggests IL is harder in this setting. To address this issue, we propose a new adversarial formulation where the reinforcement learning problem is replaced by a mean-field control (MFC) problem, suggesting progress in IL within MFGs may have to build upon MFC.