Mean Field Multi-Agent Reinforcement Learning

TL;DR

This paper introduces Mean Field Reinforcement Learning, a scalable approach for multi-agent systems that approximates agent interactions with a mean effect, enabling effective learning in large populations.

Contribution

It proposes practical mean field Q-learning and Actor-Critic algorithms, analyzing their convergence and demonstrating their effectiveness on complex multi-agent tasks.

Findings

Successfully applied to Gaussian squeeze, Ising model, and battle games.

First to solve the Ising model with model-free reinforcement learning.

Shows convergence to Nash equilibrium in large agent populations.

Abstract

Existing multi-agent reinforcement learning methods are limited typically to a small number of agents. When the agent number increases largely, the learning becomes intractable due to the curse of the dimensionality and the exponential growth of agent interactions. In this paper, we present \emph{Mean Field Reinforcement Learning} where the interactions within the population of agents are approximated by those between a single agent and the average effect from the overall population or neighboring agents; the interplay between the two entities is mutually reinforced: the learning of the individual agent's optimal policy depends on the dynamics of the population, while the dynamics of the population change according to the collective patterns of the individual policies. We develop practical mean field Q-learning and mean field Actor-Critic algorithms and analyze the convergence of the solution to Nash equilibrium. Experiments on Gaussian squeeze, Ising model, and battle games justify the learning effectiveness of our mean field approaches. In addition, we report the first result to solve the Ising model via model-free reinforcement learning methods.