Graphon Mean-Field Control for Cooperative Multi-Agent Reinforcement Learning

TL;DR

This paper introduces a graphon mean-field control framework for cooperative multi-agent reinforcement learning, enabling nonuniform interactions among agents and demonstrating scalable, competitive performance compared to existing algorithms.

Contribution

It extends mean-field reinforcement learning by incorporating graphon theory to handle nonhomogeneous agent interactions, with theoretical approximation guarantees and practical scalable algorithms.

Findings

Approximation order of $rac{1}{\sqrt{N}}$ for the control framework.

Block GMFC effectively approximates cooperative MARL.

Empirical results show competitive performance with better scalability.

Abstract

The marriage between mean-field theory and reinforcement learning has shown a great capacity to solve large-scale control problems with homogeneous agents. To break the homogeneity restriction of mean-field theory, a recent interest is to introduce graphon theory to the mean-field paradigm. In this paper, we propose a graphon mean-field control (GMFC) framework to approximate cooperative multi-agent reinforcement learning (MARL) with nonuniform interactions and show that the approximate order is of $\mathcal{O}(\frac{1}{\sqrt{N}})$, with $N$ the number of agents. By discretizing the graphon index of GMFC, we further introduce a smaller class of GMFC called block GMFC, which is shown to well approximate cooperative MARL. Our empirical studies on several examples demonstrate that our GMFC approach is comparable with the state-of-art MARL algorithms while enjoying better scalability.