Mean Field Reinforcement Learning

2026-07-01

AI Summary

This work addresses the computational intractability arising from complex agent interactions in large-scale multi-agent reinforcement learning by proposing a scalable learning framework grounded in mean-field control theory. By leveraging mean-field approximation to characterize population behavior, the approach constructs a representative agent model and integrates it with a Markov decision process subject to common noise, thereby establishing a rigorous theoretical link between finite-population systems and their mean-field limits. The study presents the first systematic unification of mean-field control and reinforcement learning, offering formal analyses of propagation of chaos and algorithmic convergence. It further incorporates dynamic programming, Q-learning, policy gradient, and DDPG methods within this framework. Empirical validation on both general and linear-quadratic models demonstrates the efficacy of the proposed algorithms in efficiently approximating solutions for large-scale stochastic multi-agent systems.

Abstract

This monograph provides an introduction to mean field reinforcement learning through the lens of Markov decision processes arising from large-population stochastic control with mean field interactions and common noise. Starting from the connection between multi-agent reinforcement learning and mean field control, it develops the probabilistic, mathematical, and control-theoretic framework needed to formulate representative-agent learning problems, analyze their relationship with finite-population systems, and study both general and linear-quadratic models. The presentation includes dynamic programming principles, propagation-of-chaos limits, and theoretical analyses of tabular Q-learning and policy-gradient methods. It also discusses numerical implementations, including tabular schemes and deep reinforcement learning methods such as deep deterministic policy gradient. The goal is to give readers a coherent bridge between mean field control theory and reinforcement learning methodology, emphasizing the mathematical structure of the problems and the design of tractable learning approaches for large stochastic populations.

Problem

• mean field reinforcement learning
• large-population stochastic control
• Markov decision processes
• mean field interactions
• common noise

Innovation

• Mean Field Reinforcement Learning
• Propagation of Chaos
• Multi-agent Reinforcement Learning
• Linear-Quadratic Control
• Deep Deterministic Policy Gradient