Model-Free Mean-Field Reinforcement Learning: Mean-Field MDP and Mean-Field Q-Learning

TL;DR

This paper introduces a framework for mean-field reinforcement learning using Mean Field Markov Decision Processes, establishing connections between control policies and RL methods, with convergence guarantees and numerical demonstrations.

Contribution

It develops a novel mean-field RL framework connecting MFC and MFMDP, proposing adapted RL algorithms with convergence guarantees for population-based control problems.

Findings

Existence of optimal closed-loop policies for MFC.

Development of RL algorithms for mean-field settings.

Numerical validation of the proposed methods.

Abstract

We study infinite horizon discounted Mean Field Control (MFC) problems with common noise through the lens of Mean Field Markov Decision Processes (MFMDP). We allow the agents to use actions that are randomized not only at the individual level but also at the level of the population. This common randomization allows us to establish connections between both closed-loop and open-loop policies for MFC and Markov policies for the MFMDP. In particular, we show that there exists an optimal closed-loop policy for the original MFC. Building on this framework and the notion of state-action value function, we then propose reinforcement learning (RL) methods for such problems, by adapting existing tabular and deep RL methods to the mean-field setting. The main difficulty is the treatment of the population state, which is an input of the policy and the value function. We provide convergence guarantees for tabular algorithms based on discretizations of the simplex. Neural network based algorithms are more suitable for continuous spaces and allow us to avoid discretizing the mean field state space. Numerical examples are provided.