Deep Reinforcement Learning for Infinite Horizon Mean Field Problems in Continuous Spaces

TL;DR

This paper introduces a novel reinforcement learning algorithm that combines actor-critic methods with mean field distribution representations to solve continuous-space mean field game and control problems efficiently, with convergence guarantees.

Contribution

It develops a unified RL framework for continuous mean field problems using actor-critic and score function representations, adaptable to MFG, MFC, and MFCGs.

Findings

Effective in linear-quadratic benchmarks

Converges to MFG equilibrium or MFC optimum

Handles mixed mean field control games

Abstract

We present the development and analysis of a reinforcement learning (RL) algorithm designed to solve continuous-space mean field game (MFG) and mean field control (MFC) problems in a unified manner. The proposed approach pairs the actor-critic (AC) paradigm with a representation of the mean field distribution via a parameterized score function, which can be efficiently updated in an online fashion, and uses Langevin dynamics to obtain samples from the resulting distribution. The AC agent and the score function are updated iteratively to converge, either to the MFG equilibrium or the MFC optimum for a given mean field problem, depending on the choice of learning rates. A straightforward modification of the algorithm allows us to solve mixed mean field control games (MFCGs). The performance of our algorithm is evaluated using linear-quadratic benchmarks in the asymptotic infinite horizon framework.