Deep Reinforcement Learning for Infinite Horizon Mean Field Problems in Continuous Spaces
This work addresses complex multi-agent optimization in continuous spaces, which is incremental as it builds on existing actor-critic and mean field methods.
The authors tackled the problem of solving continuous-space mean field game and control problems by developing a reinforcement learning algorithm that unifies these approaches, achieving convergence to equilibrium or optimum in linear-quadratic benchmarks.
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.