Deep Policy Iteration for High-Dimensional Mean Field Games

TL;DR

This paper proposes Deep Policy Iteration (DPI), a neural network-based method that extends policy iteration to high-dimensional mean field games, overcoming the curse of dimensionality and improving convergence in complex stochastic environments.

Contribution

The paper introduces DPI, a novel neural network framework that enhances policy iteration for high-dimensional mean field games, including separable and non-separable Hamiltonian cases.

Findings

DPI achieves convergence comparable to MFDGM.

DPI effectively handles high-dimensional problems.

Deep learning improves policy iteration in complex MFGs.

Abstract

This paper introduces Deep Policy Iteration (DPI), a novel approach that integrates the strengths of Neural Networks with the stability and convergence advantages of Policy Iteration (PI) to address high-dimensional stochastic Mean Field Games (MFG). DPI overcomes the limitations of PI, which is constrained by the curse of dimensionality to low-dimensional problems, by iteratively training three neural networks to solve PI equations and satisfy forward-backwards conditions. Our findings indicate that DPI achieves comparable convergence levels to the Mean Field Deep Galerkin Method (MFDGM), with additional advantages. Furthermore, deep learning techniques show promise in handling separable Hamiltonian cases where PI alone is less effective. DPI effectively manages high-dimensional problems, extending the applicability of PI to both separable and non-separable Hamiltonians.