# Deep Policy Iteration for High-Dimensional Mean Field Games

arXiv: https://arxiv.org/abs/2310.10827 · HTML: https://mlsanity.com/paper/2310.10827/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Oct 2023.

## Built on by (most cited first, 2 of 2)

- [Neural Mean-Field Games: Extending Mean-Field Game Theory with Neural Stochastic Differential Equations](https://mlsanity.com/paper/2504.13228/) (2025)
- [Gaussian process policy iteration with additive Schwarz acceleration for forward and inverse HJB and mean field game problems](https://mlsanity.com/paper/2505.00909/) (2025)

## Abstract (arXiv)

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.