# Policy iteration method for time-dependent Mean Field Games systems with non-separable Hamiltonians

arXiv: https://arxiv.org/abs/2110.02552 · HTML: https://mlsanity.com/paper/2110.02552/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Oct 2021.

## Built on by (most cited first, 5 of 5)

- [Mean Field LQG Social Optimization: A Reinforcement Learning Approach](https://mlsanity.com/paper/2410.15119/) (2024)
- [Deep Learning for Mean Field Games with non-separable Hamiltonians](https://mlsanity.com/paper/2301.02877/) (2023)
- [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)
- [Recurrent Structural Policy Gradient for Partially Observable Mean Field Games](https://mlsanity.com/paper/2602.20141/) (2026)
- [Towards Model-Free Learning in Dynamic Population Games: An Application to Karma Economies](https://mlsanity.com/paper/2605.11042/) (2026)

## Abstract (arXiv)

We introduce two algorithms based on a policy iteration method to numerically solve time-dependent Mean Field Game systems of partial differential equations with non-separable Hamiltonians. We prove the convergence of such algorithms in sufficiently small time intervals with Banach fixed point method. Moreover, we prove that the convergence rates are linear. We illustrate our theoretical results by numerical examples, and we discuss the performance of the proposed algorithms.