# A Policy Iteration Method for Inverse Mean Field Games

arXiv: https://arxiv.org/abs/2409.06184 · HTML: https://mlsanity.com/paper/2409.06184/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Sep 2024.

## Built on by (most cited first, 3 of 3)

- [Learning Surrogate Potential Mean Field Games via Gaussian Processes: A Data-Driven Approach to Ill-Posed Inverse Problems](https://mlsanity.com/paper/2502.11506/) (2025)
- [A Robust Model-Based Approach for Continuous-Time Policy Evaluation with Unknown L'evy Process Dynamics](https://mlsanity.com/paper/2504.01482/) (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)

We propose a policy iteration method to solve an inverse problem for a mean-field game (MFG) model, specifically to reconstruct the obstacle function in the game from the partial observation data of value functions, which represent the optimal costs for agents. The proposed approach decouples this complex inverse problem, which is an optimization problem constrained by a coupled nonlinear forward and backward PDE system in the MFG, into several iterations of solving linear PDEs and linear inverse problems. This method can also be viewed as a fixed-point iteration that simultaneously solves the MFG system and inversion. We prove its linear rate of convergence. In addition, numerical examples in 1D and 2D, along with performance comparisons to a direct least-squares method, demonstrate the superior efficiency and accuracy of the proposed method for solving inverse MFGs.