# Learning optimal policies in potential Mean Field Games: Smoothed Policy Iteration algorithms

arXiv: https://arxiv.org/abs/2212.04791 · HTML: https://mlsanity.com/paper/2212.04791/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Dec 2022.

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

- [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)
- [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 Smoothed Policy Iteration algorithms (SPIs) as rules for learning policies and methods for computing Nash equilibria in second order potential Mean Field Games (MFGs). Global convergence is proved if the coupling term in the MFG system satisfy the Lasry Lions monotonicity condition. Local convergence to a stable solution is proved for system which may have multiple solutions. The convergence analysis shows close connections between SPIs and the Fictitious Play algorithm, which has been widely studied in the MFG literature. Numerical simulation results based on finite difference schemes are presented to supplement the theoretical analysis.