# Generalized conditional gradient and learning in potential mean field games

arXiv: https://arxiv.org/abs/2209.12772 · HTML: https://mlsanity.com/paper/2209.12772/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2022.

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

- [Efficient Model-Based Concave Utility Reinforcement Learning through Greedy Mirror Descent](https://mlsanity.com/paper/2311.18346/) (2023)
- [Primal and Dual Analysis of Entropic Fictitious Play for Finite-sum Problems](https://mlsanity.com/paper/2303.02957/) (2023)
- [Learning Regularized Graphon Mean-Field Games with Unknown Graphons](https://mlsanity.com/paper/2310.17531/) (2023)
- [MetaCURL: Non-stationary Concave Utility Reinforcement Learning](https://mlsanity.com/paper/2405.19807/) (2024)
- [Networked Communication for Decentralised Agents in Mean-Field Games](https://mlsanity.com/paper/2306.02766/) (2023)

## Abstract (arXiv)

We investigate the resolution of second-order, potential, and monotone mean field games with the generalized conditional gradient algorithm, an extension of the Frank-Wolfe algorithm. We show that the method is equivalent to the fictitious play method. We establish rates of convergence for the optimality gap, the exploitability, and the distances of the variables to the unique solution of the mean field game, for various choices of stepsizes. In particular, we show that linear convergence can be achieved when the stepsizes are computed by linesearch.