# Lagrangian discretization of variational mean field games

arXiv: https://arxiv.org/abs/2010.11519 · HTML: https://mlsanity.com/paper/2010.11519/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2020.

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

- [Variational formulations of ODE-Net as a mean-field optimal control problem and existence results](https://mlsanity.com/paper/2303.05924/) (2023)
- [Control Laguerre Tessellation: Semi-discrete Optimal Transport Over Control Systems](https://mlsanity.com/paper/2607.09139/) (2026)

## Abstract (arXiv)

In this article, we introduce a method to approximate solutions of some variational mean field game problems with congestion, by finite sets of player trajectories. These trajectories are obtained by solving a minimization problem similar to the initial variational problem. In this discretized problem, congestion is penalized by a Moreau envelop with the 2-Wasserstein distance. Study of this envelop as well as efficient computation of its values and variations is done using semi-discrete optimal transport. We show convergence of the discrete sets of trajectories toward a solution of the mean field game, under some conditions on the parameters of the discretization.