3 citations · 11 across the 11 of their papers we have counts for
6 papers · 1 filter
Robust mean field control: stochastic maximum principle and variational mean field games
François Delarue, Pierre Lavigne
We introduce a class of robust control problems formulated in min-max form, in which the principal agent is viewed as a central planner facing Nature. The agent's cost is a nonline…
Robust mean-field games under entropy-based uncertainty
François Delarue, Pierre Lavigne
In this article, we introduce a new class of entropy-penalized robust mean field game problems in which the representative agent is opposed to Nature. The agent's objective is form…
HJB equations driven by the Dirichlet-Ferguson Laplacian in Wasserstein-Sobolev spaces
François Delarue, Mattia Martini, Giacomo Enrico Sodini
We study linear and nonlinear PDEs defined on the space of over the flat torus , equipped with the Dirichlet-Ferguson measure $\mathcal{D}…
Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs
Samuel Daudin, François Delarue
We address the behavior of idealized deep residual neural networks (ResNets), modeled via an optimal control problem set over continuity (or adjoint transport) equations. The conti…
On the Optimal Rate for the Convergence Problem in Mean Field Control
Samuel Daudin, François Delarue, Joe Jackson
The goal of this work is to obtain optimal rates for the convergence problem in mean field control. Our analysis covers cases where the solutions to the limiting problem may not be…
Weak solutions to the master equation of potential mean field games
Alekos Cecchin, François Delarue
The purpose of this work is to introduce a notion of weak solution to the master equation of a potential mean field game and to prove that existence and uniqueness hold under quite…