3 citations · 8 across the 10 of their papers we have counts for
14 papers
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…
Ergodicity of some stochastic Fokker-Planck equations with additive common noise
François Delarue, Etienne Tanré, Raphaël Maillet
In this paper we consider stochastic Fokker-Planck Partial Differential Equations (PDEs), obtained as the mean-field limit of weakly interacting particle systems subjected to both…
Rearranged Stochastic Heat Equation: Ergodicity and Related Gradient Descent on
François Delarue, William R. P. Hammersley
This article provides a case study for a recently introduced diffusion in the space of probability measures over the reals, namely rearranged stochastic heat, which solves a stocha…