3 citations · 11 across the 11 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…
Intrinsic regularization by noise for mean field games
François Delarue, Youssef Ouknine
The purpose of this article is to show that an intrinsic noise with values in the space of probability measures may force uniqueness to first order…
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…
Probabilistic rough paths II Lions-Taylor expansions and Random controlled rough paths
François Delarue, William Salkeld
In line with the notion of probabilistic rough paths introduced in the previous contribution \cite{salkeld2021Probabilistic}, we address corresponding random controlled rough paths…
Zero noise limit for multidimensional SDEs driven by a pointy gradient
François Delarue, Mario Maurelli
The purpose of the article is to address the limiting behavior of the solutions of stochastic differential equations driven by a pointy -dimensional gradient as the intensity of…
Selection of equilibria in a linear quadratic mean-field game
François Delarue, Rinel Foguen Tchuendom
In this paper, we address an instance of uniquely solvable mean-field game with a common noise whose corresponding counterpart without common noise has several equilibria. We study…
Numerical Probabilistic Approach to MFG
Andrea Angiuli, Christy V. Graves, Houzhi Li +3
This project investigates numerical methods for solving fully coupled forward-backward stochastic differential equations (FBSDEs) of McKean-Vlasov type. Having numerical solvers fo…
Numerical Method for FBSDEs of McKean-Vlasov Type
Jean-François Chassagneux, Dan Crisan, François Delarue
This paper is dedicated to the presentation and the analysis of a numerical scheme for forward-backward SDEs of the McKean-Vlasov type, or equivalently for solutions to PDEs on the…