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math.PR2024
The exponential turnpike phenomenon for mean field game systems: weakly monotone drifts and small interactions
Alekos Cecchin, Giovanni Conforti, Alain Durmus +1
This article aims at quantifying the long time behavior of solutions of mean field PDE systems arising in the theory of Mean Field Games and McKean-Vlasov control. Our main contrib…
stat.ML2024
Theoretical guarantees in KL for Diffusion Flow Matching
Marta Gentiloni Silveri, Giovanni Conforti, Alain Durmus
Flow Matching (FM) (also referred to as stochastic interpolants or rectified flows) stands out as a class of generative models that aims to bridge in finite time the target distrib…
math.OC2024
On the irreducibility and convergence of a class of nonsmooth nonlinear state-space models on manifolds and their applications to zeroth-order optimization
Armand Gissler, Alain Durmus, Anne Auger
In this paper, we analyze a large class of general nonlinear state-space models on a state-space X, defined by the recursion , , wh…