Long-Run Convergence of Discrete-Time Interacting Particle Systems of the McKean-Vlasov Type

Séminaire scientifique

Lieu :  IMT-Atlantique - Petit Amphi

Intervenant : Pascal Bianchi - Paris-Tech

Titre : Long-Run Convergence of Discrete-Time Interacting Particle Systems of the McKean-Vlasov Type

Abstract: We consider a discrete-time system of n coupled random vectors, also known as interacting particles. Such models have recently been shown to be interesting for studying the convergence of numerical methods in the fields of deep learning, Monte Carlo methods, and global optimization. The dynamics involve a vanishing step size, random centered perturbations, and a mean vector field that induces coupling between the particles. We study the doubly asymptotic regime where both the number of iterations and the number n of particles tend to infinity, without any constraint on the relative rates of convergence of these two parameters. The talk will be prefaced by an introduction to the theme, adapted for non-specialists.