Sharp Propagation of Chaos for the Ensemble Langevin Sampler - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2024

Sharp Propagation of Chaos for the Ensemble Langevin Sampler

Résumé

The aim of this note is to revisit propagation of chaos for a Langevin-type interacting particle system used in the context of sampling. The interacting particle system we consider coincides, in the setting of a log-quadratic target distribution, with the ensemble Kalman sampler, for which propagation of chaos was first proved by Ding and Li. Like these authors, we prove propagation of chaos using a synchronous coupling as a starting point, as in Sznitman's classical argument. Instead of relying on a boostrapping argument, however, we use a technique based on stopping times in order to handle the lack of Lipschitz continuity of the coefficients in the dynamics. This approach originates from numerical analysis and was recently employed to prove mean field limits for consensus-based optimization and related interacting particle systems. In the context of ensemble Langevin sampling, it enables proving pathwise propagation of chaos with optimal rate, whereas previous results were optimal only up to a positive ε. It also allows relaxing the log-quadratic assumption on the target distribution.
Fichier principal
Vignette du fichier
main.pdf (655.9 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04518506 , version 1 (25-03-2024)
hal-04518506 , version 2 (31-03-2024)
hal-04518506 , version 3 (10-04-2024)

Identifiants

Citer

Urbain Vaes. Sharp Propagation of Chaos for the Ensemble Langevin Sampler. 2024. ⟨hal-04518506v3⟩
10 Consultations
1 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More