The Langevin Monte Carlo algorithm in the non-smooth log-concave case

Lehec, Joseph

Lehec, Joseph (2021), The Langevin Monte Carlo algorithm in the non-smooth log-concave case. https://basepub.dauphine.psl.eu/handle/123456789/22285

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Type

Document de travail / Working paper

External document link

https://hal.archives-ouvertes.fr/hal-03129129

Date

2021

Series title

Cahier de recherche du CEREMADE

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Author(s)

Lehec, Joseph

CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]

Abstract (EN)

We prove non-asymptotic polynomial bounds on the convergence of the Langevin Monte Carlo algorithm in the case where the potential is a convex function which is globally Lipschitz on its domain, typically the maximum of a finite number of affine functions on an arbitrary convex set. In particular the potential is not assumed to be gradient Lipschitz, in contrast with most (if not all) existing works on the topic.