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

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
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https://hal.archives-ouvertes.fr/hal-03129129
Date
2021
Titre de la collection
Cahier de recherche du CEREMADE
Pages
19
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Auteur(s)
Lehec, Joseph cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Résumé (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.