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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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2101.10695.pdf (388.0Kb)
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
Pages
19
Metadata
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Author(s)
Lehec, Joseph cc
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.

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    Bubeck, Sébastien; Eldan, Ronen; Lehec, Joseph (2017) Document de travail / Working paper
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    Sampling from a log-concave distribution with Projected Langevin Monte Carlo 
    Bubeck, Sébastien; Eldan, Ronen; Lehec, Joseph (2018) Article accepté pour publication ou publié
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    Bounding the Norm of a Log-Concave Vector Via Thin-Shell Estimates 
    Eldan, Ronen; Lehec, Joseph (2014) Chapitre d'ouvrage
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    Poisson processes and a log-concave Bernstein theorem 
    Klartag, Bo'az; Lehec, Joseph (2019) Article accepté pour publication ou publié
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    Simulating Coulomb gases and log-gases with hybrid Monte Carlo algorithms 
    Chafaï, Djalil; Ferré, Gregoire (2019) Article accepté pour publication ou publié
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