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

Joseph Lehec (1)

1 LMA [Poitiers] - Laboratoire de mathématiques et applications [UMR 7348]

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.

Domaines: Statistiques [math.ST]; Probabilités [math.PR]

Joseph Lehec. The Langevin Monte Carlo algorithm in the non-smooth log-concave case. The Annals of Applied Probability, 2023, 33 (6A), ⟨10.1214/23-AAP1935⟩. ⟨hal-03129129⟩