Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2016

Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm

Abstract

In this paper, we study a method to sample from a target distribution $\pi$ over $\mathbb{R}^d$ having a positive density with respect to the Lebesgue measure, known up to a normalisation factor. This method is based on the Euler discretization of the overdamped Langevin stochastic differential equation associated with $\pi$. For both constant and decreasing step sizes in the Euler discretization, we obtain non-asymptotic bounds for the convergence to the target distribution $\pi$ in total variation distance. A particular attention is paid to the dependency on the dimension $d$, to demonstrate the applicability of this method in the high dimensional setting. These bounds improve and extend the results of (Dalalyan 2014).
Fichier principal
Vignette du fichier
main.pdf (478.59 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01176132 , version 1 (17-07-2015)
hal-01176132 , version 2 (07-03-2016)
hal-01176132 , version 3 (19-12-2016)

Identifiers

Cite

Alain Durmus, Éric Moulines. Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm. 2016. ⟨hal-01176132v3⟩
502 View
752 Download

Altmetric

Share

Gmail Facebook X LinkedIn More