Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm

3 XPOP - Modélisation en pharmacologie de population
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
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).
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https://hal.archives-ouvertes.fr/hal-01176132
Contributor : Alain Durmus <>
Submitted on : Monday, December 19, 2016 - 9:51:09 AM
Last modification on : Tuesday, December 8, 2020 - 10:29:24 AM

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• HAL Id : hal-01176132, version 3
• ARXIV : 1507.05021

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

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