# The Tamed Unadjusted Langevin Algorithm

Abstract : In this article, we consider the problem of sampling from a probability measure π having a density on R d known up to a normalizing constant, $x → e −U (x) / R d e −U (y) dy$. The Euler discretization of the Langevin stochastic differential equation (SDE) is known to be unstable in a precise sense, when the potential U is superlinear, i.e. lim inf $x→+∞ U (x) / x = +∞$. Based on previous works on the taming of superlinear drift coefficients for SDEs, we introduce the Tamed Unadjusted Langevin Algorithm (TULA) and obtain non-asymptotic bounds in V-total variation norm and Wasserstein distance of order 2 between the iterates of TULA and π, as well as weak error bounds. Numerical experiments are presented which support our findings.
Type de document :
Pré-publication, Document de travail
2017
Domaine :
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Littérature citée [44 références]

https://hal.inria.fr/hal-01648667
Contributeur : Nicolas Brosse <>
Soumis le : lundi 27 novembre 2017 - 23:26:53
Dernière modification le : jeudi 10 mai 2018 - 02:04:35

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• HAL Id : hal-01648667, version 1

### Citation

Nicolas Brosse, Alain Durmus, Eric Moulines, Sotirios Sabanis. The Tamed Unadjusted Langevin Algorithm. 2017. 〈hal-01648667〉

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