# The Tamed Unadjusted Langevin Algorithm

1 XPOP - Modélisation en pharmacologie de population
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
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.
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Journal articles
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Cited literature [44 references]

https://hal.inria.fr/hal-01648667
Contributor : Nicolas Brosse <>
Submitted on : Monday, November 27, 2017 - 11:26:53 PM
Last modification on : Friday, July 31, 2020 - 10:44:09 AM

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Nicolas Brosse, Alain Durmus, Éric Moulines, Sotirios Sabanis. The Tamed Unadjusted Langevin Algorithm. Stochastic Processes and their Applications, Elsevier, 2018, ⟨10.1016/j.spa.2018.10.002⟩. ⟨hal-01648667⟩

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