The tamed unadjusted Langevin algorithm

摘要

In this article, we consider the problem of sampling from a probability measure pi having a density on R-d proportional to x bar right arrow e(-U(x)). The Euler discretization of the Langevin stochastic differential equation (SDE) is known to be unstable, when the potential U is superlinear. 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 pi, as well as weak error bounds. Numerical experiments are presented which support our findings. (C) 2018 Elsevier B.V. All rights reserved.