Papers › The Tamed Unadjusted Langevin Algorithm
The Tamed Unadjusted Langevin Algorithm
Nicolas Brosse, Alain Durmus, Éric Moulines, Sotirios Sabanis
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In this article, we consider the problem of sampling from a probability measure π having a density on ℝᵈ known up to a normalizing constant, x↦e⁻ᵁ⁽ˣ⁾ / ∫_(ℝᵈ) e⁻ᵁ⁽ʸ⁾ d y. 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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