Sampling from a log-concave distribution with compact support with proximal Langevin Monte Carlo

Abstract : This paper presents a detailed theoretical analysis of the Langevin Monte Carlo sampling algorithm recently introduced in [DMP16] when applied to log-concave probability distributions that are restricted to a convex body K. This method relies on a regularisation procedure involving the Moreau-Yosida envelope of the indicator function associated with K. Explicit convergence bounds in total variation norm and in Wasserstein distance of order 1 are established. In particular, we show that the complexity of this algorithm given a first order oracle is polynomial in the dimension of the state space. Finally, some numerical experiments are presented to compare our method with competing MCMC approaches from the literature.
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Submitted on : Monday, November 27, 2017 - 11:27:53 PM
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Nicolas Brosse, Alain Durmus, Éric Moulines, Marcelo Pereyra. Sampling from a log-concave distribution with compact support with proximal Langevin Monte Carlo. Proceedings of Machine Learning Research, PMLR, 2017, 65, pp.319-342. 〈hal-01648665〉

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