Non-asymptotic analysis of Langevin-type Monte Carlo algorithms

arXiv:2303.12407v5 Announce Type: replace-cross
Abstract: We study Langevin-type algorithms for sampling from Gibbs distributions such that the potentials are dissipative and their weak gradients have finite moduli of continuity not necessarily convergent to zero. Our main result is a non-asymptotic upper bound of the 2-Wasserstein distance between a Gibbs distribution and the law of general Langevin-type algorithms based on the Liptser--Shiryaev theory and Poincar\'{e} inequalities. We apply this bound to show that the Langevin Monte Carlo algorithm can approximate Gibbs …

abstract algorithms analysis arxiv continuity distribution gibbs law math.pr math.st sampling stat.ml stat.th study type