[2303.12407] Non-asymptotic evaluation of Langevin-type Monte Carlo algorithms

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Summary:We examine Langevin-type algorithms for sampling from Gibbs distributions such that the potentials are dissipative and their weak gradients have finite moduli of continuity not essentially convergent to zero. Our major result’s a non-asymptotic higher certain of the 2-Wasserstein distance between a Gibbs distribution and the legislation of basic Langevin-type algorithms based mostly on the Liptser–Shiryaev concept and Poincaré inequalities. We apply this certain to indicate that the Langevin Monte Carlo algorithm can approximate Gibbs distributions with arbitrary accuracy if the potentials are dissipative and their gradients are uniformly steady. We additionally suggest Langevin-type algorithms with spherical smoothing for distributions whose potentials will not be convex or constantly differentiable.

Submission historical past

From: Shogo Nakakita [view email]
[v1]
Wed, 22 Mar 2023 09:16:17 UTC (32 KB)
[v2]
Thu, 23 Mar 2023 01:27:36 UTC (32 KB)
[v3]
Wed, 26 Apr 2023 02:42:02 UTC (27 KB)
[v4]
Tue, 9 Could 2023 12:09:06 UTC (30 KB)
[v5]
Thu, 29 Feb 2024 02:54:55 UTC (29 KB)



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