Kinetic Langevin MCMC Sampling Without Gradient Lipschitz Continuity -- the Strongly Convex Case

• URL: http://arxiv.org/abs/2301.08039v1
• Date: Thu, 19 Jan 2023 12:32:41 GMT
• Title: Kinetic Langevin MCMC Sampling Without Gradient Lipschitz Continuity -- the Strongly Convex Case
• Authors: Tim Johnston, Iosif Lytras and Sotirios Sabanis
• Abstract summary: We consider sampling from log concave distributions in Hamiltonian setting, without assuming that the objective is globally Lipschitz. We propose two algorithms based on polygonal gradient (tamed) Euler schemes, to sample from a target measure, and provide non-asymptotic 2-Wasserstein distance bounds between the law of the process of each algorithm and the target measure.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this article we consider sampling from log concave distributions in Hamiltonian setting, without assuming that the objective gradient is globally Lipschitz. We propose two algorithms based on monotone polygonal (tamed) Euler schemes, to sample from a target measure, and provide non-asymptotic 2-Wasserstein distance bounds between the law of the process of each algorithm and the target measure. Finally, we apply these results to bound the excess risk optimization error of the associated optimization problem.

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