Kinetic Langevin MCMC Sampling Without Gradient Lipschitz Continuity -- the Strongly Convex Case
Probability
2023-01-20 v1 Machine Learning
Numerical Analysis
Numerical Analysis
Optimization and Control
Machine Learning
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.
Cite
@article{arxiv.2301.08039,
title = {Kinetic Langevin MCMC Sampling Without Gradient Lipschitz Continuity -- the Strongly Convex Case},
author = {Tim Johnston and Iosif Lytras and Sotirios Sabanis},
journal= {arXiv preprint arXiv:2301.08039},
year = {2023}
}
Comments
40 pages