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

Tim Johnston, Iosif Lytras, Sotirios Sabanis
1/19/2023
math.PRcs.LGmath.NA

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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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Cite this paper

@article{johnston2023kinetic,
  title  = {Kinetic Langevin MCMC Sampling Without Gradient Lipschitz Continuity -- the Strongly Convex Case},
  author = {Tim Johnston and Iosif Lytras and Sotirios Sabanis},
  year   = {2023},
  eprint = {2301.08039},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2301.08039v1}
}

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