The Forward-Backward Envelope for Sampling with the Overdamped Langevin Algorithm
Numerical Analysis
2022-01-25 v1 Numerical Analysis
Abstract
In this paper, we analyse a proximal method based on the idea of forward-backward splitting for sampling from distributions with densities that are not necessarily smooth. In particular, we study the non-asymptotic properties of the Euler-Maruyama discretization of the Langevin equation, where the forward-backward envelope is used to deal with the non-smooth part of the dynamics. An advantage of this envelope, when compared to widely-used Moreu-Yoshida one and the MYULA algorithm, is that it maintains the MAP estimator of the original non-smooth distribution. We also study a number of numerical experiments that corroborate that support our theoretical findings.
Keywords
Cite
@article{arxiv.2201.09096,
title = {The Forward-Backward Envelope for Sampling with the Overdamped Langevin Algorithm},
author = {Armin Eftekhari and Luis Vargas and Konstantinos Zygalakis},
journal= {arXiv preprint arXiv:2201.09096},
year = {2022}
}