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arXiv · 2201.09096

The Forward-Backward Envelope for Sampling with the Overdamped Langevin Algorithm

Armin Eftekhari·Luis Vargas·Konstantinos Zygalakis
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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.

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Armin Eftekhari, Luis Vargas, Konstantinos Zygalakis. 2022-01-22. The Forward-Backward Envelope for Sampling with the Overdamped Langevin Algorithm. https://arxiv.org/abs/2201.09096

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