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

@article{Eftekhari2022TheFE, title={The Forward-Backward Envelope for Sampling with the Overdamped Langevin Algorithm}, author={Armin Eftekhari and Luisa Fernanda Vargas and Konstantinos C. Zygalakis}, journal={ArXiv}, year={2022}, volume={abs/2201.09096} }

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 nonasymptotic 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…

## 2 Citations

Bregman Proximal Langevin Monte Carlo via Bregman-Moreau Envelopes

- Computer Science, MathematicsICML
- 2022

The proposed algorithms extend existing Langevin Monte Carlo algorithms in two aspects—the ability to sample nonsmooth distributions with mirror descent-like algorithms, and the use of the more general Bregman–Moreau envelope in place of the Moreau envelope as a smooth approximation of the nonssooth part of the potential.

Bregman Proximal Langevin Monte Carlo via Bregman–Moreau Envelopes

- Computer Science, Mathematics
- 2022

The proposed algorithms extend existing Langevin Monte Carlo algorithms in two aspects—the ability to sample nonsmooth distributions with mirror descent-like algorithms, and the use of the more general Bregman–Moreau envelope in place of the Moreau envelope as a smooth approximation of the nonssooth part of the potential.

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