• Corpus ID: 246240253

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… 
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Bregman Proximal Langevin Monte Carlo via Bregman-Moreau Envelopes
TLDR
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
  • Han Liu
  • Computer Science, Mathematics
  • 2022
TLDR
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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