mlsanityData to 7 Oct 2026

Bregman Proximal Langevin Monte Carlo via Bregman--Moreau Envelopes

arXiv 2207.04387 ↗First posted 10 Jul 2022stat.ML cs.LG stat.COcited by 7

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Abstract (arXiv)

We propose efficient Langevin Monte Carlo algorithms for sampling distributions with nonsmooth convex composite potentials, which is the sum of a continuously differentiable function and a possibly nonsmooth function. We devise such algorithms leveraging recent advances in convex analysis and optimization methods involving Bregman divergences, namely the Bregman--Moreau envelopes and the Bregman proximity operators, and in the Langevin Monte Carlo algorithms reminiscent of mirror descent. 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 nonsmooth part of the potential. A particular case of the proposed scheme is reminiscent of the Bregman proximal gradient algorithm. The efficiency of the proposed methodology is illustrated with various sampling tasks at which existing Langevin Monte Carlo methods are known to perform poorly.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 42 of its 86 references that are in the map. First posted on arXiv 10 Jul 2022.

Builds on

42 of 86 references.

References · 42

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30 more
  1. 2019Stochastic gradient Markov chain Monte Carlocited by 56
  2. 2020Wasserstein Control of Mirror Langevin Monte Carlocited by 55
  3. 2020Efficient constrained sampling via the mirror-Langevin algorithmcited by 55
  4. 2015Sampling from a log-concave distribution with Projected Langevin Monte Carlocited by 52
  5. 2013Proximal Markov chain Monte Carlo algorithmscited by 46
  6. 2017Sampling from a log-concave distribution with compact support with proximal Langevin Monte Carlocited by 43
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  11. 2019Exponentiated Gradient Meets Gradient Descentcited by 32
  12. 2019Proximal Langevin Algorithm: Rapid Convergence Under Isoperimetrycited by 31
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  25. 2015Forward-Backward Splitting with Bregman Distancescited by 7
  26. 2019Bregman Forward-Backward Operator Splittingcited by 7
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  28. 2021Gradient-Based Markov Chain Monte Carlo for Bayesian Inference With Non-Differentiable Priorscited by 6
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  30. 2019Bregman Proximal Mappings and Bregman-Moreau Envelopes under Relative Prox-Regularitycited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 1; 2025: 3; 2026: 1.

7 papers.

  1. 2025Diffusion at Absolute Zero: Langevin Sampling Using Successive Moreau Envelopes [conference paper]cited by 6
  2. 2023Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithmscited by 4
  3. 2024Spurious Stationarity and Hardness Results for Bregman Proximal-Type Algorithmscited by 2
  4. 2025Efficient Bayesian Computation Using Plug-and-Play Priors for Poisson Inverse Problemscited by 2
  5. 2025Anchored Langevin Algorithmscited by 2
  6. 2023Compressive Recovery of Sparse Precision Matricescited by 1
  7. 2026Active-Trace Complexity Bounds for Moreau--Yosida Unadjusted Langevin Samplingcited by 1