mlsanityData to 7 Oct 2026

Decentralized Proximal Stochastic Gradient Langevin Dynamics

arXiv 2605.00723 ↗First posted 1 May 2026stat.ML cs.LG math.PRcited by 2

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Abstract (arXiv)

We propose Decentralized Proximal Stochastic Gradient Langevin Dynamics (DE-PSGLD), a decentralized Markov chain Monte Carlo (MCMC) algorithm for sampling from a log-concave probability distribution constrained to a convex domain. Constraints are enforced through a shared proximal regularization based on the Moreau-Yosida envelope, enabling unconstrained updates while preserving consistency with the target constrained posterior. We establish non-asymptotic convergence guarantees in the 2-Wasserstein distance for both individual agent iterates and their network averages. Our analysis shows that DE-PSGLD converges to a regularized Gibbs distribution and quantifies the bias introduced by the proximal approximation. We evaluate DE-PSGLD for different sampling problems on synthetic and real datasets. As the first decentralized approach for constrained domains, our algorithm exhibits fast posterior concentration and high predictive accuracy.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 32 of its 51 references that are in the map. First posted on arXiv 1 May 2026.

Builds on

32 of 51 references.

References · 32

  1. 2017Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descentcited by 496
  2. 2017Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysiscited by 242
  3. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 206
  4. 2018Statistical Aspects of Wasserstein Distancescited by 202
  5. 2014EXTRA: An Exact First-Order Algorithm for Decentralized Consensus Optimizationcited by 160
  6. 2013On the Convergence of Decentralized Gradient Descentcited by 158
  7. 2016High-dimensional Bayesian inference via the Unadjusted Langevin Algorithmcited by 144
  8. 2017User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradientcited by 116
  9. 2018Mirrored Langevin Dynamicscited by 61
  10. 2020Wasserstein Control of Mirror Langevin Monte Carlocited by 55
  11. 2020Efficient constrained sampling via the mirror-Langevin algorithmcited by 55
  12. 2015Sampling from a log-concave distribution with Projected Langevin Monte Carlocited by 52
20 more
  1. 2017Sampling from a log-concave distribution with compact support with proximal Langevin Monte Carlocited by 43
  2. 2020Exponential ergodicity of mirror-Langevin diffusionscited by 37
  3. 2021The Mirror Langevin Algorithm Converges with Vanishing Biascited by 37
  4. 2020Primal Dual Interpretation of the Proximal Stochastic Gradient Langevin Algorithmcited by 34
  5. 2020Projected Stochastic Gradient Langevin Algorithms for Constrained Sampling and Non-Convex Learningcited by 33
  6. 2018COLA: Decentralized Linear Learningcited by 30
  7. 2017Deep Learning: A Bayesian Perspectivecited by 20
  8. 2020Decentralized Stochastic Gradient Langevin Dynamics and Hamiltonian Monte Carlocited by 19
  9. 2022Penalized Overdamped and Underdamped Langevin Monte Carlo Algorithms for Constrained Samplingcited by 13
  10. 2018Breaking Reversibility Accelerates Langevin Dynamics for Global Non-Convex Optimizationcited by 12
  11. 2019An Accelerated Decentralized Stochastic Proximal Algorithm for Finite Sumscited by 10
  12. 2024Generalized EXTRA stochastic gradient Langevin dynamicscited by 9
  13. 2024Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamicscited by 7
  14. 2025Non-Reversible Langevin Algorithms for Constrained Samplingcited by 7
  15. 2020Non-Convex Optimization via Non-Reversible Stochastic Gradient Langevin Dynamicscited by 6
  16. 2020IDEAL: Inexact DEcentralized Accelerated Augmented Lagrangian Methodcited by 6
  17. 2022Constrained Langevin Algorithms with L-mixing External Random Variablescited by 6
  18. 2025Accelerating Langevin Monte Carlo Sampling: A Large Deviations Analysiscited by 4
  19. 2025DIGing--SGLD: Decentralized and Scalable Langevin Sampling over Time--Varying Networkscited by 4
  20. 2025Accelerating Constrained Sampling: A Large Deviations Approachcited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Reflected Anchored Langevin Algorithmscited by 1
  2. 2026Accelerating Non-Smooth and Heavy-Tailed Samplingcited by 0