# Decentralized Proximal Stochastic Gradient Langevin Dynamics

arXiv: https://arxiv.org/abs/2605.00723 · HTML: https://mlsanity.com/paper/2605.00723/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 51 references that are in the map.
- First posted on arXiv 1 May 2026.

## Builds on (most cited first, 30 of 32)

- [Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1705.09056/) (2017)
- [Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysis](https://mlsanity.com/paper/1702.03849/) (2017)
- [Theoretical guarantees for approximate sampling from smooth and log-concave densities](https://mlsanity.com/paper/1412.7392/) (2014)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [EXTRA: An Exact First-Order Algorithm for Decentralized Consensus Optimization](https://mlsanity.com/paper/1404.6264/) (2014)
- [On the Convergence of Decentralized Gradient Descent](https://mlsanity.com/paper/1310.7063/) (2013)
- [High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1605.01559/) (2016)
- [User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient](https://mlsanity.com/paper/1710.00095/) (2017)
- [Mirrored Langevin Dynamics](https://mlsanity.com/paper/1802.10174/) (2018)
- [Wasserstein Control of Mirror Langevin Monte Carlo](https://mlsanity.com/paper/2002.04363/) (2020)
- [Efficient constrained sampling via the mirror-Langevin algorithm](https://mlsanity.com/paper/2010.16212/) (2020)
- [Sampling from a log-concave distribution with Projected Langevin Monte Carlo](https://mlsanity.com/paper/1507.02564/) (2015)
- [Sampling from a log-concave distribution with compact support with proximal Langevin Monte Carlo](https://mlsanity.com/paper/1705.08964/) (2017)
- [Exponential ergodicity of mirror-Langevin diffusions](https://mlsanity.com/paper/2005.09669/) (2020)
- [The Mirror Langevin Algorithm Converges with Vanishing Bias](https://mlsanity.com/paper/2109.12077/) (2021)
- [Primal Dual Interpretation of the Proximal Stochastic Gradient Langevin Algorithm](https://mlsanity.com/paper/2006.09270/) (2020)
- [Projected Stochastic Gradient Langevin Algorithms for Constrained Sampling and Non-Convex Learning](https://mlsanity.com/paper/2012.12137/) (2020)
- [COLA: Decentralized Linear Learning](https://mlsanity.com/paper/1808.04883/) (2018)
- [Deep Learning: A Bayesian Perspective](https://mlsanity.com/paper/1706.00473/) (2017)
- [Decentralized Stochastic Gradient Langevin Dynamics and Hamiltonian Monte Carlo](https://mlsanity.com/paper/2007.00590/) (2020)
- [Penalized Overdamped and Underdamped Langevin Monte Carlo Algorithms for Constrained Sampling](https://mlsanity.com/paper/2212.00570/) (2022)
- [Breaking Reversibility Accelerates Langevin Dynamics for Global Non-Convex Optimization](https://mlsanity.com/paper/1812.07725/) (2018)
- [An Accelerated Decentralized Stochastic Proximal Algorithm for Finite Sums](https://mlsanity.com/paper/1905.11394/) (2019)
- [Generalized EXTRA stochastic gradient Langevin dynamics](https://mlsanity.com/paper/2412.01993/) (2024)
- [Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/2405.07839/) (2024)
- [Non-Reversible Langevin Algorithms for Constrained Sampling](https://mlsanity.com/paper/2501.11743/) (2025)
- [Non-Convex Optimization via Non-Reversible Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/2004.02823/) (2020)
- [IDEAL: Inexact DEcentralized Accelerated Augmented Lagrangian Method](https://mlsanity.com/paper/2006.06733/) (2020)
- [Constrained Langevin Algorithms with L-mixing External Random Variables](https://mlsanity.com/paper/2205.14192/) (2022)
- [Accelerating Langevin Monte Carlo Sampling: A Large Deviations Analysis](https://mlsanity.com/paper/2503.19066/) (2025)

## Built on by (most cited first, 2 of 2)

- [Reflected Anchored Langevin Algorithms](https://mlsanity.com/paper/2610.09522/) (2026)
- [Accelerating Non-Smooth and Heavy-Tailed Sampling](https://mlsanity.com/paper/2610.11139/) (2026)

## 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.