# Decentralized Stochastic Gradient Langevin Dynamics and Hamiltonian Monte Carlo

arXiv: https://arxiv.org/abs/2007.00590 · HTML: https://mlsanity.com/paper/2007.00590/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2020.

## Built on by (most cited first, 19 of 19)

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- [Decentralized Bayesian Learning with Metropolis-Adjusted Hamiltonian Monte Carlo](https://mlsanity.com/paper/2107.07211/) (2021)
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- [DIGing--SGLD: Decentralized and Scalable Langevin Sampling over Time--Varying Networks](https://mlsanity.com/paper/2511.12836/) (2025)
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- [Variance Reduction for Stochastic Gradient Generalized Non-reversible Langevin Monte Carlo Algorithms](https://mlsanity.com/paper/2606.28808/) (2026)
- [Quantifying the mini-batching error in Bayesian inference for Adaptive Langevin dynamics](https://mlsanity.com/paper/2105.10347/) (2021)
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- [Asynchronous Bayesian Learning over a Network](https://mlsanity.com/paper/2211.08603/) (2022)
- [Distributed Markov Chain Monte Carlo Sampling based on the Alternating Direction Method of Multipliers](https://mlsanity.com/paper/2401.15838/) (2024)
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- [Improving the stability of the covariance-controlled adaptive Langevin thermostat for large-scale Bayesian sampling](https://mlsanity.com/paper/2512.24515/) (2025)

## Abstract (arXiv)

Stochastic gradient Langevin dynamics (SGLD) and stochastic gradient Hamiltonian Monte Carlo (SGHMC) are two popular Markov Chain Monte Carlo (MCMC) algorithms for Bayesian inference that can scale to large datasets, allowing to sample from the posterior distribution of the parameters of a statistical model given the input data and the prior distribution over the model parameters. However, these algorithms do not apply to the decentralized learning setting, when a network of agents are working collaboratively to learn the parameters of a statistical model without sharing their individual data due to privacy reasons or communication constraints. We study two algorithms: Decentralized SGLD (DE-SGLD) and Decentralized SGHMC (DE-SGHMC) which are adaptations of SGLD and SGHMC methods that allow scaleable Bayesian inference in the decentralized setting for large datasets. We show that when the posterior distribution is strongly log-concave and smooth, the iterates of these algorithms converge linearly to a neighborhood of the target distribution in the 2-Wasserstein distance if their parameters are selected appropriately. We illustrate the efficiency of our algorithms on decentralized Bayesian linear regression and Bayesian logistic regression problems.