# Decentralized Langevin Dynamics

arXiv: https://arxiv.org/abs/2001.00665 · HTML: https://mlsanity.com/paper/2001.00665/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jan 2020.

## Built on by (most cited first, 1 of 1)

- [Decentralized Bayesian Learning with Metropolis-Adjusted Hamiltonian Monte Carlo](https://mlsanity.com/paper/2107.07211/) (2021)

## Abstract (arXiv)

Langevin MCMC gradient optimization is a class of increasingly popular methods for estimating a posterior distribution. This paper addresses the algorithm as applied in a decentralized setting, wherein data is distributed across a network of agents which act to cooperatively solve the problem using peer-to-peer gossip communication. We show, theoretically, results in 1) the time-complexity to ε-consensus for the continuous time stochastic differential equation, 2) convergence rate in L2 norm to consensus for the discrete implementation as defined by the Euler-Maruyama discretization and 3) convergence rate in the Wasserstein metric to the optimal stationary distribution for the discretized dynamics.