Asynchronous Stochastic Gradient MCMC with Elastic Coupling

TL;DR

This paper introduces an asynchronous parallel MCMC method using elastic coupling in stochastic gradient Hamiltonian Monte Carlo, significantly improving sampling speed and robustness against stale gradients.

Contribution

It proposes a novel elastic coupling approach that enables asynchronous parallel MCMC sampling, transforming sequential algorithms into efficient parallel methods.

Findings

Parallel sampler speeds up exploration of the target distribution.

The method is less affected by stale gradients compared to naive parallelization.

Empirical results demonstrate improved sampling efficiency.

Abstract

We consider parallel asynchronous Markov Chain Monte Carlo (MCMC) sampling for problems where we can leverage (stochastic) gradients to define continuous dynamics which explore the target distribution. We outline a solution strategy for this setting based on stochastic gradient Hamiltonian Monte Carlo sampling (SGHMC) which we alter to include an elastic coupling term that ties together multiple MCMC instances. The proposed strategy turns inherently sequential HMC algorithms into asynchronous parallel versions. First experiments empirically show that the resulting parallel sampler significantly speeds up exploration of the target distribution, when compared to standard SGHMC, and is less prone to the harmful effects of stale gradients than a naive parallelization approach.