Asynchronous Stochastic Gradient MCMC with Elastic Coupling
This work addresses inefficiencies in parallel MCMC for gradient-based problems, offering a practical improvement for researchers and practitioners in machine learning and statistics.
The paper tackled the problem of slow exploration in parallel asynchronous MCMC sampling by introducing an elastic coupling term into stochastic gradient Hamiltonian Monte Carlo (SGHMC), which significantly speeds up exploration compared to standard SGHMC and reduces issues from stale gradients.
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.