  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.
