Adaptive Hamiltonian and Riemann Manifold Monte Carlo Samplers

In this paper we address the widely-experienced difficulty in tuning Hamiltonian-based Monte Carlo samplers. We develop an algorithm that allows for the adaptation of Hamiltonian and Riemann manifold Hamiltonian Monte Carlo samplers using Bayesian optimization that allows for infinite adaptation of the parameters of these samplers. We show that the resulting sampling algorithms are ergodic, and that the use of our adaptive algorithms makes it easy to obtain more efficient samplers, in some cases precluding the need for more complex solutions. Hamiltonian-based Monte Carlo samplers are widely known to be an excellent choice of MCMC method, and we aim with this paper to remove a key obstacle towards the more widespread use of these samplers in practice.