Hamiltonian Monte Carlo Without Detailed Balance

We present a method for performing Hamiltonian Monte Carlo that largely eliminates sample re-jection. In situations that would normally lead to rejection, instead a longer trajectory is computed until a new state is reached that can be accepted. This is achieved using Markov chain transitions that satisfy the fixed point equation, but do not satisfy detailed balance. The resulting algorithm significantly suppresses the random walk behav-ior and wasted function evaluations that are typ-ically the consequence of update rejection. We demonstrate a greater than factor of two improve-ment in mixing time on three test problems. We release the source code as Python and MATLAB packages. 1