Maximizing conditional entropy of Hamiltonian Monte Carlo sampler.

The performance of Hamiltonian Monte Carlo (HMC) sampler depends critically on some algorithm parameters such as the integration time. One approach to tune these parameters is to optimize them with respect to certain prescribed design criterion or performance measure. We propose a conditional entropy based design criterion to optimize the integration time, which can avoid some potential issues in the often used jumping-distance based measures. For near-Gaussian distributions, we are able to derive the optimal integration time with respect to the conditional entropy criterion analytically. Based on the results, we propose an adaptive HMC algorithm, and we then demonstrate the performance of the proposed algorithm with numerical examples.