Recycling intermediate steps to improve Hamiltonian Monte Carlo

TL;DR

This paper introduces a simple, provably accurate method to enhance Hamiltonian Monte Carlo by recycling intermediate states along trajectories, significantly improving efficiency with minimal additional computational cost.

Contribution

The authors propose a novel recycling technique for intermediate states in HMC that is easy to implement and improves computational efficiency without extra cost.

Findings

Substantial efficiency gains demonstrated in experiments

Applicable to the no-U-turn sampler, a popular HMC variant

Requires minimal programming effort

Abstract

Hamiltonian Monte Carlo (HMC) and related algorithms have become routinely used in Bayesian computation. In this article, we present a simple and provably accurate method to improve the efficiency of HMC and related algorithms with essentially no extra computational cost. This is achieved by {recycling the intermediate states along simulated trajectories of Hamiltonian dynamics. Standard algorithms use only the end points of trajectories, wastefully discarding all the intermediate states. Compared to the alternative methods for utilizing the intermediate states, our algorithm is simpler to apply in practice and requires little programming effort beyond the usual implementations of HMC and related algorithms. Our algorithm applies straightforwardly to the no-U-turn sampler, arguably the most popular variant of HMC. Through a variety of experiments, we demonstrate that our recycling algorithm yields substantial computational efficiency gains.