Counterdiabatic Hamiltonian Monte Carlo

TL;DR

Counterdiabatic Hamiltonian Monte Carlo (CHMC) introduces a learned counterdiabatic term to improve the efficiency of Hamiltonian Monte Carlo, especially for challenging multimodal distributions, by accelerating the sampling process.

Contribution

This paper proposes CHMC, a novel method that incorporates a learned counterdiabatic term into HMC to enhance sampling efficiency for complex distributions.

Findings

CHMC accelerates convergence on benchmark problems.

It reduces the need for slow distribution interpolation.

Demonstrates improved sampling efficiency over traditional HMC.

Abstract

Hamiltonian Monte Carlo (HMC) is a state of the art method for sampling from distributions with differentiable densities, but can converge slowly when applied to challenging multimodal problems. Running HMC with a time varying Hamiltonian, in order to interpolate from an initial tractable distribution to the target of interest, can address this problem. In conjunction with a weighting scheme to eliminate bias, this can be viewed as a special case of Sequential Monte Carlo (SMC) sampling \cite{doucet2001introduction}. However, this approach can be inefficient, since it requires slow change between the initial and final distribution. Inspired by \cite{sels2017minimizing}, where a learned \emph{counterdiabatic} term added to the Hamiltonian allows for efficient quantum state preparation, we propose \emph{Counterdiabatic Hamiltonian Monte Carlo} (CHMC), which can be viewed as an SMC sampler with a more efficient kernel. We establish its relationship to recent proposals for accelerating gradient-based sampling with learned drift terms, and demonstrate on simple benchmark problems.