Accelerate Langevin Sampling with Birth-Death Process and Exploration Component

TL;DR

This paper introduces a novel sampling method combining birth-death processes and exploration strategies to efficiently sample multimodal distributions, accelerating convergence and improving exploration capabilities.

Contribution

The paper proposes a new sampling algorithm that leverages dual-temperature samplers and theoretical analysis to enhance multimodal distribution exploration.

Findings

Accelerates sampling of multimodal distributions.

Proves exponential convergence under mild conditions.

Outperforms previous methods in experiments.

Abstract

Sampling a probability distribution with known likelihood is a fundamental task in computational science and engineering. Aiming at multimodality, we propose a new sampling method that takes advantage of both birth-death process and exploration component. The main idea of this method is look before you leap. We keep two sets of samplers, one at warmer temperature and one at original temperature. The former one serves as pioneer in exploring new modes and passing useful information to the other, while the latter one samples the target distribution after receiving the information. We derive a mean-field limit and show how the exploration component accelerates the sampling process. Moreover, we prove exponential asymptotic convergence under mild assumption. Finally, we test on experiments from previous literature and compare our methodology to previous ones.