Accelerate Langevin Sampling with Birth-Death Process and Exploration Component
This work addresses a fundamental challenge in computational science for researchers and practitioners dealing with complex, multimodal distributions, though it appears incremental as it builds on existing sampling techniques.
The authors tackled the problem of sampling multimodal probability distributions by proposing a new method that combines a birth-death process with an exploration component, using two sets of samplers at different temperatures to accelerate convergence. They demonstrated exponential asymptotic convergence and tested it on experiments, showing improved performance compared to previous methods.
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.