Accelerate Langevin Sampling with Birth-Death process and Exploration Component

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 \textit{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 process determines sampling efficiency. Moreover, we prove exponential asymptotic convergence under mild assumption. Finally, we test on experiments from previous literature and compared our methodology to previous ones.