Accelerate Langevin Sampling with Birth-Death process and Exploration
  Component
Lezhi Tan Jianfeng Lu
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.