Convergence of a Sequential Monte Carlo algorithm towards multimodal distributions

We study a sequential Monte Carlo (SMC) algorithm to sample from the Gibbs measure with a non-convex energy function at a low temperature. Sampling from multimodal distributions is a challenge that the classical algorithms become extremely slow, for example, the time complexity of obtaining good samples by Langevin Monte Carlo is exponential in the inverse temperature. Our main results show that under general non-degeneracy conditions, the Annealed Sequential Monte Carlo (ASMC) algorithm produces samples from multimodal distributions with time complexity that is a polynomial in the inverse temperature, with a precise dimension independent degree. Part of the talk is based on the joint work with Gautam Iyer and Dejan Slepcev.