Convergence of a Sequential Monte Carlo algorithm towards multimodal distributions on Rd

Abstract: We study a sequential Monte Carlo algorithm to sample from the Gibbs measure supported on Rd with a non-convex energy function at a low temperature. In an earlier joint work, we proved that the algorithm samples from Gibbs measures supported on torus with time complexity that is polynomial in the inverse temperature; however, the approach breaks down in the non-compact setting. This work overcomes this obstacle and establishes a similar result for sampling from Gibbs measures supported on Rd. Our main result shows convergence of Monte Carlo estimators with time complexity that, approximately, scales like the seventh power of the inverse temperature, the square of the inverse allowed absolute error and the square of the inverse allowed probability error.