An Improved Analysis of Langevin Algorithms with Prior Diffusion for Non-Log-Concave Sampling

arXiv:2403.06183v1 Announce Type: new
Abstract: Understanding the dimension dependency of computational complexity in high-dimensional sampling problem is a fundamental problem, both from a practical and theoretical perspective. Compared with samplers with unbiased stationary distribution, e.g., Metropolis-adjusted Langevin algorithm (MALA), biased samplers, e.g., Underdamped Langevin Dynamics (ULD), perform better in low-accuracy cases just because a lower dimension dependency in their complexities. Along this line, Freund et al. (2022) suggest that the modified Langevin algorithm with prior diffusion is able to converge …

abstract algorithm algorithms analysis arxiv complexity computational cs.lg diffusion distribution dynamics math.oc math.st metropolis perspective practical prior sampling stat.ml stat.th type unbiased understanding