Convergence of Langevin AIS for multimodal distributions
Probability
2026-04-21 v1 Statistics Theory
Statistics Theory
Abstract
We study convergence rates of the annealed importance sampling algorithm (Neal '01) combined with Langevin Monte Carlo when the target is a multimodal Gibbs measure. The main result shows that for a fixed error threshold, the time complexity is quadratic in the inverse temperature. We identify a simple and useful quantity that controls the sampling error for AIS in a general setting, and then bound this quantity in our setting using spectral estimates. We also study an autonormalized version and obtain bounds for the time complexity in terms of the inverse temperature.
Keywords
Cite
@article{arxiv.2604.17526,
title = {Convergence of Langevin AIS for multimodal distributions},
author = {Akshat Agarwal and Gautam Iyer and Aidan Jameson and Seungjae Son and Wyatt Wimmer},
journal= {arXiv preprint arXiv:2604.17526},
year = {2026}
}