Double-Loop Unadjusted Langevin Algorithm
Abstract
A well-known first-order method for sampling from log-concave probability distributions is the Unadjusted Langevin Algorithm (ULA). This work proposes a new annealing step-size schedule for ULA, which allows to prove new convergence guarantees for sampling from a smooth log-concave distribution, which are not covered by existing state-of-the-art convergence guarantees. To establish this result, we derive a new theoretical bound that relates the Wasserstein distance to total variation distance between any two log-concave distributions that complements the reach of Talagrand T2 inequality. Moreover, applying this new step size schedule to an existing constrained sampling algorithm, we show state-of-the-art convergence rates for sampling from a constrained log-concave distribution, as well as improved dimension dependence.
Cite
@article{arxiv.2007.01147,
title = {Double-Loop Unadjusted Langevin Algorithm},
author = {Paul Rolland and Armin Eftekhari and Ali Kavis and Volkan Cevher},
journal= {arXiv preprint arXiv:2007.01147},
year = {2020}
}