Double-Loop Unadjusted Langevin Algorithm

Part of Proceedings of the International Conference on Machine Learning 1 pre-proceedings (ICML 2020)

Bibtex »Metadata »Paper »Supplemental »

Bibtek download is not availble in the pre-proceeding


Authors

Paul Rolland, Armin Eftekhari, Ali Kavis, Volkan Cevher

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 $T_2$ 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.