Stochastic Particle-Optimization Sampling and the Non-Asymptotic Convergence Theory

Jianyi Zhang, Ruiyi Zhang, Lawrence Carin, Changyou Chen*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Particle-optimization-based sampling (POS) is a recently developed effective sampling technique that interactively updates a set of particles to approximate a target distribution. A representative algorithm is the Stein variational gradient descent (SVGD). We prove, under certain conditions, SVGD experiences a theoretical pitfall, i.e., particles tend to collapse. As a remedy, we generalize POS to a stochastic setting by injecting random noise into particle updates, thus termed stochastic particle-optimization sampling (SPOS). Notably, for the first time, we develop non asymptotic convergence theory for the SPOS framework (related to SVGD), characterizing algorithm convergence in terms of the 1-Wasserstein distance w.r.t. the numbers of particles and iterations. Somewhat surprisingly, with the same number of updates (not too large) for each particle, our theory suggests adopting more particles does not necessarily lead to a better approximation of a target distribution, due to limited computational budget and numerical errors. This phenomenon is also observed in SVGD and verified via a synthetic experiment. Extensive experimental results verify our theory and demonstrate the effectiveness of our proposed framework.

Original languageEnglish
Title of host publicationINTERNATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE AND STATISTICS, VOL 108
EditorsS Chiappa, R Calandra
PublisherADDISON-WESLEY PUBL CO
Pages1877-1886
Number of pages10
StatePublished - 2020
Externally publishedYes
Event23rd International Conference on Artificial Intelligence and Statistics (AISTATS) -
Duration: Aug 26 2020Aug 28 2020

Publication series

NameProceedings of Machine Learning Research
PublisherADDISON-WESLEY PUBL CO
Volume108
ISSN (Print)2640-3498

Conference

Conference23rd International Conference on Artificial Intelligence and Statistics (AISTATS)
Period08/26/2008/28/20

Keywords

  • GRANULAR MEDIA EQUATIONS

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