Stochastic particle-optimization sampling (SPOS) is a recently-developed scalable Bayesian sampling framework unifying stochastic gradient MCMC (SG-MCMC) and Stein variational gradient descent (SVGD) algorithms based on Wasserstein gradient flows. With a rigorous nonasymptotic convergence theory developed, SPOS can avoid the particle-collapsing pitfall of SVGD. However, the variance-reduction effect in SPOS has not been clear. In this paper, we address this gap by presenting several variancereduction techniques for SPOS. Specifically, we propose three variants of variance-reduced SPOS, called SAGA particle-optimization sampling (SAGA-POS), SVRG particle-optimization sampling (SVRG-POS) and a variant of SVRGPOS which avoids full gradient computations, denoted as SVRG-POS+. Importantly, we provide non-Asymptotic convergence guarantees for these algorithms in terms of the 2-Wasserstein metric and analyze their complexities. The results show our algorithms yield better convergence rates than existing variance-reduced variants of stochastic Langevin dynamics, though more space is required to store the particles in training. Our theory aligns well with experimental results on both synthetic and real datasets.
|Original language||English (US)|
|Title of host publication||37th International Conference on Machine Learning, ICML 2020|
|Editors||Hal Daume, Aarti Singh|
|Publisher||International Machine Learning Society (IMLS)|
|Number of pages||10|
|State||Published - 2020|
|Event||37th International Conference on Machine Learning, ICML 2020 - Virtual, Online|
Duration: Jul 13 2020 → Jul 18 2020
|Name||37th International Conference on Machine Learning, ICML 2020|
|Conference||37th International Conference on Machine Learning, ICML 2020|
|Period||07/13/20 → 07/18/20|
Bibliographical noteFunding Information:
The research performed at Duke University was supported in part by DARPA, DOE, NSF and ONR.
© 2020 by the Authors All rights reserved.
Copyright 2021 Elsevier B.V., All rights reserved.
ASJC Scopus subject areas
- Computational Theory and Mathematics
- Human-Computer Interaction