Title
Momentum Schemes with Stochastic Variance Reduction for Nonconvex Composite Optimization.
Abstract
Two new stochastic variance-reduced algorithms named SARAH and SPIDER have been recently proposed, and SPIDER has been shown to achieve a near-optimal gradient oracle complexity for nonconvex optimization. However, the theoretical advantage of SPIDER does not lead to substantial improvement of practical performance over SVRG. To address this issue, momentum technique can be a good candidate to improve the performance of SPIDER. However, existing momentum schemes used in variance-reduced algorithms are designed specifically for convex optimization, and are not applicable to nonconvex scenarios. In this paper, we develop novel momentum schemes with flexible coefficient settings to accelerate SPIDER for nonconvex and nonsmooth composite optimization, and show that the resulting algorithms achieve the near-optimal gradient oracle complexity for achieving a generalized first-order stationary condition. Furthermore, we generalize our algorithm to online nonconvex and nonsmooth optimization, and establish an oracle complexity result that matches the state-of-the-art. Our extensive experiments demonstrate the superior performance of our proposed algorithm over other stochastic variance-reduced algorithms.
Year
Venue
DocType
2019
arXiv: Optimization and Control
Journal
Volume
Citations 
PageRank 
abs/1902.02715
1
0.35
References 
Authors
13
5
Name
Order
Citations
PageRank
Yi Zhou16517.55
Wang, Zhe244.13
Kaiyi Ji3146.58
Yingbin Liang41646147.64
Vahid Tarokh5103731461.51