Momentum-based variance-reduced proximal stochastic gradient method for composite nonconvex stochastic optimization

• URL: http://arxiv.org/abs/2006.00425v3
• Date: Fri, 29 Apr 2022 11:45:38 GMT
• Title: Momentum-based variance-reduced proximal stochastic gradient method for composite nonconvex stochastic optimization
• Authors: Yangyang Xu and Yibo Xu
• Abstract summary: gradient learning methods (SGMs) have been extensively used for solving problems or large-scale machine learning problems. We propose a new SGM, PStorm, for solving nonsmooth problems.
• Score: 8.014215296763435
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Stochastic gradient methods (SGMs) have been extensively used for solving stochastic problems or large-scale machine learning problems. Recent works employ various techniques to improve the convergence rate of SGMs for both convex and nonconvex cases. Most of them require a large number of samples in some or all iterations of the improved SGMs. In this paper, we propose a new SGM, named PStorm, for solving nonconvex nonsmooth stochastic problems. With a momentum-based variance reduction technique, PStorm can achieve the optimal complexity result $O(\varepsilon^{-3})$ to produce a stochastic $\varepsilon$-stationary solution, if a mean-squared smoothness condition holds. Different from existing optimal methods, PStorm can achieve the ${O}(\varepsilon^{-3})$ result by using only one or $O(1)$ samples in every update. With this property, PStorm can be applied to online learning problems that favor real-time decisions based on one or $O(1)$ new observations. In addition, for large-scale machine learning problems, PStorm can generalize better by small-batch training than other optimal methods that require large-batch training and the vanilla SGM, as we demonstrate on training a sparse fully-connected neural network and a sparse convolutional neural network.

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