Guaranteed Sufficient Decrease for Stochastic Variance Reduced Gradient Optimization

By Fanhua Shang, Yuanyuan Liu, Kaiwen Zhou, James Cheng, Kelvin Kai Wing Ng, Yuichi Yoshida. 2018

9 citations recorded by the source corpus.

In this paper, we propose a novel sufficient decrease technique for stochastic variance reduced gradient descent methods such as SVRG and SAGA. In order to make sufficient decrease for stochastic optimization, we design a new sufficient decrease criterion, which yields sufficient decrease versions of stochastic variance reduction algorithms such as SVRG-SD and SAGA-SD as a byproduct. We introduce a coefficient to scale current iterate and to satisfy the sufficient decrease property, which takes the decisions to shrink, expand or even move in the opposite direction, and then give two specific update rules of the coefficient for Lasso and ridge regression. Moreover, we analyze the convergence properties of our algorithms for strongly convex problems, which show that our algorithms attain linear convergence rates. We also provide the convergence guarantees of our algorithms for non-strongly convex problems. Our experimental results further verify that our algorithms achieve significantly better performance than their counterparts.

Subfields: Artificial Intelligence, Computational Mechanics, Optimization & Training

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Citations in the corpus

Painless Stochastic Gradient: Interpolation, Line-Search, and Convergence Rates (2019, methodology): “Moreover, VR makes setting the learning rate easier and there has been work exploring the use of line-search techniques for automatically setting the step-size for these methods [74, 73, 83, 78].”