Guaranteed Sufficient Decrease for Stochastic Variance Reduced Gradient Optimization

Fanhua Shang, Yuanyuan Liu, Kaiwen Zhou, James Cheng, Kelvin Kai Wing Ng, Yuichi Yoshida
Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, PMLR 84:1027-1036, 2018.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v84-shang18a, title = {Guaranteed Sufficient Decrease for Stochastic Variance Reduced Gradient Optimization}, author = {Shang, Fanhua and Liu, Yuanyuan and Zhou, Kaiwen and Cheng, James and Ng, Kelvin Kai Wing and Yoshida, Yuichi}, booktitle = {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics}, pages = {1027--1036}, year = {2018}, editor = {Storkey, Amos and Perez-Cruz, Fernando}, volume = {84}, series = {Proceedings of Machine Learning Research}, month = {09--11 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v84/shang18a/shang18a.pdf}, url = {https://proceedings.mlr.press/v84/shang18a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Guaranteed Sufficient Decrease for Stochastic Variance Reduced Gradient Optimization %A Fanhua Shang %A Yuanyuan Liu %A Kaiwen Zhou %A James Cheng %A Kelvin Kai Wing Ng %A Yuichi Yoshida %B Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2018 %E Amos Storkey %E Fernando Perez-Cruz %F pmlr-v84-shang18a %I PMLR %P 1027--1036 %U https://proceedings.mlr.press/v84/shang18a.html %V 84 %X 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.
APA
Shang, F., Liu, Y., Zhou, K., Cheng, J., Ng, K.K.W. & Yoshida, Y.. (2018). Guaranteed Sufficient Decrease for Stochastic Variance Reduced Gradient Optimization. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 84:1027-1036 Available from https://proceedings.mlr.press/v84/shang18a.html.

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