Guaranteed Sufficient Decrease for Variance Reduced Stochastic Gradient Descent

TL;DR

This paper introduces a new sufficient decrease technique for variance reduced stochastic gradient descent methods, improving convergence and performance in convex and non-convex optimization tasks.

Contribution

It proposes a novel sufficient decrease criterion and algorithms with proven linear convergence for strongly convex problems and guarantees for non-strongly convex cases.

Findings

Algorithms outperform existing methods in experiments

Achieve linear convergence in strongly convex cases

Show improved performance in non-strongly convex problems

Abstract

In this paper, we propose a novel sufficient decrease technique for variance reduced stochastic gradient descent methods such as SAG, 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 variance reduction algorithms such as SVRG-SD and SAGA-SD as a byproduct. We introduce a coefficient to scale current iterate and satisfy the sufficient decrease property, which takes the decisions to shrink, expand or 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 both of 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.