Guaranteed Sufficient Decrease for Stochastic Variance Reduced Gradient Optimization

TL;DR

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

Contribution

The paper proposes a novel sufficient decrease criterion and algorithms (SVRG-SD and SAGA-SD) 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 settings.

Show improved performance in practical applications.

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.