Guaranteed Sufficient Decrease for Stochastic Variance Reduced Gradient Optimization
This work addresses optimization efficiency for machine learning practitioners by providing incremental improvements to existing stochastic variance reduction methods.
The paper tackles the problem of improving stochastic variance reduced gradient methods like SVRG and SAGA by introducing a sufficient decrease technique, resulting in algorithms such as SVRG-SD and SAGA-SD that achieve linear convergence rates for strongly convex problems and show significantly better performance in experiments.
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.