Guaranteed Sufficient Decrease for Variance Reduced Stochastic Gradient Descent
This work addresses optimization efficiency for machine learning practitioners by offering incremental improvements to existing variance reduction methods.
The paper tackles the problem of improving convergence in variance-reduced stochastic gradient descent methods by proposing a novel sufficient decrease technique, resulting in algorithms like 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 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.