Guaranteed Sufficient Decrease for Stochastic Variance Reduced Gradient Optimization
arXiv:1802.09933
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.
arXiv comment24 pages, 10 figures, AISTATS 2018. arXiv admin note: text overlap with arXiv:1703.06807
References in corpus (4)
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- A Stochastic Gradient Method with an Exponential Convergence Rate for Finite Training Sets
- Making Gradient Descent Optimal for Strongly Convex Stochastic Optimization
- Stochastic Gradient Descent for Non-smooth Optimization: Convergence Results and Optimal Averaging Schemes