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arXiv · 1901.10682

On the Convergence of (Stochastic) Gradient Descent with Extrapolation for Non-Convex Optimization

Yi Xu·Zhuoning Yuan·Sen Yang·Rong Jin·Tianbao Yang
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Abstract

Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine learning tasks. However, it has not been analyzed for non-convex minimization and there still remains a gap between the theory and the practice. In this paper, we analyze gradient descent and stochastic gradient descent with extrapolation for finding an approximate first-order stationary point in smooth non-convex optimization problems. Our convergence upper bounds show that the algorithms with extrapolation can be accelerated than without extrapolation.

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Yi Xu, Zhuoning Yuan, Sen Yang, Rong Jin, Tianbao Yang. 2019-02-05. On the Convergence of (Stochastic) Gradient Descent with Extrapolation for Non-Convex Optimization. https://arxiv.org/abs/1901.10682

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