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

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 methods with extrapolation for finding an approximate first-order stationary point of smooth non-convex optimization problems. Our convergence upper bounds show that the algorithms with extrapolation could be potentially faster than without extrapolation.