Convergence Analysis of Proximal Gradient with Momentum for Nonconvex Optimization
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Proceedings of the 34th International Conference on Machine Learning, PMLR 70:21112119, 2017.
Abstract
In this work, we investigate the accelerated proximal gradient method for nonconvex programming (APGnc). The method compares between a usual proximal gradient step and a linear extrapolation step, and accepts the one that has a lower function value to achieve a monotonic decrease. In specific, under a general nonsmooth and nonconvex setting, we provide a rigorous argument to show that the limit points of the sequence generated by APGnc are critical points of the objective function. Then, by exploiting the KurdykaLojasiewicz (KL) property for a broad class of functions, we establish the linear and sublinear convergence rates of the function value sequence generated by APGnc. We further propose a stochastic variance reduced APGnc (SVRGAPGnc), and establish its linear convergence under a special case of the KL property. We also extend the analysis to the inexact version of these methods and develop an adaptive momentum strategy that improves the numerical performance.
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