On the Convergence of Adaptive Gradient Methods for Nonconvex Optimization

Published: 16 Mar 2024, Last Modified: 16 Mar 2024Accepted by TMLREveryoneRevisionsBibTeX
Abstract: Adaptive gradient methods are workhorses in deep learning. However, the convergence guarantees of adaptive gradient methods for nonconvex optimization have not been thoroughly studied. In this paper, we provide a fine-grained convergence analysis for a general class of adaptive gradient methods including AMSGrad, RMSProp and AdaGrad. For smooth nonconvex functions, we prove that adaptive gradient methods in expectation converge to a first-order stationary point. Our convergence rate is better than existing results for adaptive gradient methods in terms of dimension. In addition, we also prove high probability bounds on the convergence rates of AMSGrad, RMSProp as well as AdaGrad, which have not been established before. Our analyses shed light on better understanding the mechanism behind adaptive gradient methods in optimizing nonconvex objectives.
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Submission Length: Regular submission (no more than 12 pages of main content)
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Assigned Action Editor: ~Peter_Richtarik1
Submission Number: 1878