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Restarted Nonconvex Accelerated Gradient Descent: No More Polylogarithmic Factor in the $O(\epsilon^{-7/4})$ Complexity
Huan Li · Zhouchen Lin
This paper studies the accelerated gradient descent for general nonconvex problems under the gradient Lipschitz and Hessian Lipschitz assumptions. We establish that a simple restarted accelerated gradient descent (AGD) finds an $\epsilon$-approximate first-order stationary point in $O(\epsilon^{-7/4})$ gradient computations with simple proofs. Our complexity does not hide any polylogarithmic factors, and thus it improves over the state-of-the-art one by the $O(\log\frac{1}{\epsilon})$ factor. Our simple algorithm only consists of Nesterov's classical AGD and a restart mechanism, and it does not need the negative curvature exploitation or the optimization of regularized surrogate functions. Technically, our simple proof does not invoke the analysis for the strongly convex AGD, which is crucial to remove the $O(\log\frac{1}{\epsilon})$ factor.
Author Information
Huan Li (Nankai University)
Zhouchen Lin (Peking University)
Related Events (a corresponding poster, oral, or spotlight)
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2022 Poster: Restarted Nonconvex Accelerated Gradient Descent: No More Polylogarithmic Factor in the $O(\epsilon^{-7/4})$ Complexity »
Tue. Jul 19th through Wed the 20th Room Hall E #609
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