Web: http://arxiv.org/abs/2201.11411

Jan. 28, 2022, 2:11 a.m. | Huan Li, Zhouchen Lin

cs.LG updates on arXiv.org arxiv.org

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 …

arxiv complexity gradient math

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