@inproceedings{e663077bd41d443c90871e3c8f05708f,
title = "{"}Convex until proven guilty{"}: Dimension-free acceleration of gradient descent on non-convex functions",
abstract = "We develop and analyze a variant of Nesterov's accelerated gradient descent (AGD) for minimization of smooth non-convex functions. We prove that one of two cases occurs: either our AGD variant converges quickly, as if the function was convex, or we produce a certificate that the function is {"}guilty{"} of being non-convex. This non-convexity certificate allows us to exploit negative curvature and obtain deterministic, dimension-free acceleration of convergence for non-convex functions. For a function /with Lipschitz continuous gradient and Hessian, we compute a point x with ∥Vf(x)∥ ≤ ϵ in O(ϵ-7/4 log(l/ϵ)) gradient and function evaluations. Assuming additionally that the third derivative is Lipschitz, we require only O(ϵ-5/3log(1/ϵ)) evaluations.",
author = "Yair Cannon and Duchi, {John C.} and Oliver Hinder and Aaron Sidford",
note = "Publisher Copyright: {\textcopyright} 2017 by the author(s).; 34th International Conference on Machine Learning, ICML 2017 ; Conference date: 06-08-2017 Through 11-08-2017",
year = "2017",
language = "الإنجليزيّة",
series = "34th International Conference on Machine Learning, ICML 2017",
pages = "1069--1091",
booktitle = "34th International Conference on Machine Learning, ICML 2017",
}