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arXiv · 1711.02838

Stochastic Cubic Regularization for Fast Nonconvex Optimization

Nilesh Tripuraneni·Mitchell Stern·Chi Jin·Jeffrey Regier·Michael I. Jordan
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Abstract

This paper proposes a stochastic variant of a classic algorithm---the cubic-regularized Newton method [Nesterov and Polyak 2006]. The proposed algorithm efficiently escapes saddle points and finds approximate local minima for general smooth, nonconvex functions in only $\mathcal{\tilde{O}}(\epsilon^{-3.5})$ stochastic gradient and stochastic Hessian-vector product evaluations. The latter can be computed as efficiently as stochastic gradients. This improves upon the $\mathcal{\tilde{O}}(\epsilon^{-4})$ rate of stochastic gradient descent. Our rate matches the best-known result for finding local minima without requiring any delicate acceleration or variance-reduction techniques.

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BibTeXRIS

Nilesh Tripuraneni, Mitchell Stern, Chi Jin, Jeffrey Regier, Michael I. Jordan. 2017-11-08. Stochastic Cubic Regularization for Fast Nonconvex Optimization. https://arxiv.org/abs/1711.02838

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