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Stochastic Cubic Regularization for Fast Nonconvex Optimization
Nilesh Tripuraneni · Mitchell Stern · Chi Jin · Jeffrey Regier · Michael Jordan

Wed Dec 05 12:50 PM -- 01:05 PM (PST) @ Room 517 CD
This paper proposes a stochastic variant of a classic algorithm---the cubic-regularized Newton method [Nesterov and Polyak]. 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.

Author Information

Nilesh Tripuraneni (UC Berkeley)
Mitchell Stern (UC Berkeley)
Chi Jin (University of California, Berkeley)
Jeffrey Regier (UC Berkeley)
Michael Jordan (UC Berkeley)

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