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Stochastic Cubic Regularization for Fast Nonconvex Optimization

2020-02-13 | |  66 |   37 |   0

Abstract

 This paper proposes a stochastic variant of a classic algorithm—the cubicregularized 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 image.png stochastic gradient and stochastic Hessian-vector product evaluations. The latter can be computed as efficiently as stochastic gradients. This improves upon the image.png 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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