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We propose a stochastic variance-reduced cubic regularized Newton method fornon-convex optimization. At the core of our algorithm is a novelsemi-stochastic gradient along with a semi-stochastic Hessian, which arespecifically designed for cubic regularization method. We show that ouralgorithm is guaranteed to converge to an$(\epsilon,\sqrt{\epsilon})$-approximately local minimum within$\tilde{O}(n^{4/5}/\epsilon^{3/2})$ second-order oracle calls, whichoutperforms the state-of-the-art cubic regularization algorithms includingsubsampled cubic regularization. Our work also sheds light on the applicationof variance reduction technique to high-order non-convex optimization methods.Thorough experiments on various non-convex optimization problems support ourtheory.

Stochastic Variance-Reduced Cubic Regularized Newton Method