We propose a stochastic variance-reduced cubic regularized Newton method for non-convex optimization. At the core of our algorithm is a novel semi-stochastic gradient along with a semi-stochastic Hessian, which are specifically designed for cubic regularization method. We show that our algorithm is guaranteed to converge to an ( , √ )-approximately local minimum within O(n 4/5 / 3/2 ) second-order oracle calls, which outperforms the state-of-the-art cubic regularization algorithms including subsampled cubic regularization. Our work also sheds light on the application of variance reduction technique to high-order non-convex optimization methods. Thorough experiments on various non-convex optimization problems support our theory.
Recently, stochastic variance reduced cubic regularization method (SVRC) REF was proposed, which achieves the best-known second-order oracle complexity among existing cubic regularization methods.
Stochastic Variance-Reduced Cubic Regularized Newton Method
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