Stochastic Variance-Reduced Cubic Regularized Newton Method

Understand

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 $(\epsilon,\sqrt{\epsilon})$-approximately local minimum within $\tilde{O}(n^{4/5}/\epsilon^{3/2})$ 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.