Natasha 2: Faster Non-Convex Optimization Than SGD

We design a stochastic algorithm to train any smooth neural network to $\epsilon$-approximate local minima, using $O({\epsilon }^{-3.25})$ backpropagations. The best result was essentially $O({\epsilon }^{-4})$ by SGD. More broadly, it finds $\epsilon$-approximate local minima of any smooth nonconvex function in rate $O({\epsilon }^{-3.25})$, with only oracle access to stochastic gradients.