Natasha 2: Faster Non-Convex Optimization Than SGD

We design a stochastic algorithm to find $\varepsilon$-approximate local minima of any smooth nonconvex function in rate $O(\varepsilon^{-3.25})$, with only oracle access to stochastic gradients. The best result before this work was $O(\varepsilon^{-4})$ by stochastic gradient descent (SGD).