Title: Natasha 2: Faster Non-Convex Optimization Than SGD,
Abstract: We design a stochastic algorithm to train any smooth neural network to
$\varepsilon$-approximate local minima, using $O(\varepsilon^{-3.25})$
backpropagations. The best result was essentially $O(\varepsilon^{-4})$ by SGD.
More broadly, it finds $\varepsilon$-approximate local minima of any smooth
nonconvex function in rate $O(\varepsilon^{-3.25})$, with only oracle access to
stochastic gradients.