Natasha 2: Faster Non-Convex Optimization Than SGD

Understand

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.