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We present new algorithms for optimizing non-smooth, non-convex stochasticobjectives based on a novel analysis technique. This improves the currentbest-known complexity for finding a $(\delta,\epsilon)$-stationary point from$O(\epsilon^{-4}\delta^{-1})$ stochastic gradient queries to$O(\epsilon^{-3}\delta^{-1})$, which we also show to be optimal. Our primarytechnique is a reduction from non-smooth non-convex optimization to onlinelearning, after which our results follow from standard regret bounds in onlinelearning. For deterministic and second-order smooth objectives, applying moreadvanced optimistic online learning techniques enables a new complexity of$O(\epsilon^{-1.5}\delta^{-0.5})$. Our techniques also recover all optimal orbest-known results for finding $\epsilon$ stationary points of smooth orsecond-order smooth objectives in both stochastic and deterministic settings.

Optimal Stochastic Non-smooth Non-convex Optimization through Online-to-Non-convex Conversion