Robust stochastic optimization with the proximal point method

07/31/2019

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by   Damek Davis, et al.

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Standard results in stochastic convex optimization bound the number of samples that an algorithm needs to generate a point with small function value in expectation. In this work, we show that a wide class of such algorithms on strongly convex problems can be augmented with sub-exponential confidence bounds at an overhead cost that is only polylogarithmic in the condition number and the confidence level. We discuss consequences both for streaming and offline algorithms.