UniXGrad: A Universal, Adaptive Algorithm with Optimal Guarantees for Constrained Optimization

We propose a novel adaptive, accelerated algorithm for the stochastic constrained convex optimization setting. Our method, which is inspired by the Mirror-Prox method, \emph{simultaneously} achieves the optimal rates for smooth/non-smooth problems with either deterministic/stochastic first-order oracles. This is done without any prior knowledge of the smoothness nor the noise properties of the problem. To the best of our knowledge, this is the first adaptive, unified algorithm that achieves the optimal rates in the constrained setting. We demonstrate the practical performance of our framework through extensive numerical experiments.


Published in:
[Proceedings of NEURips 2019]
Presented at:
NeurIPS 2019 : Thirty-third Conference on Neural Information Processing Systems, Vancouver, Canada, December 8-14, 2019
Year:
2019
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 Record created 2019-09-17, last modified 2019-11-29

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