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arXiv · 2106.15207

Optimal Rates for Random Order Online Optimization

Uri Sherman·Tomer Koren·Yishay Mansour
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Abstract

We study online convex optimization in the random order model, recently proposed by \citet{garber2020online}, where the loss functions may be chosen by an adversary, but are then presented to the online algorithm in a uniformly random order. Focusing on the scenario where the cumulative loss function is (strongly) convex, yet individual loss functions are smooth but might be non-convex, we give algorithms that achieve the optimal bounds and significantly outperform the results of \citet{garber2020online}, completely removing the dimension dependence and improving their scaling with respect to the strong convexity parameter. Our analysis relies on novel connections between algorithmic stability and generalization for sampling without-replacement analogous to those studied in the with-replacement i.i.d.~setting, as well as on a refined average stability analysis of stochastic gradient descent.

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Uri Sherman, Tomer Koren, Yishay Mansour. 2021-06-29. Optimal Rates for Random Order Online Optimization. https://arxiv.org/abs/2106.15207

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