Optimal Rates for Random Order Online Optimization
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.
Cite
@article{arxiv.2106.15207,
title = {Optimal Rates for Random Order Online Optimization},
author = {Uri Sherman and Tomer Koren and Yishay Mansour},
journal= {arXiv preprint arXiv:2106.15207},
year = {2021}
}