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arXiv · 1810.10132

Smoothed Online Optimization for Regression and Control

Gautam Goel·Adam Wierman
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Abstract

We consider Online Convex Optimization (OCO) in the setting where the costs are $m$-strongly convex and the online learner pays a switching cost for changing decisions between rounds. We show that the recently proposed Online Balanced Descent (OBD) algorithm is constant competitive in this setting, with competitive ratio $3 + O(1/m)$, irrespective of the ambient dimension. Additionally, we show that when the sequence of cost functions is $\epsilon$-smooth, OBD has near-optimal dynamic regret and maintains strong per-round accuracy. We demonstrate the generality of our approach by showing that the OBD framework can be used to construct competitive algorithms for a variety of online problems across learning and control, including online variants of ridge regression, logistic regression, maximum likelihood estimation, and LQR control.

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Gautam Goel, Adam Wierman. 2018-10-23. Smoothed Online Optimization for Regression and Control. https://arxiv.org/abs/1810.10132

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