Smoothed Online Optimization for Regression and Control [article]

Gautam Goel, Adam Wierman
<span title="2019-04-04">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
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 ϵ-smooth, OBD has near-optimal dynamic regret and maintains
more &raquo; ... rong 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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