An Online Algorithm for Smoothed Online Convex Optimization

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. We demonstrate the generality of our approach by showing that the OBD framework can be used to construct competitive a algorithm for LQR control.

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