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We consider Online Convex Optimization (OCO) in the setting where the costsare $m$-strongly convex and the online learner pays a switching cost forchanging decisions between rounds. We show that the recently proposed OnlineBalanced Descent (OBD) algorithm is constant competitive in this setting, withcompetitive 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 strongper-round accuracy. We demonstrate the generality of our approach by showingthat the OBD framework can be used to construct competitive algorithms for avariety of online problems across learning and control, including onlinevariants of ridge regression, logistic regression, maximum likelihoodestimation, and LQR control.

Smoothed Online Optimization for Regression and Control