  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.
