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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<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1810.10132v2">arXiv:1810.10132v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wmglvcrpsff2beqx4cl662hyra">fatcat:wmglvcrpsff2beqx4cl662hyra</a> </span>
more »... 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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