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As a metric to measure the performance of an online method, dynamic regretwith switching cost has drawn much attention for online decision makingproblems. Although the sublinear regret has been provided in many previousresearches, we still have little knowledge about the relation between thedynamic regret and the switching cost. In the paper, we investigate therelation for two classic online settings: Online Algorithms (OA) and OnlineConvex Optimization (OCO). We provide a new theoretical analysis framework,which shows an interesting observation, that is, the relation between theswitching cost and the dynamic regret is different for settings of OA and OCO.Specifically, the switching cost has significant impact on the dynamic regretin the setting of OA. But, it does not have an impact on the dynamic regret inthe setting of OCO. Furthermore, we provide a lower bound of regret for thesetting of OCO, which is same with the lower bound in the case of no switchingcost. It shows that the switching cost does not change the difficulty of onlinedecision making problems in the setting of OCO.

Understand Dynamic Regret with Switching Cost for Online Decision Making