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

中文翻译：

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了解在线决策转换成本的动态后悔

作为衡量在线方法性能的指标，具有切换成本的动态后悔已经引起了在线决策问题的广泛关注。尽管在之前的许多研究中已经提供了亚线性遗憾，但我们对两者之间的关系仍然知之甚少。动态后悔和转换成本. 在本文中，我们研究了两种经典在线设置的关系：在线算法 (OA) 和在线凸优化 (OCO)。我们提供了一个新的理论分析框架，展示了一个有趣的观察结果；也就是说，切换成本和动态后悔之间的关系对于 OA 和 OCO 的设置是不同的。具体来说，转换成本对OA设置中的动态后悔有显着影响。但对OCO设置中的动态后悔没有影响。此外，我们为 OCO 的设置提供了一个遗憾的下限，这与没有切换成本的情况下的下限相同。说明切换成本并没有改变OCO设置中在线决策问题的难度。