We study the framework of universal dynamic regret minimization with strongly convex losses. We answer an open problem in Baby and Wang 2021 by showing that in a proper learning setup, Strongly Adaptive algorithms can achieve the near optimal dynamic regret of $\tilde O(d^{1/3} n^{1/3}\text{TV}[u_{1:n}]^{2/3} \vee d)$ against any comparator sequence $u_1,\ldots,u_n$ simultaneously, where $n$ is the time horizon and $\text{TV}[u_{1:n}]$ is the Total Variation of comparator. These results are facilitated by exploiting a number of new structures imposed by the KKT conditions that were not considered in Baby and Wang 2021 which also lead to other improvements over their results such as: (a) handling non-smooth losses and (b) improving the dimension dependence on regret. Further, we also derive near optimal dynamic regret rates for the special case of proper online learning with exp-concave losses and an $L_\infty$ constrained decision set.

本文研究了强凸损失函数下的动态遗憾最小化框架，通过利用KKT条件所施加的许多新约束条件，我们回答了Baby和Wang 2021年提出的一个开放性问题，并展示了强适应算法在适当的学习设置下可以同时针对任何比较序列达到几乎最优的动态遗憾。此外，在处理非平滑损失和改善回避维度依赖性等方面，我们还取得了Baby和Wang 2021年工作的其他改进，并针对exp-concave损失和一个L∞受限决策集的特殊情况导出了几乎最优的动态遗憾率。

强凸损失理论在适当在线学习中的最优动态遗憾及其扩展