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.
翻译：我们研究普遍动态减低遗憾的框架,并同时研究强力降低损失。我们在婴儿和王2021年解决了一个尚未解决的问题,我们通过表明在适当的学习设置中,强大的适应性算法可以实现几乎最佳的动态减慢,即:$tilde O(d ⁇ 1/3}n ⁇ 1/3 ⁇ text{TV}[u ⁇ 1:n}} ⁇ 2/3}\vee d)美元,而任何参照序列为$u_1\\ldots,u_n美元,其中美元是时间跨度,$\text{TV}[u ⁇ 1:n}]美元是参照国的完全挥霍。这些结果通过利用KKT规定的一些新结构得到促进,而Baby和Wang 2021年没有考虑到这些条件,这也导致其结果的其他改进,例如:(a) 处理非移动损失和(b) 改善对遗憾的维度依赖度。此外,我们还获得了几乎最佳的动态减速率,用于适当在线学习的排除损失和限制决定设定的美元。
相关内容
微信扫码咨询专知VIP会员