We introduce a transformation framework that can be utilized to develop online algorithms with low $\epsilon$-approximate regret in the random-order model from offline approximation algorithms. We first give a general reduction theorem that transforms an offline approximation algorithm with low average sensitivity to an online algorithm with low $\epsilon$-approximate regret. We then demonstrate that offline approximation algorithms can be transformed into a low-sensitivity version using a coreset construction method. To showcase the versatility of our approach, we apply it to various problems, including online $(k,z)$-clustering, online matrix approximation, and online regression, and successfully achieve polylogarithmic $\epsilon$-approximate regret for each problem. Moreover, we show that in all three cases, our algorithm also enjoys low inconsistency, which may be desired in some online applications.

翻译：我们提出了一种转换框架，可用于从离线近似算法出发，在随机顺序模型下设计具有低$\epsilon$-近似遗憾的在线算法。首先，我们给出一个通用归约定理，该定理将具有低平均灵敏度的离线近似算法转换为具有低$\epsilon$-近似遗憾的在线算法。接着，我们证明通过使用核心集构造方法，可以将离线近似算法转换为低灵敏度版本。为展示该方法的通用性，我们将其应用于多种问题，包括在线$(k,z)$-聚类、在线矩阵近似和在线回归，并成功为每个问题实现了多对数级别的$\epsilon$-近似遗憾。此外，我们证明在以上三种情形中，我们的算法还具备低不一致性，这在某些在线应用中可能具有重要价值。