A major technique in learning-augmented online algorithms is combining multiple algorithms or predictors. Since the performance of each predictor may vary over time, it is desirable to use not the single best predictor as a benchmark, but rather a dynamic combination which follows different predictors at different times. We design algorithms that combine predictions and are competitive against such dynamic combinations for a wide class of online problems, namely, metrical task systems. Against the best (in hindsight) unconstrained combination of $\ell$ predictors, we obtain a competitive ratio of $O(\ell^2)$, and show that this is best possible. However, for a benchmark with slightly constrained number of switches between different predictors, we can get a $(1+\epsilon)$-competitive algorithm. Moreover, our algorithms can be adapted to access predictors in a bandit-like fashion, querying only one predictor at a time. An unexpected implication of one of our lower bounds is a new structural insight about covering formulations for the $k$-server problem.

翻译：学习增强型在线算法中的一项主要技术是结合多种算法或预测器。由于每个预测器的性能可能随时间变化，因此理想的基准并非单一最佳预测器，而是能够在不同时间跟随不同预测器动态组合。我们设计了在广泛在线问题类（即度量任务系统）中，能够结合预测并与此类动态组合竞争的算法。针对（事后最优的）$\ell$个预测器的无约束组合，我们实现了$O(\ell^2)$的竞争比，并证明这是最优的。然而，对于不同预测器间切换次数略受约束的基准，我们能够获得$(1+\epsilon)$-竞争比的算法。此外，我们的算法可适用于以赌博机方式访问预测器，即每次仅查询一个预测器。我们下界中的一个意外推论，是关于$k$-服务器问题覆盖公式的新结构性见解。