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，因此不应使用单一最佳预测器作为基准，而应采用能够根据不同时间点跟随不同预测器的动态组合。我们设计了能够结合预测的算法，并在广泛的在线问题（即度量任务系统）中与这种动态组合竞争。针对（事后最优的）无约束组合（包含ℓ个预测器），我们获得了O(ℓ²)的竞争比，并证明这是最佳可能结果。然而，对于预测器切换次数略有约束的基准，我们能够实现(1+ε)-竞争算法。此外，我们的算法可调整为以类似赌博机的方式访问预测器，每次仅查询一个预测器。我们其中一个下界的一个意外含义，是关于k-服务器问题覆盖公式的新的结构洞见。