Learning-augmented algorithms have been attracting increasing interest, but have only recently been considered in the setting of explorable uncertainty where precise values of uncertain input elements can be obtained by a query and the goal is to minimize the number of queries needed to solve a problem. We study learning-augmented algorithms for sorting and hypergraph orientation under uncertainty, assuming access to untrusted predictions for the uncertain values. Our algorithms provide improved performance guarantees for accurate predictions while maintaining worst-case guarantees that are best possible without predictions. For hypergraph orientation, for any $\gamma \geq 2$, we give an algorithm that achieves a competitive ratio of $1+1/\gamma$ for correct predictions and $\gamma$ for arbitrarily wrong predictions. For sorting, we achieve an optimal solution for accurate predictions while still being $2$-competitive for arbitrarily wrong predictions. These tradeoffs are the best possible. We also consider different error metrics and show that the performance of our algorithms degrades smoothly with the prediction error in all the cases where this is possible.

翻译：学习增强型算法日益受到关注，但直到最近才被引入可探索不确定性（explorable uncertainty）场景——在该场景中，可以通过查询获取不确定输入元素的精确值，目标是最小化解题所需的查询次数。我们研究在不确定性条件下，利用不可信预测值进行排序与超图定向的学习增强型算法。我们的算法能在保持最优最坏情况保证（即使无预测时）的同时，为准确预测提供更优的性能保障。对于超图定向，针对任意γ≥2，我们设计的算法在预测正确时实现1+1/γ的竞争比，在预测完全错误时达到γ的竞争比。对于排序问题，我们在预测准确时获得最优解，同时在任意错误预测情况下仍保持2-竞争比。这些权衡结果均为理论最优。我们还考虑了不同误差度量指标，并证明在可能的情况下，算法性能随预测误差呈平滑退化趋势。