The burgeoning field of algorithms with predictions studies the problem of using possibly imperfect machine learning predictions to improve online algorithm performance. While nearly all existing algorithms in this framework make no assumptions on prediction quality, a number of methods providing uncertainty quantification (UQ) on machine learning models have been developed in recent years, which could enable additional information about prediction quality at decision time. In this work, we investigate the problem of optimally utilizing uncertainty-quantified predictions in the design of online algorithms. In particular, we study two classic online problems, ski rental and online search, where the decision-maker is provided predictions augmented with UQ describing the likelihood of the ground truth falling within a particular range of values. We demonstrate that non-trivial modifications to algorithm design are needed to fully leverage the UQ predictions. Moreover, we consider how to utilize more general forms of UQ, proposing an online learning framework that learns to exploit UQ to make decisions in multi-instance settings.

翻译：预测算法这一新兴领域研究如何利用可能不完美的机器学习预测来提升在线算法性能。尽管该框架下几乎所有现有算法均不对预测质量做任何假设，但近年来已发展出多种为机器学习模型提供不确定性量化（UQ）的方法，这些方法可在决策时提供关于预测质量的附加信息。本文研究在线算法设计中如何最优化利用不确定性量化预测的问题。具体而言，我们探讨了两个经典在线问题——滑雪租赁和在线搜索，其中决策者获得的预测附带有UQ信息，用于描述真实值落入特定数值范围的可能性。我们证明，需要对算法设计进行非平凡修改才能充分利用UQ预测。此外，我们研究了如何利用更一般形式的UQ，提出一种在线学习框架，该框架能够学习在多实例场景中利用UQ进行决策。