Online algorithms with predictions have become a trending topic in the field of beyond worst-case analysis of algorithms. These algorithms incorporate predictions about the future to obtain performance guarantees that are of high quality when the predictions are good, while still maintaining bounded worst-case guarantees when predictions are arbitrarily poor. In general, the algorithm is assumed to be unaware of the prediction's quality. However, recent developments in the machine learning literature have studied techniques for providing uncertainty quantification on machine-learned predictions, which describes how certain a model is about its quality. This paper examines the question of how to optimally utilize uncertainty-quantified predictions in the design of online algorithms. In particular, we consider predictions augmented with uncertainty quantification describing the likelihood of the ground truth falling in a certain range, designing online algorithms with these probabilistic predictions for two classic online problems: ski rental and online search. In each case, we demonstrate that non-trivial modifications to algorithm design are needed to fully leverage the probabilistic predictions. Moreover, we consider how to utilize more general forms of uncertainty quantification, proposing a framework based on online learning that learns to exploit uncertainty quantification to make optimal decisions in multi-instance settings.

翻译：预测辅助的在线算法已成为超越最坏情况分析算法领域的热门课题。这类算法利用关于未来的预测，在预测质量良好时获得高性能保证，同时即使在预测完全失效时仍能保持有界的最坏情况保证。通常，算法假设其未知预测质量。然而，机器学习领域的最新进展已研究出对机器学习预测进行不确定性量化的技术，用于描述模型对其预测结果的置信程度。本文探讨如何在在线算法设计中最优地利用带有不确定性量化的预测。具体而言，我们考虑带有不确定性量化的预测（描述真实值落在特定区间的可能性），并为滑雪租赁和在线搜索这两个经典在线问题设计了基于概率预测的在线算法。在每个问题中，我们证明必须对算法设计进行非平凡修改才能充分利用概率预测。此外，我们探讨如何利用更一般形式的不确定性量化，提出一个基于在线学习的框架，该框架通过学习利用不确定性量化在多实例场景中做出最优决策。