Online Algorithms with Uncertainty-Quantified Predictions

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.