Near-Optimal Consistency-Robustness Trade-Offs for Learning-Augmented Online Knapsack Problems

We study the problem of improving the performance of online algorithms by incorporating machine-learned predictions. The goal is to design algorithms that are both consistent and robust, meaning that the algorithm performs well when predictions are accurate and maintains worst-case guarantees. Such algorithms have been studied in a recent line of work initiated by Lykouris and Vassilvitskii (ICML '18) and Kumar, Purohit and Svitkina (NeurIPS '18). They provide robustness-consistency trade-offs for a variety of online problems. However, they leave open the question of whether these trade-offs are tight, i.e., to what extent to such trade-offs are necessary. In this paper, we provide the first set of non-trivial lower bounds for competitive analysis using machine-learned predictions. We focus on the classic problems of ski rental and non-clairvoyant scheduling and provide optimal trade-offs in various settings. 34th Conference on Neural Information Processing Systems (NeurIPS 2020), Vancouver, Canada.