Discrete-Smoothness in Online Algorithms with Predictions

Yossi Azar, Debmalya Panigrahi, Noam Touitou

Keywords: Online, Predictions, Learning-augmented, Facility Location, Set Cover

TL;DR: We introduce a new notion called discrete-smoothness in online algorithms with predictions that smoothly interpolates between the established desiderata of consistency and robustness.

Abstract: In recent years, there has been an increasing focus on designing online algorithms with (machine-learned) predictions. The ideal learning-augmented algorithm is comparable to the optimum when given perfect predictions (consistency), to the best online approximation for arbitrary predictions (robustness), and should interpolate between these extremes as a smooth function of the prediction error. In this paper, we quantify these guarantees in terms of a general property that we call discrete-smoothness, and achieve discrete-smooth algorithms for online covering, specifically the facility location and set cover problems. For set cover, our work improves the results of Bamas, Maggiori, and Svensson (2020) by augmenting consistency and robustness with smoothness guarantees. For facility location, our work improves on prior work by Almanza et al. (2021) by generalizing to nonuniform costs and also providing smoothness guarantees by augmenting consistency and robustness.

Submission Number: 4645