Learning-Augmented Algorithms for the Bahncard Problem

Hailiang Zhao, Xueyan Tang, Peng Chen, Shuiguang Deng

Keywords: algorithms with predictions, competitive analysis, consistency, robustness

TL;DR: We develop an improved learning-augmented algorithm for the Bahncard problem and derive its competitive ratio under any prediction errors.

Abstract: In this paper, we study learning-augmented algorithms for the Bahncard problem. The Bahncard problem is a generalization of the ski-rental problem, where a traveler needs to irrevocably and repeatedly decide between a cheap short-term solution and an expensive long-term one with an unknown future. Even though the problem is canonical, only a primal-dual-based learning-augmented algorithm was explicitly designed for it. We develop a new learning-augmented algorithm, named PFSUM, that incorporates both history and short-term future to improve online decision making. We derive the competitive ratio of PFSUM as a function of the prediction error and conduct extensive experiments to show that PFSUM outperforms the primal-dual-based algorithm.

Primary Area: Optimization (convex and non-convex, discrete, stochastic, robust)

Submission Number: 10170