Learning-Augmented Algorithms for the Bahncard Problem
This work addresses an incremental improvement in online algorithms for a specific optimization problem, benefiting researchers in algorithmic design and competitive analysis.
The paper tackles the Bahncard problem, a generalization of ski-rental, by developing a new learning-augmented algorithm called PFSUM that uses history and short-term future predictions to improve online decision-making, and it shows through experiments that PFSUM outperforms an existing primal-dual-based algorithm.
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.