Learning-Augmented Algorithms for the Bahncard Problem

TL;DR

This paper introduces PFSUM, a new learning-augmented algorithm for the Bahncard problem, which improves decision-making by leveraging historical data and short-term predictions, outperforming previous primal-dual methods.

Contribution

We develop PFSUM, a novel learning-augmented algorithm that integrates history and short-term forecasts for better online decisions in the Bahncard problem.

Findings

PFSUM achieves a better competitive ratio than previous algorithms.

Experimental results show PFSUM outperforms primal-dual-based algorithms.

The algorithm effectively utilizes prediction errors to adapt its performance.

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.