Combinatorial Ski Rental Problem: Robust and Learning-Augmented Algorithms

Ziwei Li, Bo Sun, Zhiqiu Zhang, Mohammad Hajiesmaili, Binghan Wu, Lin Yang, Yang Gao

Keywords: combinatorial ski rental problem, competitive analysis, learning-augmented algorithm, online optimization

Abstract: We introduce and study the Combinatorial Ski Rental (CSR) problem, which involves multiple items that can be rented or purchased, either individually or in combination. At each time step, a decision-maker must make an irrevocable buy-or-rent decision for items that have not yet been purchased, without knowing the end of the time horizon. We propose a randomized online algorithm, Sorted Optimal Amortized Cost (SOAC), that achieves the optimal competitive ratio. Moreover, SOAC can be extended to address various well-known ski rental variants, including the multi-slope, multi-shop, multi-commodity ski rental and CSR with upgrading problems. Building on the proposed SOAC algorithm, we further develop a learning-augmented algorithm that leverages machine-learned predictions to improve the performance of CSR. This algorithm is capable of recovering or improving upon existing results of learning-augmented algorithms in both the classic ski rental and multi-shop ski rental problems. Experimental results validate our theoretical analysis and demonstrate the advantages of our algorithms over baseline methods for ski rental problems.

Primary Area: Theory (e.g., control theory, learning theory, algorithmic game theory)

Submission Number: 10569