In this paper, we present improved learning-augmented algorithms for the multi-option ski rental problem. Learning-augmented algorithms take ML predictions as an added part of the input and incorporates these predictions in solving the given problem. Due to their unique strength that combines the power of ML predictions with rigorous performance guarantees, they have been extensively studied in the context of online optimization problems. Even though ski rental problems are one of the canonical problems in the field of online optimization, only deterministic algorithms were previously known for multi-option ski rental, with or without learning augmentation. We present the first randomized learning-augmented algorithm for this problem, surpassing previous performance guarantees given by deterministic algorithms. Our learning-augmented algorithm is based on a new, provably best-possible randomized competitive algorithm for the problem. Our results are further complemented by lower bounds for deterministic and randomized algorithms, and computational experiments evaluating our algorithms' performance improvements.

翻译：本文针对多选项滑雪租赁问题提出了改进的学习增强算法。学习增强算法将机器学习预测作为输入的一部分，并将其融入问题求解过程中。由于这种算法兼具机器学习预测的强大能力与严格的性能保证，已在在线优化问题领域得到广泛研究。尽管滑雪租赁问题是在线优化领域的经典问题之一，但此前已知的多选项滑雪租赁算法（无论是否采用学习增强）均为确定性算法。我们首次提出该问题的随机化学习增强算法，其性能超越了现有确定性算法。该学习增强算法基于一种全新的、理论上可证明的最优随机化竞争算法。此外，我们通过确定性算法与随机化算法的下界分析，以及评估算法性能提升的计算实验，对研究结果进行了补充论证。