用贝叶斯方法融合预测信息，让滑雪租赁问题更智能且鲁棒。
Learning-Augmented Ski Rental with Discrete Distributions: A Bayesian Approach
- 基于离散贝叶斯框架，精确维护时间跨度的后验分布。
- 在准确先验下接近最优，最坏情况仍具保证性能。
- 适合有先验知识、追求稳健决策的在线学习场景。
我们从贝叶斯决策视角重新审视经典的滑雪租赁问题。传统算法在无假设下最小化最坏情况成本，而近期学习增强方法利用有噪声的预测并提供鲁棒性保障。本文提出一种离散贝叶斯框架，能精确维护时间范围上的后验分布，实现合理的不确定性量化，并自然融入专家先验。该算法获得依赖先验的竞争力保证，平滑过渡于最坏情况与完全知情之间。大量实验表明，其在多样化场景中表现优异：在准确先验下接近最优，同时保持最坏情况下的鲁棒性。该框架可自然扩展至多预测、非均匀先验和上下文信息，凸显贝叶斯推理在不完美预测的在线决策中的实际优势。
原文摘要 · Abstract (English)
We revisit the classic ski rental problem through the lens of Bayesian decision-making and machine-learned predictions. While traditional algorithms minimize worst-case cost without assumptions, and recent learning-augmented approaches leverage noisy forecasts with robustness guarantees, our work unifies these perspectives. We propose a discrete Bayesian framework that maintains exact posterior distributions over the time horizon, enabling principled uncertainty quantification and seamless incorporation of expert priors. Our algorithm achieves prior-dependent competitive guarantees and gracefully interpolates between worst-case and fully-informed settings. Our extensive experimental evaluation demonstrates superior empirical performance across diverse scenarios, achieving near-optimal results under accurate priors while maintaining robust worst-case guarantees. This framework naturally extends to incorporate multiple predictions, non-uniform priors, and contextual information, highlighting the practical advantages of Bayesian reasoning in online decision problems with imperfect predictions.
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