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.

翻译：本文从贝叶斯决策与机器学习预测的视角重新审视经典的滑雪板租赁问题。传统算法在无假设条件下最小化最坏情况成本，而近期学习增强方法则利用带有鲁棒性保证的噪声预测。本研究统一了这两种视角，提出了一个离散贝叶斯框架，该框架在时间维度上维持精确的后验分布，实现了原则性的不确定性量化与专家先验的无缝融合。我们的算法实现了先验依赖的竞争性保证，并在最坏情况与完全信息设定之间实现平滑过渡。大量实验评估表明，该框架在多样化场景中展现出卓越的实证性能：在准确先验条件下获得接近最优的结果，同时保持鲁棒的最坏情况保证。该框架可自然扩展至多预测融合、非均匀先验及上下文信息整合，凸显了贝叶斯推理在具有不完美预测的在线决策问题中的实践优势。