Robust and Consistent Ski Rental with Distributional Advice
Jihwan Kim, Chenglin Fan

TL;DR
This paper develops a framework for the ski rental problem that leverages full distributional advice to improve decision-making, ensuring robustness and consistency even with imperfect predictions.
Contribution
It introduces a systematic approach to incorporate distributional advice into ski rental algorithms, with new policies that balance robustness and consistency.
Findings
The optimal threshold-buy algorithm is derived under perfect distributional predictions.
The Clamp Policy maintains performance with large prediction errors and improves as predictions become accurate.
Experimental results show significant improvement in consistency over point-prediction methods while preserving robustness.
Abstract
The ski rental problem is a canonical model for online decision-making under uncertainty, capturing the fundamental trade-off between repeated rental costs and a one-time purchase. While classical algorithms focus on worst-case competitive ratios and recent "learning-augmented" methods leverage point-estimate predictions, neither approach fully exploits the richness of full distributional predictions while maintaining rigorous robustness guarantees. We address this gap by establishing a systematic framework that integrates distributional advice of unknown quality into both deterministic and randomized algorithms. For the deterministic setting, we formalize the problem under perfect distributional prediction and derive an efficient algorithm to compute the optimal threshold-buy day. We provide a rigorous performance analysis, identifying sufficient conditions on the predicted…
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