Learning-Augmented Ski Rental with Discrete Distributions: A Bayesian Approach

TL;DR

This paper introduces a Bayesian framework for the ski rental problem that effectively combines prior knowledge and predictions to improve decision-making, balancing worst-case guarantees with empirical performance.

Contribution

It presents a discrete Bayesian approach that maintains exact posteriors, enabling uncertainty quantification and superior empirical results while preserving robustness.

Findings

Achieves prior-dependent competitive guarantees.

Demonstrates near-optimal performance with accurate priors.

Maintains robust worst-case guarantees.

Abstract

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.