Learning-augmented Online Algorithm for Two-level Ski-rental Problem
This work addresses cost optimization in online decision-making for resource allocation, offering a hybrid approach that balances robustness and efficiency, though it is incremental in combining existing methods.
The paper tackles the two-level ski-rental problem by developing a learning-augmented online algorithm (LADTSR) that integrates machine learning predictions into a robust online algorithm, achieving improved average performance under accurate predictions while maintaining worst-case guarantees.
In this paper, we study the two-level ski-rental problem,where a user needs to fulfill a sequence of demands for multiple items by choosing one of the three payment options: paying for the on-demand usage (i.e., rent), buying individual items (i.e., single purchase), and buying all the items (i.e., combo purchase). Without knowing future demands, the user aims to minimize the total cost (i.e., the sum of the rental, single purchase, and combo purchase costs) by balancing the trade-off between the expensive upfront costs (for purchase) and the potential future expenses (for rent). We first design a robust online algorithm (RDTSR) that offers a worst-case performance guarantee. While online algorithms are robust against the worst-case scenarios, they are often overly cautious and thus suffer a poor average performance in typical scenarios. On the other hand, Machine Learning (ML) algorithms typically show promising average performance in various applications but lack worst-case performance guarantees. To harness the benefits of both methods, we develop a learning-augmented algorithm (LADTSR) by integrating ML predictions into the robust online algorithm, which outperforms the robust online algorithm under accurate predictions while ensuring worst-case performance guarantees even when predictions are inaccurate. Finally, we conduct numerical experiments on both synthetic and real-world trace data to corroborate the effectiveness of our approach.