Improved Learning-Augmented Algorithms for the Multi-Option Ski Rental Problem via Best-Possible Competitive Analysis

TL;DR

This paper introduces the first randomized learning-augmented algorithm for the multi-option ski rental problem, achieving superior performance guarantees by leveraging ML predictions and establishing best-possible competitive ratios.

Contribution

It presents the first randomized learning-augmented algorithm for multi-option ski rental, surpassing deterministic methods with provably optimal competitive guarantees.

Findings

New randomized learning-augmented algorithm outperforms deterministic ones.

Established lower bounds for deterministic and randomized algorithms.

Computational experiments demonstrate improved practical performance.

Abstract

In this paper, we present improved learning-augmented algorithms for the multi-option ski rental problem. Learning-augmented algorithms take ML predictions as an added part of the input and incorporates these predictions in solving the given problem. Due to their unique strength that combines the power of ML predictions with rigorous performance guarantees, they have been extensively studied in the context of online optimization problems. Even though ski rental problems are one of the canonical problems in the field of online optimization, only deterministic algorithms were previously known for multi-option ski rental, with or without learning augmentation. We present the first randomized learning-augmented algorithm for this problem, surpassing previous performance guarantees given by deterministic algorithms. Our learning-augmented algorithm is based on a new, provably best-possible randomized competitive algorithm for the problem. Our results are further complemented by lower bounds for deterministic and randomized algorithms, and computational experiments evaluating our algorithms' performance improvements.