Learning-Augmented Approximation for Unrelated-Machines Makespan Scheduling

2026-06-11

AI Summary

This work proposes the first learning-augmented approximation algorithm for the NP-hard unrelated machine scheduling problem to minimize makespan (R||C_max), introducing prediction-guided strategies into scheduling and resolving an open question posed by Antoniadis et al. The algorithm leverages predictions about the assignment of “heavy” jobs: when predictions are accurate, it achieves a (1+ε)-approximation; as prediction error increases, its performance degrades smoothly to a 2-approximation, matching the best-known worst-case bound. This trade-off yields theoretically tight robustness guarantees. Empirical evaluations demonstrate the algorithm’s practical effectiveness in real-world scenarios.

Abstract

Recently, Antoniadis et al. (ICLR 2025) proposed a framework for incorporating predictions to approximate NP-hard selection problems. Despite its simplicity, this approach tightly matches theoretical lower bounds, making its generalization highly compelling. We address an open question raised in the work of Antoniadis et al., concerning the extension of this approach to other important problems outside the class of selection problems, such as scheduling. We develop a learning-augmented algorithm for the makespan minimization problem on unrelated machines, denoted by $R\|C_{\max}$. By using predictions of heavy job assignments, we achieve a polynomial-time $(1+\varepsilon)$-approximation for accurate predictions that smoothly degrades to a worst-case 2-approximation as the error increases. We conclude our work with an empirical analysis of our method.

Problem

• unrelated-machines scheduling
• makespan minimization
• learning-augmented algorithms
• approximation algorithms
• NP-hard scheduling

Innovation

• learning-augmented algorithms
• unrelated-machines scheduling
• makespan minimization
• approximation algorithms
• prediction-based optimization