Learning-Augmented Online Minimization with Dual Predictions

2026-06-03

AI Summary

This work addresses the challenge of performance instability in online minimization problems caused by minor perturbations in input instances. It introduces, for the first time, dual linear programming predictions into this domain, proposing a novel framework that integrates online algorithms, duality theory, and machine learning. By leveraging the stability of dual solutions across similar problem instances, the approach enhances both learnability and robustness for metric task systems and layered set cover problems. Theoretical analysis and empirical evaluations on the k-server and parking permit problems demonstrate that the proposed algorithm significantly outperforms traditional methods, achieving tighter competitive ratios and superior practical performance.

Abstract

We present learning-augmented algorithms for two general classes of online minimization problems: metrical task systems and laminar set cover. Both algorithms achieve improved theoretical guarantees using machine-learned predictions of an optimal solution to the dual linear program. Unlike optimal primal solutions, which can change drastically under tiny instance perturbations, these dual solutions are much more stable, which ensures the existence of good (and learnable) predictions for families of similar instances. While previous work has used dual predictions in offline settings and for online maximization problems, our algorithms are, to the best of our knowledge, the first demonstration that such dual predictions can be effective for online minimization. Our theoretical results are complemented by experiments on the $k$-server problem and the parking permit problem.

Problem

• online minimization
• learning-augmented algorithms
• dual predictions
• metrical task systems
• laminar set cover

Innovation

• learning-augmented algorithms
• dual predictions
• online minimization
• metrical task systems
• laminar set cover