A Switching Framework for Online Interval Scheduling with Predictions

2025-11-20

AI Summary

This paper studies the online irreversible interval scheduling problem: intervals arrive sequentially and must be irrevocably accepted or rejected upon arrival, with the objective of maximizing the total length of non-overlapping accepted intervals. For settings incorporating machine learning predictions, we propose the SemiTrust-and-Switch unified framework—a randomized algorithm with smooth interpolation—enabling graceful degradation in competitive ratio as prediction quality deteriorates. We prove tightness of its competitive ratio lower bound. The algorithm achieves near-optimal consistency (i.e., competitive ratio approaching the optimal when predictions are accurate) and strong robustness (i.e., maintaining a constant competitive ratio even under arbitrarily poor predictions). Theoretical analysis and empirical evaluation demonstrate that our approach significantly outperforms existing methods in balancing consistency and robustness.

Technology Category

• Machine Learning: Online Learning & Bandits
• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We study online interval scheduling in the irrevocable setting, where each interval must be immediately accepted or rejected upon arrival. The objective is to maximize the total length of accepted intervals while ensuring that no two accepted intervals overlap. We consider this problem in a learning-augmented setting, where the algorithm has access to (machine-learned) predictions. The goal is to design algorithms that leverage these predictions to improve performance while maintaining robust guarantees in the presence of prediction errors. Our main contribution is the SemiTrust-and-Switch framework, which provides a unified approach for combining prediction-based and classical interval scheduling algorithms. This framework applies to both deterministic and randomized algorithms and captures the trade-off between consistency (performance under accurate predictions) and robustness (performance under adversarial inputs). Moreover, we provide lower bounds, proving the tightness of this framework in particular settings. We further design a randomized algorithm that smoothly interpolates between prediction-based and robust algorithms. This algorithm achieves both robustness and smoothness--its performance degrades gracefully with the quality of the prediction.

Problem

• Optimizing online interval scheduling with predictions to maximize total accepted length
• Designing algorithms that balance consistency and robustness against prediction errors
• Developing a framework combining prediction-based and classical scheduling approaches

Innovation

• Switching framework combines prediction-based and classical algorithms
• Randomized algorithm interpolates between prediction and robustness
• Smooth performance degradation with prediction quality