Unified Precision-Guaranteed Stopping Rules for Contextual Learning

2026-04-09

AI Summary

This study addresses the stopping problem in contextual learning: how to terminate data collection as early as possible while ensuring policy accuracy. To this end, the authors propose a unified stopping rule based on a generalized likelihood ratio statistic that does not require decoupling uncertainty in the mean and variance, and is applicable to both unstructured and structured linear settings with unknown variance. Leveraging a novel time-uniform deviation inequality, the work provides, for the first time, finite-sample theoretical guarantees simultaneously for both context-level and policy-value-level accuracy. Experimental results demonstrate that the proposed method achieves the target accuracy with significantly fewer samples than existing benchmarks across synthetic data and two real-world case studies.

Abstract

Contextual learning seeks to learn a decision policy that maps an individual's characteristics to an action through data collection. In operations management, such data may come from various sources, and a central question is when data collection can stop while still guaranteeing that the learned policy is sufficiently accurate. We study this question under two precision criteria: a context-wise criterion and an aggregate policy-value criterion. We develop unified stopping rules for contextual learning with unknown sampling variances in both unstructured and structured linear settings. Our approach is based on generalized likelihood ratio (GLR) statistics for pairwise action comparisons. To calibrate the corresponding sequential boundaries, we derive new time-uniform deviation inequalities that directly control the self-normalized GLR evidence and thus avoid the conservativeness caused by decoupling mean and variance uncertainty. Under the Gaussian sampling model, we establish finite-sample precision guarantees for both criteria. Numerical experiments on synthetic instances and two case studies demonstrate that the proposed stopping rules achieve the target precision with substantially fewer samples than benchmark methods. The proposed framework provides a practical way to determine when enough information has been collected in personalized decision problems. It applies across multiple data-collection environments, including historical datasets, simulation models, and real systems, enabling practitioners to reduce unnecessary sampling while maintaining a desired level of decision quality.

Problem

• contextual learning
• stopping rules
• precision guarantees
• data collection
• decision policy

Innovation

• generalized likelihood ratio
• time-uniform deviation inequalities
• contextual learning
• precision-guaranteed stopping rules
• self-normalized statistics