Unified Precision-Guaranteed Stopping Rules for Contextual Learning

TL;DR

This paper introduces unified, statistically rigorous stopping rules for contextual learning that guarantee decision policy accuracy with fewer samples across various data collection settings.

Contribution

It develops generalized likelihood ratio-based stopping rules with new deviation inequalities, applicable to unstructured and structured linear models, ensuring finite-sample guarantees.

Findings

Rules achieve target precision with fewer samples than benchmarks.

Numerical experiments confirm efficiency and accuracy of the proposed stopping rules.

Applicable across multiple data environments, including real systems and simulations.

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.