Beyond Surrogates: A Quantitative Analysis for Inter-Metric Relationships

2026-03-08

AI Summary

This work addresses the misalignment between offline evaluation metrics and online performance objectives in industrial applications by establishing a unified theoretical framework that systematically quantifies the relationships among diverse evaluation metrics for the first time. By introducing the concepts of Bayes-optimal sets and regret transfer mechanisms, the study reveals structural asymmetries among metrics and provides a principled classification and relational modeling of metrics with varying mathematical forms. Theoretically characterizing metric consistency and transferability, this research offers novel insights and a methodological foundation for designing offline evaluation systems that are aligned with online objectives and backed by rigorous theoretical guarantees.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Evaluation and Analysis
• Multiagent Systems: Mechanism Design

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

The Consistency property between surrogate losses and evaluation metrics has been extensively studied to ensure that minimizing a loss leads to metric optimality. However, the direct relationship between different evaluation metrics remains significantly underexplored. This theoretical gap results in the"Metric Mismatch"frequently observed in industrial applications, where gains in offline validation metrics fail to translate into online performance. To bridge this disconnection, this paper proposes a unified theoretical framework designed to quantify the relationships between metrics. We categorize metrics into different classes to facilitate a comparative analysis across different mathematical forms and interrogates these relationships through Bayes-Optimal Set and Regret Transfer. Through this framework, we provide a new perspective on identifying the structural asymmetry in regret transfer, enabling the design of evaluation systems that are theoretically guaranteed to align offline improvements with online objectives.

Problem

• Metric Mismatch
• Inter-Metric Relationships
• Evaluation Metrics
• Offline-Online Alignment
• Consistency

Innovation

• Inter-Metric Relationships
• Regret Transfer
• Bayes-Optimal Set
• Metric Consistency
• Evaluation Metrics Alignment