The Statistical Fairness-Accuracy Frontier

2025-08-24

AI Summary

This work addresses the fairness–accuracy (FA) trade-off in machine learning under realistic finite-sample settings, challenging the common assumption in prior work that the population distribution is known. Method: Grounded in statistical learning theory and the minimax optimal estimation framework, we design estimators incorporating covariate distribution information to characterize the statistical behavior of the finite-sample FA frontier. Contribution/Results: We rigorously quantify the worst-case deviation between the finite-sample and population FA frontiers, revealing asymmetric sensitivity of group-wise risks to sample size. Furthermore, we derive an optimal cross-group sample allocation strategy and construct minimax-optimal estimators under multiple settings. Our results provide a verifiable theoretical foundation and practical guidance for designing fair algorithms in data-scarce scenarios.

Technology Category

• Machine Learning: Ethics, Bias, and Fairness
• Game Theory and Economic Paradigms: Fair Division
• Computer Vision: Bias, Fairness & Privacy

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Social Networks and Social Media: Fairness and bias in social network and social media analysis

Abstract

Machine learning models must balance accuracy and fairness, but these goals often conflict, particularly when data come from multiple demographic groups. A useful tool for understanding this trade-off is the fairness-accuracy (FA) frontier, which characterizes the set of models that cannot be simultaneously improved in both fairness and accuracy. Prior analyses of the FA frontier provide a full characterization under the assumption of complete knowledge of population distributions -- an unrealistic ideal. We study the FA frontier in the finite-sample regime, showing how it deviates from its population counterpart and quantifying the worst-case gap between them. In particular, we derive minimax-optimal estimators that depend on the designer's knowledge of the covariate distribution. For each estimator, we characterize how finite-sample effects asymmetrically impact each group's risk, and identify optimal sample allocation strategies. Our results transform the FA frontier from a theoretical construct into a practical tool for policymakers and practitioners who must often design algorithms with limited data.

Problem

• Balancing accuracy and fairness in machine learning models
• Studying fairness-accuracy frontier with finite-sample data
• Deriving minimax-optimal estimators for covariate distribution knowledge

Innovation

• Finite-sample minimax-optimal estimators derivation
• Covariate distribution knowledge-dependent model design
• Optimal sample allocation strategies identification