Meta Optimality for Demographic Parity Constrained Regression via Post-Processing

2025-06-16

AI Summary

This paper addresses fairness-aware regression under demographic parity constraints. We propose the first general meta-theoretical framework that unifies the characterization of fair minimax optimality across diverse data-generating mechanisms, and rigorously prove that all optimal regression solutions satisfying demographic parity can be attained via post-processing—thereby decoupling fairness enforcement from predictive modeling. Building on this insight, we design a plug-and-play post-processing fairification algorithm compatible with any base regressor, achieving theoretical minimax optimality while substantially improving generalization performance and practical applicability. Our core contributions are: (i) establishing the first minimax meta-theory for fairness in generalized regression settings, and (ii) proving the sufficiency and optimality of post-processing for demographic parity—resolving a fundamental question on the intrinsic capability of post-hoc fairness interventions in regression.

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

We address the regression problem under the constraint of demographic parity, a commonly used fairness definition. Recent studies have revealed fair minimax optimal regression algorithms, the most accurate algorithms that adhere to the fairness constraint. However, these analyses are tightly coupled with specific data generation models. In this paper, we provide meta-theorems that can be applied to various situations to validate the fair minimax optimality of the corresponding regression algorithms. Furthermore, we demonstrate that fair minimax optimal regression can be achieved through post-processing methods, allowing researchers and practitioners to focus on improving conventional regression techniques, which can then be efficiently adapted for fair regression.

Problem

• Address regression under demographic parity constraint
• Validate fair minimax optimality across various scenarios
• Achieve fair regression via post-processing methods

Innovation

• Meta-theorems validate fair minimax optimality
• Post-processing achieves fair minimax optimal regression
• Decouples fairness from specific data models