Maximin Relative Improvement: Fair Learning as a Bargaining Problem

2026-02-04

AI Summary

This work addresses the failure of conventional fairness methods when deploying a single predictor across subpopulations with heterogeneous predictability. It introduces the first formulation of group fairness as a bargaining problem, proposing relative improvement—the ratio of actual risk reduction to the maximum possible reduction—as a fairness metric, which corresponds to the Kalai-Smorodinsky bargaining solution. This criterion enjoys scale invariance and individual monotonicity, providing an axiomatic foundation for fair learning. By integrating game-theoretic principles, robust optimization, and finite-sample analysis, the paper establishes convergence guarantees for estimating relative improvement under mild conditions, effectively overcoming the limitations of worst-group loss approaches in settings with heterogeneous predictability.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Machine Learning: Ethics, Bias, and Fairness
• Search and Optimization: Learning to Search

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
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

When deploying a single predictor across multiple subpopulations, we propose a fundamentally different approach: interpreting group fairness as a bargaining problem among subpopulations. This game-theoretic perspective reveals that existing robust optimization methods such as minimizing worst-group loss or regret correspond to classical bargaining solutions and embody different fairness principles. We propose relative improvement, the ratio of actual risk reduction to potential reduction from a baseline predictor, which recovers the Kalai-Smorodinsky solution. Unlike absolute-scale methods that may not be comparable when groups have different potential predictability, relative improvement provides axiomatic justification including scale invariance and individual monotonicity. We establish finite-sample convergence guarantees under mild conditions.

Problem

• fair learning
• bargaining problem
• group fairness
• relative improvement
• scale invariance

Innovation

• relative improvement
• fair learning
• bargaining problem
• Kalai-Smorodinsky solution
• scale invariance