Operationalizing Individual Fairness via Gradient Descent and Bradley-Terry Models

2026-05-21

AI Summary

This work addresses the practical challenge of individual fairness, which is often hindered by the difficulty of learning effective individual similarity metrics from data. The authors propose a Mahalanobis distance metric learning approach based on triplet queries, operating under the Bradley–Terry pairwise comparison model. Their method uniquely integrates spectral initialization with gradient descent to optimize a non-convex loss function—a first in the context of individual fairness metric learning. Theoretically, the learned metric is shown to effectively approximate the true underlying fairness structure, and the algorithm enjoys fast convergence guarantees. Empirical evaluations demonstrate that predictors trained using this metric achieve significantly improved individual fairness while maintaining predictive utility.

Abstract

Individual fairness, the notion that "similar individuals should be treated similarly," provides a strong and flexible fairness guarantee for algorithmic decision makers. However, a barrier to implementing individual fairness in practice is the difficulty of learning the similarity metric over individuals. In this work, we present an algorithm for learning a Mahalanobis similarity metric from triplet queries of the form "is individual $i$ more similar to individual $j$ or $k$?" We work in the standard Bradley-Terry model for pairwise comparisons. Our algorithm consists of a spectral initialization step followed by gradient descent. We provide extensive theoretical guarantees on our algorithm, showing that it converges quickly to the ground truth metric despite the non-convexity of the loss in our model. Because our focus is on fairness, we also show that individual fairness with respect to an estimated metric is sufficient to achieve similar fairness with respect to the true metric. We also discuss potential applications of our work to AI model tuning. Finally, we present experimental results that demonstrate the convergence of our algorithm and the fairness performance of downstream fair predictors trained on our estimated metric.

Problem

• individual fairness
• similarity metric
• Mahalanobis metric
• triplet queries
• Bradley-Terry model

Innovation

• individual fairness
• Mahalanobis metric learning
• Bradley-Terry model
• gradient descent
• triplet queries