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.

We study the proportional clustering problem of Chen et al. (ICML '19) and relate

In this section, we report the hyperparameters of each base model used in our paper, details in Table 2. The only hyperparameter that is tuned is done per dataset using a 10% validation split. In this Section, we discuss the experimental convergence of our U-DIF algorithm to the global optimum. In order to approximately compute the true global optimum, we use the following numerical scheme. (exact numbers vary by network and are given in Figure 4).

To combat this, there has been a surge of interest in algorithmic fairness metrics (Mehrabi et al., 2021).

Unlikepriorworkon individual fairness, we do not assume the similarity measure among individuals is known, nor do we assume that such measure takes a certain parametric form.