Optimal Fairness under Local Differential Privacy
Hrad Ghoukasian, Shahab Asoodeh
TL;DR
This work addresses fairness under local differential privacy by designing optimal LDP-based pre-processing of sensitive attributes to minimize data unfairness. It delivers a closed-form solution for binary attributes and a tractable min–max linear fractional programming formulation for non-binary attributes, with a theoretical result linking data unfairness to classification fairness under DA-optimality. Empirically, the proposed OPT mechanisms achieve substantial reductions in data and classifier unfairness while preserving accuracy near non-private baselines, and outperform comparable LDP mechanisms as well as pre-/post-processing fairness methods across several datasets. The approach highlights local privacy as a principled and effective fairness intervention, offering practical gains in accuracy-fairness-privacy trade-offs and compatibility with existing fairness pipelines.
Abstract
We investigate how to optimally design local differential privacy (LDP) mechanisms that reduce data unfairness and thereby improve fairness in downstream classification. We first derive a closed-form optimal mechanism for binary sensitive attributes and then develop a tractable optimization framework that yields the corresponding optimal mechanism for multi-valued attributes. As a theoretical contribution, we establish that for discrimination-accuracy optimal classifiers, reducing data unfairness necessarily leads to lower classification unfairness, thus providing a direct link between privacy-aware pre-processing and classification fairness. Empirically, we demonstrate that our approach consistently outperforms existing LDP mechanisms in reducing data unfairness across diverse datasets and fairness metrics, while maintaining accuracy close to that of non-private models. Moreover, compared with leading pre-processing and post-processing fairness methods, our mechanism achieves a more favorable accuracy-fairness trade-off while simultaneously preserving the privacy of sensitive attributes. Taken together, these results highlight LDP as a principled and effective pre-processing fairness intervention technique.