Privacy Cost as Equity Input: A Group Fairness Criterion for Differentially Private Machine Learning

2026-07-17

AI Summary

This work addresses the unequal privacy costs borne by different demographic groups in differentially private machine learning—a disparity overlooked by conventional fairness metrics. It introduces a compensatory fairness framework that explicitly incorporates privacy cost into fairness considerations and proposes the Privacy Cost Equity Ratio (PCER) as a group fairness measure. PCER estimates privacy exposure via the gap between training and test accuracy for each group, enabling posterior fairness auditing without requiring shadow models. Through experiments on six tabular and NLP datasets using DP-SGD, membership inference attack bounds, and overfitting gap analysis, the study demonstrates that PCER reveals a “double disadvantage” phenomenon masked by traditional metrics. Furthermore, under stringent privacy guarantees, group-specific overfitting converges, rendering exposure-based auditing ineffective.

Abstract

Differential privacy (DP) is increasingly deployed to limit membership inference risk in machine-learning systems. Prior work has shown that DP-SGD can widen accuracy disparities across demographic groups, but this framing treats fairness as a purely outcome-side concern. We argue that privacy cost, the information leakage borne by each group, is itself a form of harm, and adopt a compensatory-fairness framework in which a group that involuntarily bears greater privacy exposure is owed proportionally greater benefit from the system. From this principle we derive the \emph{Privacy-Cost Equity Ratio} (PCER), a group fairness metric defined as a group's positive prediction rate normalized by its per-group overfitting gap. By a standard membership inference bound, this overfitting gap upper-bounds each group's vulnerability to inference attacks, making PCER a conservative measure of benefit relative to exposure. PCER needs only per-group train and test accuracy (no shadow models), making it a practical post-hoc audit tool. We evaluate PCER alongside standard fairness metrics across six benchmark--attribute combinations spanning tabular and NLP domains, under DP-SGD at a range of privacy budgets, and validate the overfitting-gap proxy against a direct threshold membership-inference attack. The results reveal patterns that outcome-based metrics miss. On COMPAS, PCER uncovers a persistent double disadvantage: the protected group bears both greater privacy exposure and worse predictive outcomes, something demographic parity gap masks entirely. Sensitivity analysis shows very strong privacy guarantees collapse both groups' overfitting to a numerical floor, rendering exposure-based audits uninformative in that regime. Together, these findings show that fairness audits of privacy-preserving systems must account for who bears the cost of protection, not only who benefits from its outcomes.

Problem

• differential privacy
• group fairness
• privacy cost
• membership inference
• fairness audit

Innovation

• Privacy-Cost Equity Ratio
• Differential Privacy
• Group Fairness
• Membership Inference
• Overfitting Gap