Fairness-Aware Differential Privacy: A Fairly Proportional Noise Mechanism

Differential privacy (DP) is a leading paradigm for privacy preservation in statistical analysis and learning. Traditional DP mechanisms add noise independently of the original data, which yields inconsistent perturbations across groups and raises fairness concerns in downstream decision and learning tasks. Prior work often assesses fairness via bias and variance, while overlooking noise direction and the scale of the underlying query. We propose a novel Fairly Proportional Noise Mechanism (FPNM) that uniquely considers both the direction and magnitude of noise relative to raw query results. We define mathematical formulations for unfairness, factoring in weighting and temporal decay to allow nonlinear amplification of unfairness. The privacy analysis shows a negative correlation between unfairness and privacy strength that higher privacy levels lead to increased noise and thus greater unfairness. We then generalize to group-level assessment using the average unfairness and the Frobenius norm ($F$-Norm). We also prove that adaptive budget reallocation within a data independent feasible domain preserves the overall$(\epsilon ,\delta )$-DP guarantee. Experiments on both decision and learning tasks demonstrate consistent gains. In decision tasks, the proposed FPNM effectively reduces unfairness, achieving average reductions of 19.17% and 17.32% in$F$-Norm and average unfairness, respectively. In learning tasks, integrating FPNM with DP-SGD achieves fairness comparable to fairness-aware baselines and better accuracy. Besides, empirical privacy remains intact under membership inference attacks. These results highlight its effectiveness in improving utility while preserving privacy, offering a robust and comprehensive approach to enhancing fairness in DP.