On the Vulnerability of Fairness Constrained Learning to Malicious Noise
Avrim Blum, Princewill Okoroafor, Aadirupa Saha, Kevin Stangl
TL;DR
This work analyzes how fairness-constrained learning responds to malicious noise and introduces a randomized post-processing mechanism, the $(P,Q)$-expansion, to enable improper learning and improve robustness. The results reveal a nuanced, notion-dependent robustness: Demographic Parity can withstand adversarial perturbations with only $O(\\alpha)$ accuracy loss, Equal Opportunity matches the same order with $O(\\sqrt{\\alpha})$ and a matching lower bound, while Equalized Odds and related notions suffer $\\Omega(1)$ losses in the worst case. Calibration-related notions, including Predictive Parity and Parity Calibration, exhibit regimes where $O(\\alpha)$, $O(\\sqrt{\\alpha})$, or $\\Omega(1)$ losses arise, depending on group sizes and calibration strategies. Overall, the paper provides a finer-grained view of fairness robustness under adversarial corruption and demonstrates that randomized, improper learning can significantly alter the robustness landscape for group fairness constraints, with implications for deploying fair learning in noisy real-world data.
Abstract
We consider the vulnerability of fairness-constrained learning to small amounts of malicious noise in the training data. Konstantinov and Lampert (2021) initiated the study of this question and presented negative results showing there exist data distributions where for several fairness constraints, any proper learner will exhibit high vulnerability when group sizes are imbalanced. Here, we present a more optimistic view, showing that if we allow randomized classifiers, then the landscape is much more nuanced. For example, for Demographic Parity we show we can incur only a $Θ(α)$ loss in accuracy, where $α$ is the malicious noise rate, matching the best possible even without fairness constraints. For Equal Opportunity, we show we can incur an $O(\sqrtα)$ loss, and give a matching $Ω(\sqrtα)$lower bound. In contrast, Konstantinov and Lampert (2021) showed for proper learners the loss in accuracy for both notions is $Ω(1)$. The key technical novelty of our work is how randomization can bypass simple "tricks" an adversary can use to amplify his power. We also consider additional fairness notions including Equalized Odds and Calibration. For these fairness notions, the excess accuracy clusters into three natural regimes $O(α)$,$O(\sqrtα)$ and $O(1)$. These results provide a more fine-grained view of the sensitivity of fairness-constrained learning to adversarial noise in training data.