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We consider the vulnerability of fairness-constrained learning to smallamounts of malicious noise in the training data. Konstantinov and Lampert(2021) initiated the study of this question and presented negative resultsshowing there exist data distributions where for several fairness constraints,any proper learner will exhibit high vulnerability when group sizes areimbalanced. Here, we present a more optimistic view, showing that if we allowrandomized classifiers, then the landscape is much more nuanced. For example,for Demographic Parity we show we can incur only a $\Theta(\alpha)$ loss inaccuracy, where $\alpha$ is the malicious noise rate, matching the bestpossible even without fairness constraints. For Equal Opportunity, we show wecan incur an $O(\sqrt{\alpha})$ loss, and give a matching$\Omega(\sqrt{\alpha})$lower bound. In contrast, Konstantinov and Lampert(2021) showed for proper learners the loss in accuracy for both notions is$\Omega(1)$. The key technical novelty of our work is how randomization canbypass simple "tricks" an adversary can use to amplify his power. We alsoconsider additional fairness notions including Equalized Odds and Calibration.For these fairness notions, the excess accuracy clusters into three naturalregimes $O(\alpha)$,$O(\sqrt{\alpha})$ and $O(1)$. These results provide a morefine-grained view of the sensitivity of fairness-constrained learning toadversarial noise in training data.

On the Vulnerability of Fairness Constrained Learning to Malicious Noise