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 $\Theta(\alpha)$ loss in accuracy, where $\alpha$ is the malicious noise rate, matching the best possible even without fairness constraints. For Equal Opportunity, we show we can 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 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 $O(\alpha)$,$O(\sqrt{\alpha})$ and $O(1)$. These results provide a more fine-grained view of the sensitivity of fairness-constrained learning to adversarial noise in training data.

翻译：我们研究了公平性约束学习对训练数据中少量恶意噪声的脆弱性。Konstantinov和Lampert（2021）首次探讨了该问题，并给出了负面结论：在某些数据分布下，当群体规模不平衡时，采用多种公平性约束的恰当学习器将表现出高度脆弱性。本文提出了更为乐观的观点，表明若允许随机分类器，则该问题的图景会更加精细。例如，对于人口统计均等性，我们证明仅需承受$\Theta(\alpha)$的精度损失（其中$\alpha$为恶意噪声率），该损失与无公平性约束时的最优结果匹配。对于机会均等性，我们证明可承受$O(\sqrt{\alpha})$的精度损失，并给出了匹配的下界$\Omega(\sqrt{\alpha})$。相比之下，Konstantinov和Lampert（2021）指出，对于恰当学习器，两种公平性概念的精度损失均为$\Omega(1)$。本文的技术新颖之处在于揭示了随机化如何规避攻击者用于放大破坏力的简单"技巧"。我们还研究了其他公平性概念，包括均等化赔率与校准。对于这些公平性概念，超额精度损失自然地分为三个区间：$O(\alpha)$、$O(\sqrt{\alpha})$和$O(1)$。这些结果提供了公平性约束学习对训练数据中对抗性噪声敏感性的更精细视角。