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：我们研究了公平约束学习对训练数据中少量恶意噪声的脆弱性。Konstantinov和Lampert（2021）开创了该问题的研究，并给出了负面结果：对于若干公平约束，存在某些数据分布，当群体规模不平衡时，任何适当的学习器都会表现出高度脆弱性。本文提出了一种更为乐观的观点，表明若允许使用随机化分类器，则该问题的图景将更为复杂多元。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），该结果与无公平约束时的最优界相匹配。对于机会均等性，我们证明可承受$O(\sqrt{\alpha})$的损失，并给出了匹配的$\Omega(\sqrt{\alpha})$下界。相比之下，Konstantinov和Lampert（2021）证明对于适当学习器，两种公平性概念的精度损失均为$\Omega(1)$。本工作的核心技术创新在于揭示了随机化机制如何规避攻击者可能使用的简单"技巧"以放大其攻击效力。我们还研究了包括均衡几率与校准在内的其他公平性概念。对于这些公平性概念，超额精度自然地聚集为三个典型区间：$O(\alpha)$、$O(\sqrt{\alpha})$和$O(1)$。这些结果为理解公平约束学习对训练数据中对抗性噪声的敏感性提供了更细粒度的视角。