Fair supervised learning algorithms assigning labels with little dependence on a sensitive attribute have attracted great attention in the machine learning community. While the demographic parity (DP) notion has been frequently used to measure a model's fairness in training fair classifiers, several studies in the literature suggest potential impacts of enforcing DP in fair learning algorithms. In this work, we analytically study the effect of standard DP-based regularization methods on the conditional distribution of the predicted label given the sensitive attribute. Our analysis shows that an imbalanced training dataset with a non-uniform distribution of the sensitive attribute could lead to a classification rule biased toward the sensitive attribute outcome holding the majority of training data. To control such inductive biases in DP-based fair learning, we propose a sensitive attribute-based distributionally robust optimization (SA-DRO) method improving robustness against the marginal distribution of the sensitive attribute. Finally, we present several numerical results on the application of DP-based learning methods to standard centralized and distributed learning problems. The empirical findings support our theoretical results on the inductive biases in DP-based fair learning algorithms and the debiasing effects of the proposed SA-DRO method.

翻译：在机器学习领域，以对敏感属性依赖程度极小的方式分配标签的公平监督学习算法引起了广泛关注。尽管在训练公平分类器时，人口统计学均等性这一概念常被用于衡量模型的公平性，但文献中的多项研究表明，在公平学习算法中强制执行人口统计学均等性可能产生潜在影响。本文旨在分析标准基于人口统计学均等性的正则化方法对给定敏感属性条件下预测标签条件分布的影响。理论分析表明：当训练数据集存在类别不平衡且敏感属性呈非均匀分布时，分类规则会偏向于训练数据中占多数的敏感属性结果。为控制基于人口统计学均等性的公平学习中的这种归纳偏差，我们提出了一种基于敏感属性分布鲁棒优化的方法，该方法能提升对敏感属性边缘分布的鲁棒性。最后，我们展示了将基于人口统计学均等性的学习方法应用于标准集中式与分布式学习问题的数值实验结果。实证发现支持了关于基于人口统计学均等性的公平学习算法中存在归纳偏差的理论结论，并验证了所提出的分布鲁棒优化方法的去偏效果。