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：公平监督学习算法旨在分配标签时尽量减少对敏感属性的依赖，这一研究方向已在机器学习领域引起广泛关注。尽管人口统计均等（DP）概念常被用于衡量公平分类器训练中的模型公平性，但现有文献中的多项研究表明，在公平学习算法中强制实施DP可能会产生潜在影响。本文通过解析方法研究了基于标准DP的正则化方法对给定敏感属性的预测标签条件分布的影响。分析表明，当训练数据集存在敏感属性分布不均衡时，可能导致分类规则偏向于训练数据占多数的敏感属性结果。为控制基于DP的公平学习中的此类归纳偏好，我们提出了一种基于敏感属性的分布鲁棒优化（SA-DRO）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DP的学习方法应用于标准集中式与分布式学习问题的若干数值结果。实证结果支持了关于基于DP的公平学习算法中归纳偏好的理论结论，并验证了所提SA-DRO方法的去偏效果。