Fairness in machine learning has attracted increasing attention in recent years. The fairness methods improving algorithmic fairness for in-distribution data may not perform well under distribution shift. In this paper, we first theoretically demonstrate the inherent connection between distribution shift, data perturbation, and weight perturbation. Subsequently, we analyze the sufficient conditions to guarantee fairness (i.e., low demographic parity) for the target dataset, including fairness for the source dataset, and low prediction difference between the source and target dataset for each sensitive attribute group. Motivated by these sufficient conditions, we propose robust fairness regularization (RFR) by considering the worst case within the weight perturbation ball for each sensitive attribute group. In this way, the maximization problem can be simplified as two forward and two backward propagations for each update of model parameters. We evaluate the effectiveness of our proposed RFR algorithm on synthetic and real distribution shifts across various datasets. Experimental results demonstrate that RFR achieves better fairness-accuracy trade-off performance compared with several baselines.

翻译：机器学习中的公平性近年来受到越来越多的关注。针对分布内数据提升算法公平性的公平性方法，在分布偏移下可能表现不佳。本文首先从理论上证明了分布偏移、数据扰动与权重扰动之间的内在联系。随后，我们分析了确保目标数据集公平性（即低人口统计平价）的充分条件，包括源数据集的公平性，以及每个敏感属性组在源数据集与目标数据集之间的低预测差异。受这些充分条件的启发，我们提出了一种稳健公平正则化方法（RFR），通过考虑每个敏感属性组的权重扰动球内的最坏情况来实现。通过这种方式，最大化问题可简化为每次更新模型参数时的两次前向传播和两次反向传播。我们在多种数据集的合成及真实分布偏移场景下评估了所提RFR算法的有效性。实验结果表明，与多个基线方法相比，RFR在公平性与准确率的权衡性能上表现更优。