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：近些年来,机器学习的公平性引起了越来越多的关注。 提高分配数据在算法上的公正性的公平性方法在分布变化中可能不会很好地发挥作用。 在本文中,我们首先从理论上展示了分布变化、数据扰动和重量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(即人口均等程度低)的充分条件,包括源数据集的公平性,以及每个敏感属性组源和目标数据集之间的预测差异低。受这些足够条件的驱动,我们建议通过考虑每个敏感属性组重量扰动球中最坏的情况来大力实现公平性规范化(RFR)。这样,最大化问题可以简化为每次更新模型参数时的两个前向和两个向后传播。我们评估了我们提议的RFR算法在各种数据集的合成和真实分布变化上的有效性。 实验结果表明,与几个基线相比,RFR实现了更好的公平性-准确性交易性业绩。</s>