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 shifts. In this paper, we first theoretically demonstrate the inherent connection between distribution shift, data perturbation, and model 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 datasets for each sensitive attribute group. Motivated by these sufficient conditions, we propose robust fairness regularization (RFR) by considering the worst case within the model weight perturbation ball for each sensitive attribute group. 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. The source code is available at \url{https://github.com/zhimengj0326/RFR_NeurIPS23}.

翻译：机器学习中的公平性近年来受到越来越多的关注。针对同分布数据改进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、数据扰动与模型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（即低人口统计平等）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。基于这些充分条件，我们通过考虑每个敏感属性组在模型权重扰动球内的最坏情况，提出了稳健公平性正则化方法（RFR）。我们在多种数据集上评估了所提出的RFR算法在合成和真实分布偏移下的有效性。实验结果表明，与几种基线方法相比，RFR实现了更好的公平性-准确率权衡性能。源代码可在 \url{https://github.com/zhimengj0326/RFR_NeurIPS23} 获取。