Despite their promise, fair machine learning methods often yield Pareto-inefficient models, in which the performance of certain groups can be improved without degrading that of others. This issue arises frequently in traditional in-processing approaches such as fairness-through-regularization. In contrast, existing Pareto-efficient approaches are biased towards a certain perspective on fairness and fail to adapt to the broad range of fairness metrics studied in the literature. In this paper, we present BADR, a simple framework to recover the optimal Pareto-efficient model for any fairness metric. Our framework recovers its models through a Bilevel Adaptive Rescalarisation procedure. The lower level is a weighted empirical risk minimization task where the weights are a convex combination of the groups, while the upper level optimizes the chosen fairness objective. We equip our framework with two novel large-scale, single-loop algorithms, BADR-GD and BADR-SGD, and establish their convergence guarantees. We release badr, an open-source Python toolbox implementing our framework for a variety of learning tasks and fairness metrics. Finally, we conduct extensive numerical experiments demonstrating the advantages of BADR over existing Pareto-efficient approaches to fairness.

翻译：尽管前景广阔，公平机器学习方法常常产生帕累托低效模型，其中某些群体的性能可以在不损害其他群体性能的情况下得到提升。这一问题在传统的处理中方法（如通过正则化实现公平性）中频繁出现。相比之下，现有的帕累托高效方法偏向于特定的公平性视角，无法适应文献中研究的广泛公平性指标。本文提出BADR——一个为任意公平性指标恢复最优帕累托高效模型的简洁框架。我们的框架通过双层自适应重标量化程序恢复模型：下层是加权经验风险最小化任务（权重为各群体的凸组合），上层则优化选定的公平性目标。我们为该框架配备了两个新颖的大规模单循环算法BADR-GD和BADR-SGD，并建立了其收敛性保证。我们发布了badr——一个开源的Python工具箱，为多种学习任务和公平性指标实现了我们的框架。最后，我们通过大量数值实验证明了BADR相较于现有帕累托高效公平性方法的优势。