While the accuracy-fairness trade-off has been frequently observed in the literature of fair machine learning, rigorous theoretical analyses have been scarce. To demystify this long-standing challenge, this work seeks to develop a theoretical framework by characterizing the shape of the accuracy-fairness trade-off Pareto frontier (FairFrontier), determined by a set of all optimal Pareto classifiers that no other classifiers can dominate. Specifically, we first demonstrate the existence of the trade-off in real-world scenarios and then propose four potential categories to characterize the important properties of the accuracy-fairness Pareto frontier. For each category, we identify the necessary conditions that lead to corresponding trade-offs. Experimental results on synthetic data suggest insightful findings of the proposed framework: (1) When sensitive attributes can be fully interpreted by non-sensitive attributes, FairFrontier is mostly continuous. (2) Accuracy can suffer a \textit{sharp} decline when over-pursuing fairness. (3) Eliminate the trade-off via a two-step streamlined approach. The proposed research enables an in-depth understanding of the accuracy-fairness trade-off, pushing current fair machine-learning research to a new frontier.

翻译：尽管精度-公平性权衡在公平机器学习文献中屡见不鲜，但严格的理论分析仍较为匮乏。为阐明这一长期存在的挑战，本文致力于构建一个理论框架，通过刻画由所有无法被其他分类器支配的最优帕累托分类器集合所确定的精度-公平性权衡帕累托边界（FairFrontier）的形态。具体而言，我们首先在真实场景中验证了该权衡的存在性，继而提出四种潜在类别来刻画精度-公平性帕累托边界的重要性质，并针对每个类别识别了导致相应权衡的必要条件。基于合成数据的实验结果表明：（1）当敏感属性可被非敏感属性完全解释时，FairFrontier通常呈现连续性；（2）过度追求公平性会导致精度出现\textit{急剧}下降；（3）可通过两步精简流程消除该权衡。本研究为深入理解精度-公平性权衡提供了理论支撑，推动当前公平机器学习研究迈向新前沿。