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

A Theoretical Approach to Characterize the Accuracy-Fairness Trade-off Pareto Frontier