To address the bias exhibited by machine learning models, fairness criteria
impose statistical constraints for ensuring equal treatment to all demographic
groups, but typically at a cost to model performance. Understanding this
tradeoff, therefore, underlies the design of fair and effective algorithms.
This paper completes the characterization of the inherent tradeoff of
demographic parity on classification problems in the most general multigroup,
multiclass, and noisy setting. Specifically, we show that the minimum error
rate is given by the optimal value of a Wasserstein-barycenter problem. More
practically, this reformulation leads to a simple procedure for post-processing
any pre-trained predictors to satisfy demographic parity in the general
setting, which, in particular, yields the optimal fair classifier when applied
to the Bayes predictor. We provide suboptimality and finite sample analyses for
our procedure, and demonstrate precise control of the tradeoff of error rate
for fairness on real-world datasets provided sufficient data.

该论文研究了机器学习中的公平性问题，提出了在保持公平的前提下如何提高预测模型性能的方法，并且证明了最小误差率可以通过 Wasserstein 平均问题的最优值来计算，从而提出了一种简单的后处理方法来保证模型的公平性。