We study supervised learning problems for predicting properties of individuals who belong to one of two demographic groups, and we seek predictors that are fair according to statistical parity. This means that the distributions of the predictions within the two groups should be close with respect to the Kolmogorov distance, and fairness is achieved by penalizing the dissimilarity of these two distributions in the objective function of the learning problem. In this paper, we showcase conceptual and computational benefits of measuring unfairness with integral probability metrics (IPMs) other than the Kolmogorov distance. Conceptually, we show that the generator of any IPM can be interpreted as a family of utility functions and that unfairness with respect to this IPM arises if individuals in the two demographic groups have diverging expected utilities. We also prove that the unfairness-regularized prediction loss admits unbiased gradient estimators if unfairness is measured by the squared $\mathcal L^2$-distance or by a squared maximum mean discrepancy. In this case, the fair learning problem is susceptible to efficient stochastic gradient descent (SGD) algorithms. Numerical experiments on real data show that these SGD algorithms outperform state-of-the-art methods for fair learning in that they achieve superior accuracy-unfairness trade-offs -- sometimes orders of magnitude faster. Finally, we identify conditions under which statistical parity can improve prediction accuracy.

翻译：本文研究针对分属两个人口群体的个体属性预测的监督学习问题，我们寻求满足统计平权条件的公平预测器。这意味着两群体预测结果的分布需在科尔莫戈罗夫距离下保持接近，并通过在目标函数中引入两分布差异惩罚项实现公平性。本文展示了使用积分概率度量而非科尔莫戈罗夫距离衡量不公平性的概念与计算优势。理论上，我们证明任意积分概率度量的生成器可解释为效用函数族，当两群体个体的期望效用存在差异时即产生该度量下的不公平性。我们还证明，若以平方$\mathcal L^2$距离或平方最大均值差异度量不公平性时，不公平性正则化预测损失可得到无偏梯度估计量，此时公平学习问题适用于高效随机梯度下降算法。真实数据数值实验表明，这些随机梯度下降算法在准确率-不公平性权衡方面优于现有最优公平学习方法——有时可实现数量级的速度提升。最后，我们识别出统计平权能提升预测准确率的条件。