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：我们研究对属于两个人口群体之一的个人的属性进行预测的监督学习问题,我们寻求根据统计等同而公平的预测数据。这意味着这两个群体内部预测的分布应接近科尔莫戈洛夫距离,而公平则是通过惩罚这两种分布在学习问题客观功能中的差异性来实现的。在本文中,我们展示了衡量不公平的概念和计算效益,衡量整体概率指标(IPMs)而不是科尔莫戈洛夫距离。从概念上看,我们表明任何IPM的生成者都可以被解释为一个具有效用功能的大家庭,如果两个人口群体中的个人有不同的预期效用,那么这两个群体内部预测的分布就会产生不公平现象。我们还证明,如果以正方元L%2美元距离或正方位最大平均差异来衡量不公平性,则不公平性预测性损失将不带偏差的梯度估计值。在本案中,公平学习问题很容易被解释为高效的梯度梯度梯度下降(SGD)算法(SGD),如果两个人口群体中的个人有不同的预期效用,则会产生对IPM的不公分值的不公平性。 数字性预测性测算,我们有时在精确度的精确性统计方法下,在精确度上可以发现这些精确的精确度的精确度的精确度分析方法显示这些精确度。