We propose a distributionally robust classification model with a fairness constraint that encourages the classifier to be fair in view of the equality of opportunity criterion. We use a type-$\infty$ Wasserstein ambiguity set centered at the empirical distribution to model distributional uncertainty and derive a conservative reformulation for the worst-case equal opportunity unfairness measure. We establish that the model is equivalent to a mixed binary optimization problem, which can be solved by standard off-the-shelf solvers. To improve scalability, we further propose a convex, hinge-loss-based model for large problem instances whose reformulation does not incur any binary variables. Moreover, we also consider the distributionally robust learning problem with a generic ground transportation cost to hedge against the uncertainties in the label and sensitive attribute. Finally, we numerically demonstrate that our proposed approaches improve fairness with negligible loss of predictive accuracy.
翻译:我们提出一个分配上稳健的分类模式,以公平为限,鼓励分类员在机会均等标准下做到公平。我们使用以经验分配为中心、以分配不确定性为模型的瓦西斯坦(Wasserstein)型型模数模糊的模数,以模拟分配上的不确定性,并为最坏情况下的机会均等不公平措施进行保守的重新拟订。我们确定,该模式相当于混合的二进制优化问题,可以通过标准现成的解决方案加以解决。为了提高可缩放性,我们进一步为重塑不产生二进制变量的大型问题案例提出一个螺旋式、基于链点损失的模型。此外,我们还考虑使用通用地面运输成本的分布上稳健的学习问题,以防范标签和敏感属性的不确定性。最后,我们用数字来表明,我们提出的方法提高了公平性,但预测准确性损失微乎其微。