The increasing use of machine learning in high-stakes domains -- where people's livelihoods are impacted -- creates an urgent need for interpretable, fair, and highly accurate algorithms. With these needs in mind, we propose a mixed integer optimization (MIO) framework for learning optimal classification trees -- one of the most interpretable models -- that can be augmented with arbitrary fairness constraints. In order to better quantify the "price of interpretability", we also propose a new measure of model interpretability called decision complexity that allows for comparisons across different classes of machine learning models. We benchmark our method against state-of-the-art approaches for fair classification on popular datasets; in doing so, we conduct one of the first comprehensive analyses of the trade-offs between interpretability, fairness, and predictive accuracy. Given a fixed disparity threshold, our method has a price of interpretability of about 4.2 percentage points in terms of out-of-sample accuracy compared to the best performing, complex models. However, our method consistently finds decisions with almost full parity, while other methods rarely do.

翻译：在高风险领域（例如影响人们生计的领域）中，机器学习的日益普及催生了对可解释、公平且高精度算法的迫切需求。基于这些需求，我们提出了一种混合整数优化（MIO）框架，用于学习最优分类树——可解释性最强的模型之一，并可通过任意公平性约束进行增强。为更好地量化“可解释性的代价”，我们还提出了一种新的模型可解释性度量指标——决策复杂度，该指标支持跨不同类别机器学习模型的比较。我们在常用数据集上，将我们的方法与最先进的公平分类方法进行对比；在此过程中，我们首次全面分析了可解释性、公平性与预测准确性之间的权衡。在给定固定差异阈值的情况下，与性能最佳但结构复杂的模型相比，我们的方法在样本外准确性上的可解释性代价约为4.2个百分点。然而，我们的方法始终能发现几乎完全等效的决策结果，而其他方法很少能做到这一点。