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：机器学习在高风险领域——即影响人民生计的领域——的日益广泛应用，迫切需要可解释、公平且高精度的算法。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——最具可解释性的模型之一——并可附加任意公平性约束。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，称为决策复杂度，允许在不同类别的机器学习模型之间进行比较。我们将所提方法与公平分类领域最先进的方法在流行数据集上进行基准测试；在此过程中，我们首次全面分析了可解释性、公平性和预测准确性之间的权衡。在固定差异阈值下，与性能最佳的复杂模型相比，我们的方法在样本外准确性方面的可解释性代价约为4.2个百分点。然而，我们的方法始终能够找到几乎完全平等的决策，而其他方法很少能做到这一点。