Automated AI classifiers should be able to defer the prediction to a human decision maker to ensure more accurate predictions. In this work, we jointly train a classifier with a rejector, which decides on each data point whether the classifier or the human should predict. We show that prior approaches can fail to find a human-AI system with low misclassification error even when there exists a linear classifier and rejector that have zero error (the realizable setting). We prove that obtaining a linear pair with low error is NP-hard even when the problem is realizable. To complement this negative result, we give a mixed-integer-linear-programming (MILP) formulation that can optimally solve the problem in the linear setting. However, the MILP only scales to moderately-sized problems. Therefore, we provide a novel surrogate loss function that is realizable-consistent and performs well empirically. We test our approaches on a comprehensive set of datasets and compare to a wide range of baselines.

翻译：自动化AI分类器应能委托人类决策者进行预测，以确保更高准确性。在本研究中，我们联合训练一个分类器与一个拒绝器，后者为每个数据点决定是由分类器还是人类进行预测。我们证明，即使存在线性分类器和拒绝器可实现零误差（可实例化设置），先前方法也可能无法找到低误分类误差的人机系统。我们证明，即使问题可实例化，获得低误差线性配对也是NP难的。为补充这一负面结论，我们提出一种混合整数线性规划（MILP）公式，可在线性设置下最优求解该问题。然而，MILP仅适用于中等规模问题。因此，我们提出一种新颖的代理损失函数，该函数具有可实例化一致性且经验性能良好。我们在全面数据集上测试方法，并与广泛基线进行对比。