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Automated AI classifiers should be able to defer the prediction to a humandecision maker to ensure more accurate predictions. In this work, we jointlytrain a classifier with a rejector, which decides on each data point whetherthe classifier or the human should predict. We show that prior approaches canfail to find a human-AI system with low misclassification error even when thereexists a linear classifier and rejector that have zero error (the realizablesetting). We prove that obtaining a linear pair with low error is NP-hard evenwhen the problem is realizable. To complement this negative result, we give amixed-integer-linear-programming (MILP) formulation that can optimally solvethe problem in the linear setting. However, the MILP only scales tomoderately-sized problems. Therefore, we provide a novel surrogate lossfunction that is realizable-consistent and performs well empirically. We testour approaches on a comprehensive set of datasets and compare to a wide rangeof baselines.

Who Should Predict? Exact Algorithms For Learning to Defer to Humans