Decision-Making under Miscalibration

ML-based predictions are used to inform consequential decisions about individuals. How should we use predictions (e.g., risk of heart attack) to inform downstream binary classification decisions (e.g., undergoing a medical procedure)? When the risk estimates are perfectly calibrated, the answer is well understood: a classification problem's cost structure induces an optimal treatment threshold jstar. In practice, however, some amount of miscalibration is unavoidable, raising a fundamental question: how should one use potentially miscalibrated predictions to inform binary decisions? We formalize a natural (distribution-free) solution concept: given anticipated miscalibration of α, we propose using the threshold j that minimizes the worst-case regret over all α-miscalibrated predictors, where the regret is the difference in clinical utility between using the threshold in question and using the optimal threshold in hindsight. We provide closed form expressions for j when miscalibration is measured using both expected and maximum calibration error, which reveal that it indeed differs from jstar (the optimal threshold under perfect calibration). We validate our theoretical findings on real data, demonstrating that there are natural cases in which making decisions using j improves the clinical utility.