Treatment Allocation under Uncertain Costs
This paper addresses the problem of optimal treatment allocation under a budget constraint when treatment costs vary heterogeneously with covariates. We propose a threshold rule based on a priority score and establish, for the first time, a theoretical link between optimal allocation under uncertain costs and instrumental variable (IV) estimation of heterogeneous treatment effects. We rigorously derive the optimal threshold structure and prove its learnability. Our method integrates randomized controlled trial data, priority score modeling, threshold-based decision making, and an IV estimation framework. Empirically, the approach significantly outperforms standard benchmarks across multiple evaluation metrics, achieving maximal social value or firm profit within budget constraints. It provides a new paradigm—statistically rigorous yet practically implementable—for applications including scarce healthcare resource allocation and dynamic pricing.