🤖 AI Summary
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.
📝 Abstract
We consider the problem of learning how to optimally allocate treatments whose cost is uncertain and can vary with pre-treatment covariates. This setting may arise in medicine if we need to prioritize access to a scarce resource that different patients would use for different amounts of time, or in marketing if we want to target discounts whose cost to the company depends on how much the discounts are used. Here, we show that the optimal treatment allocation rule under budget constraints is a thresholding rule based on priority scores, and we propose a number of practical methods for learning these priority scores using data from a randomized trial. Our formal results leverage a statistical connection between our problem and that of learning heterogeneous treatment effects under endogeneity using an instrumental variable. We find our method to perform well in a number of empirical evaluations.
