# Treatment Allocation under Uncertain Costs

arXiv: https://arxiv.org/abs/2103.11066 · HTML: https://mlsanity.com/paper/2103.11066/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Mar 2021.

## Built on by (most cited first, 10 of 10)

- [Evaluating Treatment Prioritization Rules via Rank-Weighted Average Treatment Effects](https://mlsanity.com/paper/2111.07966/) (2021)
- [Machine Learning Who to Nudge: Causal vs Predictive Targeting in a Field Experiment on Student Financial Aid Renewal](https://mlsanity.com/paper/2310.08672/) (2023)
- [Evaluating the Effectiveness of Index-Based Treatment Allocation](https://mlsanity.com/paper/2402.11771/) (2024)
- [Mind the Gap: Optimal and Equitable Encouragement Policies](https://mlsanity.com/paper/2309.07176/) (2023)
- [Incentive-Aware Synthetic Control: Accurate Counterfactual Estimation via Incentivized Exploration](https://mlsanity.com/paper/2312.16307/) (2023)
- [Deployment of AI-Assisted Interventions: Capacity Constraints and Noisy Compliance](https://mlsanity.com/paper/2604.14370/) (2026)
- [Set-Valued Policy Learning](https://mlsanity.com/paper/2605.19830/) (2026)
- [Learning Treatment Effects during Resource Allocation via Priority-Queue Randomization](https://mlsanity.com/paper/2605.25169/) (2026)
- [Certificates without Electrons? Theory and Evidence on Impacts from AI-Driven Power Demand](https://mlsanity.com/paper/2606.00811/) (2026)
- [What Would it Cost to End Extreme Poverty?](https://mlsanity.com/paper/2609.02013/) (2026)

## Abstract (arXiv)

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 (those with a higher score are treated first), 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.