Good Allocations from Bad Estimates

2026-01-09

arXiv.org

AI Summary

This work addresses the high sample complexity of traditional conditional average treatment effect (CATE) methods, which require large datasets to enable precise interventions in heterogeneous populations. The authors propose a novel framework that achieves near-optimal aggregate intervention outcomes with only \(O(M/\varepsilon)\) samples by leveraging coarse treatment effect estimates combined with a greedy allocation strategy under budget constraints. The key insight lies in distinguishing between the goals of effect estimation and intervention allocation, demonstrating that highly accurate CATE estimates are unnecessary for effective decision-making. By exploiting structural properties of the underlying data distribution and incorporating stratified sampling, the method further reduces sample requirements. Empirical evaluations on multiple real-world randomized controlled trial datasets confirm the approach’s efficiency and practical utility.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Conditional average treatment effect (CATE) estimation is the de facto gold standard for targeting a treatment to a heterogeneous population. The method estimates treatment effects up to an error $\epsilon>0$ in each of $M$ different strata of the population, targeting individuals in decreasing order of estimated treatment effect until the budget runs out. In general, this method requires $O(M/\epsilon^2)$ samples. This is best possible if the goal is to estimate all treatment effects up to an $\epsilon$ error. In this work, we show how to achieve the same total treatment effect as CATE with only $O(M/\epsilon)$ samples for natural distributions of treatment effects. The key insight is that coarse estimates suffice for near-optimal treatment allocations. In addition, we show that budget flexibility can further reduce the sample complexity of allocation. Finally, we evaluate our algorithm on various real-world RCT datasets. In all cases, it finds nearly optimal treatment allocations with surprisingly few samples. Our work highlights the fundamental distinction between treatment effect estimation and treatment allocation: the latter requires far fewer samples.

Problem

• treatment allocation
• sample complexity
• conditional average treatment effect
• heterogeneous populations
• budget constraints

Innovation

• treatment allocation
• sample complexity
• CATE estimation
• budget flexibility
• heterogeneous treatment effects