Good Allocations from Bad Estimates

TL;DR

This paper reframes treatment allocation as a distinct objective from CATE estimation, showing that near-optimal allocations can be achieved with much fewer samples than full CATE estimation when τ(u) values are drawn from smooth distributions. The authors introduce a low-accuracy, non-adaptive allocation algorithm that estimates τ(u) to a coarse accuracy ρ = Θ(√ε) and relies on quantile information of the τ distribution, yielding an $O(M/\epsilon)$ sample complexity under ρ-regularity. They provide a general optimality condition, show how to compute key quantities from the τCDF, and demonstrate that even very coarse estimates can produce near-optimal allocations in practice, validated across five real-world RCTs. The work also discusses budget-flexible strategies (underspending/overspending) to maintain near-optimality when the threshold sits in hard regions, with actionable guidance for policymakers. Overall, the paper establishes a fundamental separation between estimation and allocation, offering practical, sample-efficient methods for welfare-maximizing interventions.

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 $ε> 0$ 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 $O(M/ε^2)$ samples. This is best possible if the goal is to estimate all treatment effects up to an $ε$ error. In this work, we show how to achieve the same total treatment effect as CATE with only $O(M/ε)$ 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.

Figures (36)

• Figure 1: For the purposes of treatment allocation, we do not require highly-accurate CATE estimates for groups that have treatment effect values bounded away from the allocation threshold $\tau_K$.
• Figure 2: In all cases, we realize a close-to-optimal allocation with very few samples (blue), much less than the worst-case of $O(M/\epsilon^2)$ (red) and even less than our theoretical bound $O(M/\epsilon)$ (green).
• Figure 3: Top row: failure rate vs $\epsilon$. Bottom row: closest $K'$ value vs $\epsilon$. Each row represents one dataset (STAR, TUP, NSW, Acup., Post-op) with one of the unit grouping methods that we study.
• Figure 4: STAR dataset, school groups.
• Figure 5: STAR dataset, performance groups.

Theorems & Definitions (55)

• Theorem 1: Informal
• Definition 1
• Definition 2: Estimation oracle
• Definition 3: $\mathsf{FullCATE}$ problem
• Lemma 2
• Definition 4: Value
• Definition 5
• Definition 6: $\mathsf{ALLOC}$ problem
• Lemma 2
• proof