Good Allocations from Bad Estimates
This work addresses the sample efficiency challenge in treatment allocation for policymakers and researchers, offering a significant reduction in required samples while maintaining effectiveness, though it is incremental in improving upon existing CATE methods.
The paper tackles the problem of treatment allocation in heterogeneous populations by showing that coarse estimates of treatment effects can achieve near-optimal allocations with only O(M/ε) samples, compared to the O(M/ε²) required for precise estimation, and demonstrates this on real-world datasets with surprisingly few samples.
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.