K-armed randomized experiments require careful sample size planning to estimate conditional counterfactual expectations accurately. The study focuses on determining the minimum sample size needed to offset estimation errors and conduct simultaneous inferences. By partitioning the feature space and learning sub-groups, the study evaluates nominal guarantees using policy trees on a large dataset. The main goal is to ensure accurate inference on treatment effects at the sub-group level, emphasizing unbiased estimators and sufficient sample sizes per treatment group per leaf. The study also discusses regularity conditions, main results, and empirical evaluations using semi-synthetic simulations.
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