Treatment Locality in A/B TestingResearch Paper
Modern A/B tests must infer *lifetime* treatment effects — e.g. customer lifetime value under a new feature — from short-horizon experiment data. Chen, Simchi-Levi and Wang (arXiv:2407.19618) model the experiment as a Markov decision process and exploit a structural fact of many practical interventions: the treatment is *local*, modifying the system at a single crucial state only. This mission formalizes the core asymptotic theory of the paper: for **any** differentiable estimator built from the experiment's transition and reward statistics, *information sharing* — pooling across test arms the samples collected away from the treated state — keeps the estimator asymptotically normal with the same asymptotic bias and never increases its asymptotic variance (Theorem 9), and is asymptotically efficient among unbiased estimators (Theorem 5). The route runs through a Markov chain central limit theorem with the asymptotic variance identified as the autocovariance series, and the linearization/delta method for functionals of chain statistics.