Efficient Adaptive Experimentation with Non-Compliance

• URL: http://arxiv.org/abs/2505.17468v1
• Date: Fri, 23 May 2025 04:49:14 GMT
• Title: Efficient Adaptive Experimentation with Non-Compliance
• Authors: Miruna Oprescu, Brian M Cho, Nathan Kallus,
• Abstract summary: We study the problem of estimating the average treatment effect (ATE) in adaptive experiments where treatment can only be encouraged--rather than directly assigned--via a binary instrumental variable.<n>We introduce AMRIV, an online policy that adaptively approximates the optimal allocation with (ii) a sequential, influence-function-based estimator that attains the semi-parametric efficiency bound while retaining multiplyrobust consistency.
• Score: 39.43227019824619
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the problem of estimating the average treatment effect (ATE) in adaptive experiments where treatment can only be encouraged--rather than directly assigned--via a binary instrumental variable. Building on semiparametric efficiency theory, we derive the efficiency bound for ATE estimation under arbitrary, history-dependent instrument-assignment policies, and show it is minimized by a variance-aware allocation rule that balances outcome noise and compliance variability. Leveraging this insight, we introduce AMRIV--an \textbf{A}daptive, \textbf{M}ultiply-\textbf{R}obust estimator for \textbf{I}nstrumental-\textbf{V}ariable settings with variance-optimal assignment. AMRIV pairs (i) an online policy that adaptively approximates the optimal allocation with (ii) a sequential, influence-function-based estimator that attains the semiparametric efficiency bound while retaining multiply-robust consistency. We establish asymptotic normality, explicit convergence rates, and anytime-valid asymptotic confidence sequences that enable sequential inference. Finally, we demonstrate the practical effectiveness of our approach through empirical studies, showing that adaptive instrument assignment, when combined with the AMRIV estimator, yields improved efficiency and robustness compared to existing baselines.

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