Efficient Adaptive Experimentation with Noncompliance

TL;DR

This paper develops an efficient adaptive experimental method for estimating treatment effects using instrumental variables, optimizing allocation and providing robust, sequential inference in complex adaptive settings.

Contribution

It introduces AMRIV, a novel adaptive, multiply-robust estimator with variance-aware allocation that achieves the efficiency bound in instrumental-variable experiments.

Findings

AMRIV attains the semiparametric efficiency bound.

Adaptive instrument assignment improves estimation efficiency.

The method provides valid confidence sequences for sequential inference.

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 Adaptive, Multiply-Robust estimator for Instrumental-Variable 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.