提出自适应工具变量实验方法，提升因果推断效率与鲁棒性。
Efficient Adaptive Experimentation with Noncompliance
- 基于方差感知的动态分配策略优化实验资源
- 新估计器在任意历史依赖分配下逼近最优效率界
- 适合需要实时反馈与高可靠性的在线实验场景
我们研究了在自适应实验中通过二元工具变量仅能激励而无法直接分配处理的情形下，估计平均处理效应（ATE）的问题。基于半参数效率理论，推导出任意历史依赖工具变量分配策略下的效率界，并证明其可通过平衡结果噪声与依从性变异性的方差感知分配规则最小化。基于此，我们提出AMRIV——一种适用于工具变量设置的自适应、多重稳健估计器，结合在线策略以近似最优分配，以及基于影响函数的序列估计器，可实现半参数效率界，同时保持多重稳健一致性。我们建立了渐近正态性、明确收敛速率及任意时间有效的渐近置信序列，支持顺序推断。实证研究表明，将自适应工具变量分配与AMRIV估计器结合，相比现有基线显著提升效率与鲁棒性。
原文摘要 · Abstract (English)
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.
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