We consider the problem of efficient inference of the Average Treatment Effect in a sequential experiment where the policy governing the assignment of subjects to treatment or control can change over time. We first provide a central limit theorem for the Adaptive Augmented Inverse-Probability Weighted estimator, which is semiparametric efficient, under weaker assumptions than those previously made in the literature. This central limit theorem enables efficient inference at fixed sample sizes. We then consider a sequential inference setting, deriving both asymptotic and nonasymptotic confidence sequences that are considerably tighter than previous methods. These anytime-valid methods enable inference under data-dependent stopping times (sample sizes). Additionally, we use propensity score truncation techniques from the recent off-policy estimation literature to reduce the finite sample variance of our estimator without affecting the asymptotic variance. Empirical results demonstrate that our methods yield narrower confidence sequences than those previously developed in the literature while maintaining time-uniform error control.

翻译：我们考虑序贯实验中平均处理效应的高效推断问题，其中将受试者分配至处理组或对照组的策略可以随时间变化。我们首先在比以往文献更弱的假设条件下，为自适应增强逆概率加权估计量提供了中心极限定理，该估计量具有半参数有效性。这一中心极限定理使得在固定样本量下实现高效推断成为可能。随后我们考虑序贯推断场景，推导出比现有方法更紧凑的渐近与非渐近置信序列。这些时效有效方法支持在数据依赖的终止时间（样本量）下进行推断。此外，我们采用近期离策略估计文献中的倾向得分截断技术，在保证渐近方差不变的前提下降低估计量的有限样本方差。实证结果表明，相较于现有文献方法，我们的方法在保持时间均匀误差控制的同时能获得更窄的置信序列。