Semiparametric Efficiency in Sequential Experiments: Characterization and Design via Average Propensity
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序贯实验的半参数效率：基于平均倾向得分的刻画与设计
- 研究问题
- 在自适应分配、协变量平衡及资源约束下，序贯实验估计因果目标的效率基准如何刻画，又如何设计可实施的近有效分配？
- 方法与思路
- 作者以非预见设计诱导的平均倾向得分建立半参数下界，再通过有效影响函数回归调整或自适应协变量平衡实现分批设计。
- 材料陈述的贡献
- 摘要称统一了序贯设计的效率比较，两条设计路径可逼近共同基准；线性结局均值泛函另有尖锐二阶速率，并展示多处理应用。
- 阅读关注点
- 应核对平均倾向得分的定义、下界适用的估计量类别，以及干扰参数收敛要求、二阶速率和少量更新下逼近基准的条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审及接收未核实；摘要未给出完整速率和设计条件，不能据此断言任意自适应实验均能达到该下界。
原文摘要
Modern experiments, including evaluations of AI-enabled services and platform interventions, often depart from independent and identically distributed (i.i.d.) sampling because assignments may be adaptive, balanced across covariates, or subject to rollout constraints such as exposure, fairness, and budget limits. This paper studies the efficiency benchmark for estimating causal targets in such sequential experiments. We show that every non-anticipating design induces an average propensity score, and we establish a semiparametric lower bound: for regular locally unbiased estimators, attainable precision is bounded by the i.i.d. efficiency benchmark evaluated at this induced score. The average propensity score thereby serves as a common benchmark and design target, allowing sequential experimental design to be viewed as choosing or learning an efficient allocation rule, with operational constraints entering through the admissible set when present. We then develop implementable batched adaptive designs that approach this benchmark through two complementary mechanisms. The first uses regression adjustment based on efficient influence functions; for general smooth estimands it attains the benchmark under standard nuisance-rate conditions, while for linear functionals of outcome means it achieves a sharp second-order rate. The second uses adaptive covariate balancing to attain the same benchmark through the assignment mechanism, enabling simple moment-based estimation. Both routes require only a small number of policy updates, making them compatible with delayed feedback and easier to monitor in operational deployments. Numerical experiments and an empirical study of AI medical-assistant evaluation demonstrate the practical efficiency gains, including in multi-treatment settings. Overall, the paper provides a unified framework for characterizing and designing efficient sequential experiments.