Active Adaptive Experimental Design for Treatment Effect Estimation with Covariate Choices
This work addresses the challenge of improving statistical efficiency in treatment effect estimation for researchers conducting adaptive experiments, representing an incremental advance over existing methods that focus solely on propensity score optimization.
The study tackles the problem of efficiently estimating average treatment effects (ATEs) in adaptive experiments by proposing a method that optimizes both covariate density and propensity score, which reduces the asymptotic variance more effectively than optimizing only the propensity score, as shown through derivation of minimized semiparametric efficiency bounds.
This study designs an adaptive experiment for efficiently estimating average treatment effects (ATEs). In each round of our adaptive experiment, an experimenter sequentially samples an experimental unit, assigns a treatment, and observes the corresponding outcome immediately. At the end of the experiment, the experimenter estimates an ATE using the gathered samples. The objective is to estimate the ATE with a smaller asymptotic variance. Existing studies have designed experiments that adaptively optimize the propensity score (treatment-assignment probability). As a generalization of such an approach, we propose optimizing the covariate density as well as the propensity score. First, we derive the efficient covariate density and propensity score that minimize the semiparametric efficiency bound and find that optimizing both covariate density and propensity score minimizes the semiparametric efficiency bound more effectively than optimizing only the propensity score. Next, we design an adaptive experiment using the efficient covariate density and propensity score sequentially estimated during the experiment. Lastly, we propose an ATE estimator whose asymptotic variance aligns with the minimized semiparametric efficiency bound.