Active Adaptive Experimental Design for Treatment Effect Estimation with
  Covariate Choices
Masahiro Kato Akihiro Oga Wataru Komatsubara Ryo Inokuchi
This study designs an adaptive experiment for efficiently estimating average
treatment effect (ATEs). We consider an adaptive experiment where an
experimenter sequentially samples an experimental unit from a covariate density
decided by the experimenter and assigns a treatment. After assigning a
treatment, the experimenter observes the corresponding outcome immediately. At
the end of the experiment, the experimenter estimates an ATE using gathered
samples. The objective of the experimenter 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 a framework under which an
experimenter optimizes the covariate density, as well as the propensity score,
and find that optimizing both covariate density and propensity score reduces
the asymptotic variance more than optimizing only the propensity score. Based
on this idea, in each round of our experiment, the experimenter optimizes the
covariate density and propensity score based on past observations. To design an
adaptive experiment, we first derive the efficient covariate density and
propensity score that minimizes the semiparametric efficiency bound, a lower
bound for the asymptotic variance given a fixed covariate density and a fixed
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.