LAUSR

Significance Randomized controlled trials are central to the scientific process, but they can be costly. For example, a clinical trial may assign patients to treatments that are detrimental to them. Adaptive experimental designs, such as multiarmed bandit algorithms, reduce costs by increasing the probability of assigning promising treatments over the course of the experiment. However, because observations collected by these methods are dependent and their distribution is nonstationary, statistical inference can be challenging. We propose a treatment-effect estimator that has an asymptotically unbiased and normal test statistic under straightforward, relatively weak conditions on the adaptive design. This estimator generalizes for a variety of parameters of interest. Adaptive experimental designs can dramatically improve efficiency in randomized trials. But with adaptively collected data, common estimators based on sample means and inverse propensity-weighted means can be biased or heavy-tailed. This poses statistical challenges, in particular when the experimenter would like to test hypotheses about parameters that were not targeted by the data-collection mechanism. In this paper, we present a class of test statistics that can handle these challenges. Our approach is to adaptively reweight the terms of an augmented inverse propensity-weighting estimator to control the contribution of each term to the estimator’s variance. This scheme reduces overall variance and yields an asymptotically normal test statistic. We validate the accuracy of the resulting estimates and their CIs in numerical experiments and show that our methods compare favorably to existing alternatives in terms of mean squared error, coverage, and CI size.