Primary Submission Category: Design of Experiments
Optimal Adaptive Experimental Design for Estimating Treatment Effect
Authors: Jiachun Li, David Simchi-Levi, Yunxiao Zhao,
Presenting Author: Jiachun Li*
Given n experiment subjects with potentially heterogeneous covariates and two possible treat
ments, namely active treatment and control, this paper addresses the question of determining the optimal
accuracy in estimating the treatment effect. Furthermore, we propose an experimental design that approaches
this optimal accuracy, giving a (non-asymptotic) answer to this fundamental question. The methodological
contributions are listed as follows. First, we establish an idealized optimal estimator with minimal variance
as benchmark, and then demonstrate that adaptive experiment is necessary to achieve near-optimal esti
mation accuracy. Second, by incorporating the doubly robust method into sequential experimental design,
we frame the optimal estimation problem as an online bandit learning problem, bridging the two fields of
statistical estimation and bandit learning. Using tools and ideas from both bandit algorithm design and
adaptive statistical estimation, we propose a general low switching adaptive experiment framework, which
could be a generic research paradigm for a wide range of adaptive experimental designs. Through novel lower
bound techniques for non-i.i.d. data, we demonstrate the optimality of our proposed experiment. Numerical
result indicates that the estimation accuracy approaches optimal with as few as two or three policy updates.