Optimal Adaptive Experimental Design for Estimating Treatment Effect

TL;DR

This paper develops an adaptive experimental design framework that achieves near-optimal accuracy in estimating treatment effects by integrating bandit learning techniques and establishing theoretical lower bounds.

Contribution

It introduces a novel adaptive experiment design that combines doubly robust estimation and bandit algorithms to approach the fundamental optimal accuracy in treatment effect estimation.

Findings

Proposed a low switching adaptive experiment framework.

Achieved near-optimal estimation accuracy with minimal policy updates.

Established new lower bounds for non-i.i.d. data in experimental design.

Abstract

Given n experiment subjects with potentially heterogeneous covariates and two possible treatments, namely active treatment and control, this paper addresses the fundamental 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 yet still open question. The methodological contribution is listed as following. First, we establish an idealized optimal estimator with minimal variance as benchmark, and then demonstrate that adaptive experiment is necessary to achieve near-optimal estimation accuracy. Secondly, by incorporating the concept of 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 design. 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.