LIDS and Stats Tea Talk

“The Power of Adaptivity in Experimental Design”

Given experiment subjects with potentially heterogeneous covariates and two possible treatments, namely active treatment and control, our work quantifies the optimal accuracy in estimating the treatment effect and proposes an experimental design that approaches this optimal accuracy, giving a first (non-asymptotic) answer to this fundamental question. The methodological contribution is 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 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 information-theoretic lower bound combined with Bayes risk analysis, 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.