Stronger Neyman Regret Guarantees for Adaptive Experimental Design

We study the design of adaptive, sequential experiments for unbiased average treatment effect (ATE) estimation in the design-based potential outcomes setting. Our goal is to develop adaptive designs offering sublinear Neyman regret, meaning their efficiency must approach that of the hindsight-optimal nonadaptive design. Recent work [Dai et al, 2023] introduced ClipOGD, the first method achieving widetildeO(√T) expected Neyman regret under mild conditions. In this work, we propose adaptive designs with substantially stronger Neyman regret guarantees. In particular, we modify ClipOGD to obtain anytime widetildeO(log T) Neyman regret under natural boundedness assumptions. Further, in the setting where experimental units have pre-treatment covariates, we introduce and study a class of contextual "multigroup" Neyman regret guarantees: Given any set of possibly overlapping groups based on the covariates, the adaptive design outperforms each group's best non-adaptive designs. In particular, we develop a contextual adaptive design with widetildeO(√T) anytime multigroup Neyman regret. We empirically validate the proposed designs through an array of experiments.