2023/05/26 by Jessica Dai, Dai, Jessica, Paula Gradu +3 · 4 citations
Computer Science · Decision Sciences · Mathematics · #Advanced Multi-Objective Optimization Algorithms #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Methodology (stat.ME) #Optimal Experimental Design Methods #Statistical Methods in Clinical Trials
paper · pdf · doi:10.48550/arxiv.2305.17187
openalex publication_date 2023/05/26 · openalex created_date 2023/05/31 · openalex updated_date 2026/07/28
From clinical development of cancer therapies to investigations into partisan bias, adaptive sequential designs have become increasingly popular method for causal inference, as they offer the possibility of improved precision over their non-adaptive counterparts. However, even in simple settings (e.g. two treatments) the extent to which adaptive designs can improve precision is not sufficiently well understood. In this work, we study the problem of Adaptive Neyman Allocation in a design-based potential outcomes framework, where the experimenter seeks to construct an adaptive design which is nearly as efficient as the optimal (but infeasible) non-adaptive Neyman design, which has access to all potential outcomes. Motivated by connections to online optimization, we propose Neyman Ratio and Neyman Regret as two (equivalent) performance measures of adaptive designs for this problem. We present Clip-OGD, an adaptive design which achieves \widetildeO(√(T)) expected Neyman regret and thereby recovers the optimal Neyman variance in large samples. Finally, we construct a conservative variance estimator which facilitates the development of asymptotically valid confidence intervals. To complement our theoretical results, we conduct simulations using data from a microeconomic experiment.