Robust Control Experiments for Multivariate Tests with Covariates and Network Information

Multivariate testing has recently emerged as a promising technique in scientific decision-making and electronic information fields.Unlike standard A/B/n testing, which evaluates individual variations, multivariate testing aims to identify the best-performing combination of variations from all possible combinations.We address the challenge of robustly allocating treatments to subjects in multivariate testing when treatment effects are confounded by covariates and subjects are interconnected through a network.In this paper, for the first time we introduce the use of a mixed effect model to account for covariate uncertainty and network structure.Based on this model, we propose a criterion to measure the regret of efficiency due to incorrect specification of the covariance structure.We derive minimax robust experimental schemes and introduce a novel scheme that optimally matches the design with the robust covariance structure.Our proposed experimental schemes demonstrate: (a) resilience to various optimality criteria, (b) efficiency against model misspecification, and (c) applicability to complex scenarios.This work extends existing researches in optimal A/B testing designs, offering theoretical foundations and practical implementations that Statistica Sinica: Newly accepted Paper outperform current approaches in statistical efficiency, as demonstrated through simulations and a case study.