MODE: Minimax Optimal Deterministic Experiments for Causal Inference in the Presence of Covariates

Data-driven decision-making has become crucial across various domains. Randomization and re-randomization are standard techniques employed in controlled experiments to estimate causal effects in the presence of numerous pre-treatment covariates. This paper quantifies the worst-case mean squared error of the difference-in-means estimator as a generalized discrepancy of covariates between treatment and control groups. We demonstrate that existing randomized or re-randomized experiments utilizing Monte Carlo methods are sub-optimal in minimizing this generalized discrepancy. To address this limitation, we introduce a novel optimal deterministic experiment based on quasi-Monte Carlo techniques, which effectively minimizes the generalized discrepancy in a model-independent manner. We provide a theoretical proof indicating that the difference-in-means estimator derived from the proposed experiment converges more rapidly than those obtained from completely randomized or re-randomized experiments using Mahalanobis distance. Simulation results illustrate that the proposed experiment significantly reduces covariate imbalances and estimation uncertainties when compared to existing randomized and deterministic approaches. In summary, the proposed experiment serves as a reliable and effective framework for controlled experimentation in causal inference.