Optimizing Social Utility in Sequential Experiments

Experimental design has emerged as a powerful approach for improving the sample efficiency of A/B testing, yet existing designs rely critically on correctly specified models. We study robust sequential experimental design under model misspecification and develop a unified framework that covers both contextual bandit and dynamic settings. Theoretically, we prove that our design bounds the worst-case mean squared error of the estimated treatment effect. Empirically, we demonstrate the effectiveness of the proposed approach using synthetic and real-world datasets from a leading technology company.

Suppose a planner has a pre-trained simulator of a sequential decision problem and the option to run real experiments in the field. The simulator is cheap to query but inherits confounding and drift from its calibration data. Experimentation is unbiased but consumes one real unit per trial. We study when, and how, the planner should supplement the simulator with experiments. We give three results. First, an extended simulation lemma decomposes the simulator's value error into a calibration--deployment shift that randomization can identify and a parametric residual that no further interaction can reduce. Second, the value gap between the simulator-optimal policy and the optimum splits into a local component, on states the deployed policy already visits, and a reachability component, on states it does not. The reachability component stays bounded away from zero at any horizon under purely passive learning. Third, we propose Fisher-SEP, a simulation-aided experimental policy (SEP) that minimizes the posterior predictive variance of a target policy's value, with reward-only and transition-only specializations. Two case studies illustrate the regimes. In a vending-machine supply chain, front-loaded experimentation overtakes posterior updating once the horizon is long enough to amortize the pilot. In an HIV mobile-testing example with a corridor that separates a well-surveilled region from a poorly-surveilled one, only designed exploration reaches the poorly-surveilled region.

Randomized controlled trials typically assume that prognostic covariates are known and available at no cost. In practice, obtaining high-dimensional pretreatment data is costly, forcing a trade-off between covariate-adaptive precision and a measurement budget. We introduce Dynamic Adaptive Rerandomization via Thompson Sampling (DARTS), which treats covariate acquisition as a sequential optimization problem embedded within a design-based causal inference task. A budgeted combinatorial Thompson sampler learns which covariates are most prognostic across successive batches; selected covariates then drive rerandomization and regression adjustment to reduce batch-level average treatment effect variance. Our primary theoretical contribution is a decoupling result: adaptive covariate selection based on past batches preserves batch-level randomization validity, and the cumulative inverse-variance weighted estimator achieves at least nominal asymptotic coverage. We further derive a Bayes risk bound for the acquisition layer that matches the minimax lower bound up to logarithmic factors. Empirically, DARTS systematically concentrates the budget on informative features, significantly closing the efficiency gap to oracle designs while maintaining strict inferential validity.