DARTS: Targeting Prognostic Covariates in Budget-Constrained Sequential Experiments
For experimenters with limited measurement budgets, DARTS provides a principled method to select prognostic covariates adaptively, improving precision without compromising validity.
DARTS treats covariate acquisition as a sequential optimization problem within budget-constrained experiments, achieving near-oracle efficiency while maintaining valid inference. Empirically, it closes the efficiency gap to oracle designs with strict inferential validity.
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.