DARTS: Targeting Prognostic Covariates in Budget-Constrained Sequential Experiments

TL;DR

DARTS is a sequential experimental design method that optimally selects prognostic covariates under budget constraints, improving efficiency while maintaining valid causal inference.

Contribution

It introduces a novel adaptive covariate selection approach using Thompson sampling that preserves randomization validity and enhances experimental efficiency.

Findings

DARTS concentrates budget on informative covariates, improving efficiency.

The method achieves asymptotic coverage guarantees for treatment effect estimates.

Empirical results show DARTS closes the efficiency gap to oracle designs.

Abstract

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.