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.

We actually compare with AutoGrow in2 paragraph Growing Wider and Deeper Networks, around line 218. Due to the space limit, we move the re-3 sult to appendix. Moreover, AutoGrow can only grow layers so it does not compare with many well known4 NAS baseline. We choose DARTS because it is still a very popular baseline in recent NAS papers, which5 gives new papers a fast, gradient based, weight-sharing NAS baseline with a low error rate to compare with.6 RSPSDARTSV1/2 ENASSETNGDASOurs Acc. At least it can be validated on9 NAS-Bench-101,201.