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DARTS: Targeting Prognostic Covariates in Budget-Constrained Sequential Experiments
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Proposes DARTS, a budgeted combinatorial Thompson sampler that learns which costly covariates to measure across batches, feeding them into rerandomization and Lin-adjusted inverse-variance pooling of batch ATE estimates.
Problem
Randomized trials assume prognostic covariates are free and known, but measuring high-dimensional covariates is costly under a hard budget, and the most prognostic ones are unknown a priori.
Approach
Treat covariate acquisition as a budgeted combinatorial semi-bandit problem solved with Beta-Bernoulli Thompson sampling (CBwK-LP-TS) using fractional LASSO-based rewards from control units, while preserving design-based randomization validity across sequential batches via rerandomization and precision-weighted meta-analysis.</808>
Key results
- DARTS achieves relative efficiency up to 3.56 over DiM versus 1.26 for Random in simulations.
- On the Liang DGP comparison with variable costs, DARTS reaches Rel. RMSE 1.415 vs 1.018 for ARMM and 1.036 for MADCovar (Oracle DARTS 1.812).
- Under Liang DGP with B=2000, p=100, n=1000, posterior inclusion probabilities separate signal (mean 0.34) from noise (mean 0.11) covariates.
Surprising findings
- Separation of signal vs noise posterior probabilities collapses when p=1000 and n=100, where the sampler degrades toward random selection.
- Pure per-batch budget schemes can perform arbitrarily badly, and explore-then-commit behaves similarly to random allocation under strict budgets.
Limitations
- Regret guarantees rely on idealized Beta-Bernoulli conjugacy; fractional reward approximation error depends on an unobservable TV distance.
- Only fixed-horizon inference is valid; peeking or early stopping invalidates coverage.
- Comparison with ARMM and MADCovar is informationally asymmetric by design.
Experimental setup
Datasets: synthetic linear DGP synthetic Liang DGP
Benchmarks: synthetic linear DGP synthetic Liang DGP
Metrics: standard error reduction relative efficiency relative RMSE cumulative regret CI width coverage posterior inclusion probability separation
Baselines: DiM Random Oracle DARTS ARMM MADCovar
Builds on: CBwK-LP-UCB rerandomization Lin adjustment Russo-Van Roy information-ratio decomposition ARMM
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