When Comparison Is Easier Than Evaluation: Learning Better Randomization Designs

Randomization identifies treatment effects, but its dependence structure controls precision. Across repeated cohorts, practitioners may choose among independent assignment, matching, rerandomization, and balancing schemes that all preserve treatment probability one half. Learning the most precise law from observed outcomes seems impossible: quadratic risk depends on both potential outcomes, yet only one is observed. We show that comparison escapes this obstruction. Centered sign designs share a unit covariance diagonal, so subtracting two risks removes the unobserved within-unit products. Under independent fair reference assignment, no absolute risk is universally unbiasedly estimable from one cohort without outcome restrictions, whereas every pairwise risk difference is. This identity yields Prediction-Augmented Comparative Randomization Learning (\PCRL): occasional reference rounds and simulated ghost assignments provide sampler-only unbiased contrasts, while an inverse-reference residual corrects any clipped predictable contrast model. Optimistic mirror descent gives finite-horizon expected regret against a fixed finite contextual-policy class, and cohort-size weighting converts it into expected excess-MSE control for unequal cohorts. Fresh centered deployment preserves deterministic-horizon unbiasedness and yields an exact MSE identity; bounded equal-size cohorts additionally admit anytime-valid confidence sequences. Polynomial-hint \PCRL improves on vanilla \CRL in all 17 controlled synthetic cells ($1.83$–$10.28\%$; median $5.66\%$). Against a raw linear plug-in from the same misspecified predictor class, it improves by $3.4$–$42.3\%$ throughout a contiguous 16/36-cell region at $\beta \ge .625$, with all 16 pointwise seed-level 95% confidence intervals excluding zero, and remains below Bernoulli risk across the full surface.