Dependent Randomized Rounding for Budget Constrained Experimental Design
This work addresses the need for efficient experimental designs under strict budget limits in resource-constrained policy settings, offering a novel method for variance reduction.
The paper tackles the problem of designing budget-constrained experiments for policymakers by proposing a dependent randomized rounding framework that converts assignment probabilities into binary treatment decisions, resulting in improved estimator precision through variance reduction with theoretical guarantees and empirical validation.
Policymakers in resource-constrained settings require experimental designs that satisfy strict budget limits while ensuring precise estimation of treatment effects. We propose a framework that applies a dependent randomized rounding procedure to convert assignment probabilities into binary treatment decisions. Our proposed solution preserves the marginal treatment probabilities while inducing negative correlations among assignments, leading to improved estimator precision through variance reduction. We establish theoretical guarantees for the inverse propensity weighted and general linear estimators, and demonstrate through empirical studies that our approach yields efficient and accurate inference under fixed budget constraints.