Observationally Informed Adaptive Causal Experimental Design

Randomized Controlled Trials (RCTs) represent the gold standard for causal inference yet remain a scarce resource. While large-scale observational data is often available, it is typically used only for retrospective fusion, and remains discarded in prospective trial design due to bias concerns. We argue that this ''tabula rasa'' data acquisition strategy is inefficient when observational models contain useful structural information. In this work, we propose Active Residual Learning, a new paradigm that leverages the observational model as an informative but biased prior. This shifts the experimental focus from learning target causal quantities from scratch to estimating residual corrections that debias the observational model. To operationalize this, we introduce the R-Design framework. Theoretically, we characterize two key advantages: (1) a conditional structural efficiency gap, showing that estimating lower-complexity residual contrasts can admit faster convergence rates than reconstructing full outcomes; and (2) information efficiency, where we quantify the redundancy in standard parameter-based acquisition, demonstrating that such baselines can waste budget on task-irrelevant nuisance uncertainty. We propose R-EPIG (Residual Expected Predictive Information Gain), a unified criterion that directly targets the downstream causal quantity, reducing residual uncertainty for estimation or clarifying decision boundaries for policy. Experiments on synthetic and semi-synthetic benchmarks show that R-Design significantly outperforms baselines in the intended informative-but-biased regime, supporting the effectiveness of correcting a biased model rather than learning from scratch.