Feasible Fusion: Constrained Joint Estimation under Structural Non-Overlap

Causal inference in modern large-scale systems faces growing challenges, including high-dimensional covariates, multi-valued treatments, massive observational (OBS) data, and limited randomized controlled trial (RCT) samples due to cost constraints. We formalize treatment-induced structural non-overlap and show that, under this regime, commonly used weighted fusion methods provably fail to satisfy randomized identifying restrictions.To address this issue,we propose a constrained joint estimation framework that minimizes observational risk while enforcing causal validity through orthogonal experimental moment conditions. We further show that structural non-overlap creates a feasibility obstruction for moment enforcement in the original covariate space.We also derive a penalized primal–dual algorithm that jointly learns representations and predictors, and establish oracle inequalities decomposing error into overlap recovery, moment violation, and statistical terms.Extensive synthetic experiments demonstrate robust performance under varying degrees of non-overlap. A large-scale ride-hailing application shows that our method achieves substantial gains over existing baselines, matching the performance of models trained with significantly more RCT data.

This paper studies how to reliably integrate randomized controlled trial (RCT) data with large-scale observational (OBS) data for individualized causal effect estimation. While RCTs provide credible causal identification, they are often costly and limited in size; OBS data are abundant but vulnerable to confounding and platform-induced selection bias. The paper focuses on structural non-overlap, where certain covariate–treatment combinations are absent from observational logs due to operational constraints, making simple weighting or pooling insufficient.To address this issue, the paper proposes a causally constrained joint estimation framework that uses OBS data for efficient prediction while enforcing experimental moment constraints derived from RCT randomization. It further incorporates representation learning to recover feasible overlap when such recovery is possible. Theoretically, the paper shows that conventional weighted-fusion methods may fail under structural non-overlap and provides risk bounds decomposing error into overlap recovery, moment violation, and statistical components.