Feasible Fusion: Constrained Joint Estimation under Structural Non-Overlap

Yuxi Du, Zhiheng Zhang, Haoxuan Li, Cong Fang, Jixing Xu, Zhen Peng, Jiecheng Guo
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:26851-26885, 2026.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-du26s, title = {Feasible Fusion: Constrained Joint Estimation under Structural Non-Overlap}, author = {Du, Yuxi and Zhang, Zhiheng and Li, Haoxuan and Fang, Cong and Xu, Jixing and Peng, Zhen and Guo, Jiecheng}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {26851--26885}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/du26s/du26s.pdf}, url = {https://proceedings.mlr.press/v306/du26s.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Feasible Fusion: Constrained Joint Estimation under Structural Non-Overlap %A Yuxi Du %A Zhiheng Zhang %A Haoxuan Li %A Cong Fang %A Jixing Xu %A Zhen Peng %A Jiecheng Guo %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-du26s %I PMLR %P 26851--26885 %U https://proceedings.mlr.press/v306/du26s.html %V 306 %X 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.
APA
Du, Y., Zhang, Z., Li, H., Fang, C., Xu, J., Peng, Z. & Guo, J.. (2026). Feasible Fusion: Constrained Joint Estimation under Structural Non-Overlap. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:26851-26885 Available from https://proceedings.mlr.press/v306/du26s.html.

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