Causal Bayesian Optimization: Foundations, Methods, and Applications
Abstract
Causal Bayesian Optimization (CBO) combines causal inference with Bayesian optimization to enable sample-efficient intervention selection in systems with causal structure. This survey provides a systematic review of CBO through a unified BO-loop perspective, showing how causal assumptions shape intervention search spaces, surrogate models, acquisition functions, and decision policies. We organize existing methods by graph and system-knowledge assumptions, environment, intervention representation, surrogate architecture, and decision rule, and connect CBO to causal bandits, Bayesian experimental design, safe optimization, policy search, and causal abstraction. We also introduce a reproducibility-oriented benchmark spanning hard- and soft-intervention settings, with standardized GAP and a new trajectory-aware Path-Aware GAP (PA-GAP), evaluating seven CBO methods and a non-causal BO baseline across thirteen datasets, three budgets, and two metrics. Results show that no method dominates uniformly: rankings depend on dataset, budget, metric, and how causal information is used, while strong non-causal baselines remain competitive in several settings. Controlled graph-misspecification and omitted-variable stress tests further show that rankings can change substantially when learner-side causal information is perturbed. We conclude by identifying key open challenges, including robustness to causal-assumption violations, scalable unknown-graph optimization, mixed intervention types, realistic cost models, stronger theoretical guarantees, and integration with modern representation learning and causal abstractions.
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BibTeX
@misc{huang2026causal,
title = {{Causal Bayesian Optimization: Foundations, Methods, and Applications}},
author = {Chenfeng Huang and Thuy T. Le and Zixuan Ma and Hien Tran},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24112},
eprint = {2609.24112},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24112},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Causal Bayesian Optimization: Foundations, Methods, and Applications
AU - Chenfeng Huang
AU - Thuy T. Le
AU - Zixuan Ma
AU - Hien Tran
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24112
UR - https://arxiv.org/abs/2609.24112
AB - Causal Bayesian Optimization (CBO) combines causal inference with Bayesian optimization to enable sample-efficient intervention selection in systems with causal structure. This survey provides a systematic review of CBO through a unified BO-loop perspective, showing how causal assumptions shape intervention search spaces, surrogate models, acquisition functions, and decision policies. We organize existing methods by graph and system-knowledge assumptions, environment, intervention representation, surrogate architecture, and decision rule, and connect CBO to causal bandits, Bayesian experimental design, safe optimization, policy search, and causal abstraction. We also introduce a reproducibility-oriented benchmark spanning hard- and soft-intervention settings, with standardized GAP and a new trajectory-aware Path-Aware GAP (PA-GAP), evaluating seven CBO methods and a non-causal BO baseline across thirteen datasets, three budgets, and two metrics. Results show that no method dominates uniformly: rankings depend on dataset, budget, metric, and how causal information is used, while strong non-causal baselines remain competitive in several settings. Controlled graph-misspecification and omitted-variable stress tests further show that rankings can change substantially when learner-side causal information is perturbed. We conclude by identifying key open challenges, including robustness to causal-assumption violations, scalable unknown-graph optimization, mixed intervention types, realistic cost models, stronger theoretical guarantees, and integration with modern representation learning and causal abstractions.
ER -