Causal Bayesian Optimization: Foundations, Methods, and Applications

arXiv:2609.24112 · stat.ML, cs.LG · Submitted 2026-09-21 · Read on arXiv

stat.ML, cs.LG

Submitted: 2026-09-21

Updated: 2026-09-21

Comments: Accepted at Transactions on Machine Learning Research (TMLR), 2026

Journal ref: Transactions on Machine Learning Research, 2026

Code: https://github.com/chenfeng-huang/CBO-Benchmark-TMLR-2026

License: http://creativecommons.org/licenses/by/4.0/

The gist: Causal Bayesian Optimization (CBO) combines causal inference with Bayesian optimization to enable sample-efficient intervention selection in systems with causal structure.

Terminology

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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