Causal Bayesian Optimization: Foundations, Methods, and Applications

TMLR Paper9077 Authors

Abstract: Causal Bayesian Optimization (CBO) integrates causal inference with Bayesian optimization to enable sample-efficient intervention selection in systems governed by causal structure. This survey provides a comprehensive and systematic review of the CBO landscape, organizing the growing literature through a unified BO-loop perspective that reveals how causal assumptions shape four core components: intervention search spaces, surrogate construction, acquisition design, and decision policies. We classify methods along recurring design axes, i.e., graph knowledge, intervention representation, uncertainty source, and budget allocation, and establish formal connections between CBO and adjacent fields, including causal bandits, Bayesian experimental design, safe optimization, and policy search. To address the lack of standardized evaluation in the field, we introduce a reproducibility-oriented benchmark that covers hard- and soft-intervention settings, implements both the standard GAP metric and a new trajectory-aware Path-Aware GAP (PA-GAP) metric, and evaluates seven CBO methods alongside a non-causal BO baseline under a common scoring protocol. Our empirical study across thirteen datasets, three budget levels, and two metrics reveals that no single method dominates uniformly: rankings depend critically on the dataset, budget, and metric, and strong non-causal baselines remain competitive in several settings. We conclude by identifying six open challenges, including robustness to hidden confounding, scalable unknown-graph optimization, mixed intervention types, realistic cost models, tighter theoretical guaranties, and integration with modern representation learning, that must be addressed for CBO to transition from proof-of-concept demonstrations to reliable real-world deployment.

Submission Type: Long submission (more than 12 pages of main content)

Assigned Action Editor: ~Junpei_Komiyama1

Submission Number: 9077