Title: Leveraging Cross-Intervention Knowledge Transfer in Causal Bayesian Optimization

Abstract:

Bayesian optimization has emerged as a dominant strategy for refining costly systems, where each experiment, simulation, or intervention incurs significant time or financial expenses. Traditional Bayesian optimization approaches typically view controllable variables as simple inputs to a black-box function, lacking the ability to distinguish between mere correlation and genuine causality. Causal Bayesian optimization addresses this limitation by integrating known causal graphs with observational data to determine the most valuable variables for intervention. However, current methodologies often evaluate the impact of each potential intervention independently, ignoring the fact that in causal systems, these impacts frequently stem from shared underlying mechanisms.

To bridge this gap, we introduce graph-coupled causal Bayesian optimization, a framework that links the outcomes of different interventions by modeling uncertainty around a limited set of common causal parameters. This approach generates a causal kernel that allows evidence gathered from one intervention to refine estimates for related ones. For identifiable linear Gaussian causal models, we demonstrate that this kernel exhibits low rank, with the rank bounded by the count of shared parameters rather than the total number of available interventions. Consequently, this structure leads to an information-gain bound that increases only logarithmically with the optimization horizon. Furthermore, we derive a regret bound that distinctly partitions error into three components: optimization error, causal estimation error, and the error associated with selecting intervention sets. We also present extensions for nonlinear and adaptive scenarios.

Empirical evaluations across theory-aligned Gaussian systems, stress tests involving shared mechanisms, and standard causal optimization benchmarks confirm that our method retains the advantages of causal Bayesian optimization while effectively transferring information across related interventions. The performance improvements are most pronounced when direct interventions on the target’s parents are inaccessible, necessitating the reuse of sparse interventional data across a broad range of candidate interventions.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC