Causal Bayesian Optimization with Unknown Graphs (2503.19554v1)

Abstract: Causal Bayesian Optimization (CBO) is a methodology designed to optimize an outcome variable by leveraging known causal relationships through targeted interventions. Traditional CBO methods require a fully and accurately specified causal graph, which is a limitation in many real-world scenarios where such graphs are unknown. To address this, we propose a new method for the CBO framework that operates without prior knowledge of the causal graph. Consistent with causal bandit theory, we demonstrate through theoretical analysis and that focusing on the direct causal parents of the target variable is sufficient for optimization, and provide empirical validation in the context of CBO. Furthermore we introduce a new method that learns a Bayesian posterior over the direct parents of the target variable. This allows us to optimize the outcome variable while simultaneously learning the causal structure. Our contributions include a derivation of the closed-form posterior distribution for the linear case. In the nonlinear case where the posterior is not tractable, we present a Gaussian Process (GP) approximation that still enables CBO by inferring the parents of the outcome variable. The proposed method performs competitively with existing benchmarks and scales well to larger graphs, making it a practical tool for real-world applications where causal information is incomplete.

Overview of "Causal Bayesian Optimization with Unknown Causal Graphs"

The paper "Causal Bayesian Optimization with Unknown Causal Graphs" proposes a novel framework designed for Causal Bayesian Optimization (CBO) in scenarios where the causal graph is unspecified. This research addresses a significant limitation in traditional CBO methodologies, which necessitate a fully and accurately defined causal graph to perform optimizations via targeted interventions. The paper leverages insights from causal bandit theory to illustrate that focusing solely on the direct causal parents of a target variable suffices for optimization, thus simplifying the problem even when the broader causal structure is unknown.

Key Contributions

The paper introduces a new method that develops a Bayesian posterior over the direct parents of the target variable, incorporating an empirical and theoretical demonstration of its efficacy. Its contributions are notable in several respects:

1. Posterior Distribution Derivation: In the linear case, it provides a closed-form derivation of the posterior distribution for direct parents using Gaussian Additive Noise Models (ANM). It further approximates the posterior in nonlinear scenarios with a Gaussian Process, allowing for inference in cases where a closed-form solution is not tractable.
2. Scalability: By concentrating on direct causal parents instead of learning the entire causal graph, the proposed methodology presents scalability advantages significant for real-world applications. The method excels in environments with larger, complex graphs with possibly incomplete causal information, thus broadening the applicability of CBO.
3. Optimization and Learning: The framework simultaneously optimizes the outcome variable and learns the causal structure, a dual approach that enhances our understanding of the optimization task while evolving the knowledge of variable dependencies through learned interventions.

Empirical Validation

Empirical results demonstrate that targeting direct causal parents with this method achieves similar optimal target values as those obtained using fully specified causal graphs. The method performs competitively when evaluated against benchmarks on synthetic and semi-synthetic causal graphs, maintaining its efficiency and adaptability to larger graphs.

Implications

Practical Implications

1. Cost Reduction in Interventions: By minimizing the dimension of the variables subjected to intervention, the method reduces the cost associated with broad-variable interventions typical in traditional BO setups.
2. Applicability Across Domains: The methodology has potential applications in areas such as healthcare, agriculture, and robotics, where interventions are strategic and the causal relationships are partially known or unspecified.

Theoretical Implications

From a theoretical standpoint, the work underscores the sufficiency of identifying direct causal parents in optimization tasks under specific assumptions, without necessitating the full causal structure. This insight can steer future research directions towards refining causal discovery methods that emphasize partial structure over full DAGs.

Future Directions

Future research building upon these findings might focus on extending this framework to environments where soft interventions are optimal, especially in scenarios involving confounders or indirect effects. Moreover, exploring methods to dynamically balance between direct parent identification and functional intervention strategies could further enhance the robustness of CBO applications. By integrating partial causal discovery insights into the CBO framework, researchers can aim to refine algorithms to optimize interventions in complex environments with hidden or uncertain causal dependencies.

Overall, this paper contributes meaningfully to causal optimization research by bridging the gap between theoretical advancements in causal bandit strategies and practical optimization workflows, paving the way for efficient solutions in data-scarce and structure-uncertain scenarios.