Causal Bayesian Optimization with Unknown Graphs

2025-03-25

AI Summary

Traditional causal Bayesian optimization (CBO) relies on a known causal graph, limiting its applicability in real-world scenarios where the underlying causal structure is unknown. Method: We propose the first unified framework jointly modeling causal structure learning and Bayesian optimization. Our approach eliminates the need for prior causal knowledge by integrating structure learning directly into the CBO pipeline. For linear settings, we derive a closed-form posterior for the direct causal parents of the target variable; for nonlinear settings, we employ Gaussian process approximations. Crucially, parent identification and intervention policy optimization are performed in a coupled, end-to-end manner. Results: Experiments demonstrate that our method achieves optimization performance comparable to oracle CBO with ground-truth graphs, while exhibiting strong scalability and robustness. It significantly broadens the applicability of causal optimization to complex, real-world systems with unknown causal mechanisms.

Technology Category

• Machine Learning: Causal Learning
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• Optimizing outcomes without known causal graphs
• Learning causal parents for targeted interventions
• Scaling Bayesian optimization to incomplete causal information

Innovation

• Optimizes without known causal graph
• Learns direct parents via Bayesian posterior
• Uses GP approximation for nonlinear cases