Multi-Source Bayesian Optimization (MSBO) serves as a variant of the traditional Bayesian Optimization (BO) framework applicable to situations involving optimization of an objective black-box function over multiple information sources such as simulations, surrogate models, or real-world experiments. However, traditional MSBO assumes the input variables of the objective function to be independent and identically distributed, limiting its effectiveness in scenarios where causal information is available and interventions can be performed, such as clinical trials or policy-making. In the single-source domain, Causal Bayesian Optimization (CBO) extends standard BO with the principles of causality, enabling better modeling of variable dependencies. This leads to more accurate optimization, improved decision-making, and more efficient use of low-cost information sources. In this article, we propose a principled integration of the MSBO and CBO methodologies in the multi-source domain, leveraging the strengths of both to enhance optimization efficiency and reduce computational complexity in higher-dimensional problems. We present the theoretical foundations of both Causal and Multi-Source Bayesian Optimization, and demonstrate how their synergy informs our Multi-Source Causal Bayesian Optimization (MSCBO) algorithm. We compare the performance of MSCBO against its foundational counterparts for both synthetic and real-world datasets with varying levels of noise, highlighting the robustness and applicability of MSCBO. Based on our findings, we conclude that integrating MSBO with the causality principles of CBO facilitates dimensionality reduction and lowers operational costs, ultimately improving convergence speed, performance, and scalability.

翻译：多源贝叶斯优化（MSBO）是传统贝叶斯优化（BO）框架的一种变体，适用于涉及跨多个信息源（如仿真、代理模型或真实实验）优化目标黑箱函数的情景。然而，传统MSBO假设目标函数的输入变量独立同分布，这限制了其在可获得因果信息且可实施干预（如临床试验或政策制定）的场景中的有效性。在单源领域，因果贝叶斯优化（CBO）通过因果原理扩展了标准BO，能够更好地建模变量依赖关系。这带来了更精确的优化、更优的决策制定以及对低成本信息源更高效的利用。本文提出在多源领域将MSBO与CBO方法进行原理性整合，结合两者的优势以提升优化效率并降低高维问题的计算复杂度。我们阐述了因果贝叶斯优化与多源贝叶斯优化的理论基础，并论证了二者的协同作用如何启发我们提出多源因果贝叶斯优化（MSCBO）算法。我们在不同噪声水平的合成数据集和真实数据集上，将MSCBO的性能与其基础算法进行了比较，凸显了MSCBO的鲁棒性与适用性。基于研究结果，我们得出结论：将MSBO与CBO的因果原理相结合，有助于实现降维并降低操作成本，最终提升收敛速度、性能与可扩展性。