Maximizing a target variable as an operational objective within a structural causal model is a fundamental problem. Causal Bayesian Optimization (CBO) approaches typically achieve this either by performing interventions that modify the causal structure to increase the reward or by introducing action nodes to endogenous variables, thereby adjusting the data-generating mechanisms to meet the objective. In this paper, we propose a novel method that learns the distribution of exogenous variables-an aspect often ignored or marginalized through expectation in existing CBO frameworks. By modeling the exogenous distribution, we enhance the approximation fidelity of the data-generating structural causal models (SCMs) used in surrogate models, which are commonly trained on limited observational data. Furthermore, the ability to recover exogenous variables enables the application of our approach to more general causal structures beyond the confines of Additive Noise Models (ANMs) and single-mode Gaussian, allowing the use of more expressive priors for context noise. We incorporate the learned exogenous distribution into a new CBO method, demonstrating its advantages across diverse datasets and application scenarios.

翻译：在结构因果模型中最大化目标变量作为操作目标是一个基础性问题。因果贝叶斯优化方法通常通过两种途径实现：一是执行干预以修改因果结构来提升奖励；二是向内生变量引入行动节点，从而调整数据生成机制以满足目标。本文提出一种新方法，该方法学习外生变量的分布——这一维度在现有因果贝叶斯优化框架中常被忽略或通过期望运算被边缘化。通过对建模外生分布，我们提升了代理模型中使用的数据生成结构因果模型的近似保真度，这些代理模型通常基于有限的观测数据进行训练。此外，恢复外生变量的能力使我们的方法能够应用于更广泛的因果结构，突破加性噪声模型和单峰高斯分布的限制，从而允许使用更具表达力的先验分布来建模情境噪声。我们将学习到的外生分布整合到一种新的因果贝叶斯优化方法中，并在多样化数据集和应用场景中验证了其优势。