Maximizing a target variable as an operational objective in a structural causal model is an important problem. Existing Causal Bayesian Optimization~(CBO) methods either rely on hard interventions that alter the causal structure to maximize the reward; or introduce action nodes to endogenous variables so that the data generation mechanisms are adjusted to achieve the objective. In this paper, a novel method is introduced to learn the distribution of exogenous variables, which is typically ignored or marginalized through expectation by existing methods. Exogenous distribution learning improves the approximation accuracy of structural causal models in a surrogate model that is usually trained with limited observational data. Moreover, the learned exogenous distribution extends existing CBO to general causal schemes beyond Additive Noise Models~(ANM). The recovery of exogenous variables allows us to use a more flexible prior for noise or unobserved hidden variables. We develop a new CBO method by leveraging the learned exogenous distribution. Experiments on different datasets and applications show the benefits of our proposed method.

翻译：在结构因果模型中，以最大化目标变量作为操作目标是一个重要问题。现有的因果贝叶斯优化方法要么依赖会改变因果结构的硬干预来实现奖励最大化；要么通过向内生变量引入行动节点来调整数据生成机制以实现目标。本文提出了一种学习外生变量分布的新方法，而现有方法通常忽略该分布或通过期望进行边缘化处理。外生分布学习提高了代理模型中结构因果模型的近似精度，这类代理模型通常仅使用有限的观测数据进行训练。此外，学习到的外生分布将现有因果贝叶斯优化方法扩展到了加性噪声模型之外的通用因果框架。外生变量的恢复使我们能够对噪声或未观测隐藏变量使用更灵活的先验分布。我们基于学习到的外生分布开发了一种新的因果贝叶斯优化方法。在不同数据集和应用上的实验验证了所提方法的优势。