Maximizing a target variable as an operational objective in a structured 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 structured 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. A new CBO method is developed by leveraging the learned exogenous distribution. Experiments on different datasets and applications show the benefits of our proposed method.

翻译：在结构化因果模型中将目标变量作为操作目标进行最大化是一个重要问题。现有的因果贝叶斯优化（Causal Bayesian Optimization, CBO）方法要么依赖硬干预（改变因果结构以最大化奖励），要么通过向内生变量引入动作节点来调整数据生成机制以实现目标。本文提出了一种新颖的方法来学习外生变量的分布——现有方法通常忽略该分布或通过期望将其边缘化。外生分布学习能够提高结构化因果模型在替代模型中的近似精度（该替代模型通常使用有限的观测数据训练）。此外，学习到的外生分布将现有CBO扩展到加性噪声模型（Additive Noise Models, ANM）之外的通用因果方案。外生变量的恢复使我们能够对噪声或未观测隐变量使用更灵活的先验分布。通过利用学习到的外生分布，本文开发了一种新的CBO方法。在不同数据集和应用上的实验展示了所提方法的优势。