Causal Bayesian Optimization via Exogenous Distribution Learning

Maximizing a target variable as an operational objective in a structural causal model is an important problem. Causal Bayesian Optimization~(CBO) methods either rely on 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. This paper introduces a novel method to learn the distribution of exogenous variables, which is typically marginalized through expectation or ignored by existing CBO 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 simple Additive Noise Models~(ANMs). 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.