Causal Bayesian Optimization via Exogenous Distribution Learning

TL;DR

This paper introduces a novel causal Bayesian optimization method that learns and incorporates exogenous variable distributions, improving model fidelity and applicability to complex causal structures beyond traditional assumptions.

Contribution

It proposes a new approach to learn exogenous distributions in causal models, enhancing optimization accuracy and extending applicability beyond Additive Noise Models.

Findings

Improved optimization performance across multiple datasets.

Enhanced modeling of complex causal structures.

Demonstrated advantages over existing CBO methods.

Abstract

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.