# Causal Bayesian Optimization via Exogenous Distribution Learning

arXiv: https://arxiv.org/abs/2402.02277 · HTML: https://mlsanity.com/paper/2402.02277/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 34 references that are in the map.
- First posted on arXiv 3 Feb 2024.

## Builds on (most cited first, 15 of 15)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Efficient Model-Based Reinforcement Learning through Optimistic Policy Search and Planning](https://mlsanity.com/paper/2006.08684/) (2020)
- [Sample-Efficient Reinforcement Learning via Counterfactual-Based Data Augmentation](https://mlsanity.com/paper/2012.09092/) (2020)
- [On the Identifiability and Estimation of Causal Location-Scale Noise Models](https://mlsanity.com/paper/2210.09054/) (2022)
- [Bayesian Optimization of Composite Functions](https://mlsanity.com/paper/1906.01537/) (2019)
- [Counterfactual Identifiability of Bijective Causal Models](https://mlsanity.com/paper/2302.02228/) (2023)
- [Causal Bayesian Optimization](https://mlsanity.com/paper/2005.11741/) (2020)
- [On Online Learning in Kernelized Markov Decision Processes](https://mlsanity.com/paper/1911.01871/) (2019)
- [Bayesian Optimization of Function Networks](https://mlsanity.com/paper/2112.15311/) (2021)
- [Thinking inside the box: A tutorial on grey-box Bayesian optimization](https://mlsanity.com/paper/2201.00272/) (2022)
- [Model-based Causal Bayesian Optimization](https://mlsanity.com/paper/2211.10257/) (2022)
- [Modeling Causal Mechanisms with Diffusion Models for Interventional and Counterfactual Queries](https://mlsanity.com/paper/2302.00860/) (2023)
- [Dynamic Causal Bayesian Optimization](https://mlsanity.com/paper/2110.13891/) (2021)
- [Counterfactual (Non-)identifiability of Learned Structural Causal Models](https://mlsanity.com/paper/2301.09031/) (2023)
- [Functional Causal Bayesian Optimization](https://mlsanity.com/paper/2306.06409/) (2023)

## Built on by (most cited first, 3 of 3)

- [Multi-Objective Causal Bayesian Optimization](https://mlsanity.com/paper/2502.14755/) (2025)
- [LLM Based Bayesian Optimization for Prompt Search](https://mlsanity.com/paper/2510.04384/) (2025)
- [Transferring Information Across Interventions in Causal Bayesian Optimization](https://mlsanity.com/paper/2606.01457/) (2026)

## Abstract (arXiv)

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.