# Causal Bayesian Optimization

arXiv: https://arxiv.org/abs/2005.11741 · HTML: https://mlsanity.com/paper/2005.11741/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2020.

## Built on by (most cited first, 30 of 39)

- [Developing Optimal Causal Cyber-Defence Agents via Cyber Security Simulation](https://mlsanity.com/paper/2207.12355/) (2022)
- [Active Learning for Optimal Intervention Design in Causal Models](https://mlsanity.com/paper/2209.04744/) (2022)
- [Model-based Causal Bayesian Optimization](https://mlsanity.com/paper/2211.10257/) (2022)
- [BayesIMP: Uncertainty Quantification for Causal Data Fusion](https://mlsanity.com/paper/2106.03477/) (2021)
- [Causal Deep Learning](https://mlsanity.com/paper/2303.02186/) (2023)
- [Dynamic Causal Bayesian Optimization](https://mlsanity.com/paper/2110.13891/) (2021)
- [Causal Reasoning: Charting a Revolutionary Course for Next-Generation AI-Native Wireless Networks](https://mlsanity.com/paper/2309.13223/) (2023)
- [Causal Entropy Optimization](https://mlsanity.com/paper/2208.10981/) (2022)
- [Approximation-Aware Bayesian Optimization](https://mlsanity.com/paper/2406.04308/) (2024)
- [Intervention Generalization: A View from Factor Graph Models](https://mlsanity.com/paper/2306.04027/) (2023)
- [BoGraph: Structured Bayesian Optimization From Logs for Expensive Systems with Many Parameters](https://mlsanity.com/paper/2112.08774/) (2021)
- [Constrained Causal Bayesian Optimization](https://mlsanity.com/paper/2305.20011/) (2023)
- [Causally Abstracted Multi-armed Bandits](https://mlsanity.com/paper/2404.17493/) (2024)
- [Functional Causal Bayesian Optimization](https://mlsanity.com/paper/2306.06409/) (2023)
- [BONSAI: Structure-exploiting robust Bayesian optimization for networked black-box systems under uncertainty](https://mlsanity.com/paper/2510.03893/) (2025)
- [Adversarial Causal Bayesian Optimization](https://mlsanity.com/paper/2307.16625/) (2023)
- [Machine Learning Systems: A Survey from a Data-Oriented Perspective](https://mlsanity.com/paper/2302.04810/) (2023)
- [Causal Bayesian Optimization via Exogenous Distribution Learning](https://mlsanity.com/paper/2402.02277/) (2024)
- [Multi-Objective Causal Bayesian Optimization](https://mlsanity.com/paper/2502.14755/) (2025)
- [Contextual Causal Bayesian Optimisation](https://mlsanity.com/paper/2301.12412/) (2023)
- [CURE: Simulation-Augmented Auto-Tuning in Robotics](https://mlsanity.com/paper/2402.05399/) (2024)
- [Structured Learning of Compositional Sequential Interventions](https://mlsanity.com/paper/2406.05745/) (2024)
- [Interventional Processes for Causal Uncertainty Quantification](https://mlsanity.com/paper/2410.14483/) (2024)
- [Multi-Objective Multi-Fidelity Bayesian Optimization with Causal Priors](https://mlsanity.com/paper/2602.00788/) (2026)
- [Bayesian Optimization of Expensive Nested Grey-Box Functions](https://mlsanity.com/paper/2306.05150/) (2023)
- [Hypergame Theory for Decentralized Resource Allocation in Multi-user Semantic Communications](https://mlsanity.com/paper/2409.17985/) (2024)
- [Graph Agnostic Causal Bayesian Optimisation](https://mlsanity.com/paper/2411.03028/) (2024)
- [Causal Discovery via Bayesian Optimization](https://mlsanity.com/paper/2501.14997/) (2025)
- [ActiveCQ: Active Estimation of Causal Quantities](https://mlsanity.com/paper/2509.24293/) (2025)
- [On Transportability for Structural Causal Bandits](https://mlsanity.com/paper/2511.17953/) (2025)

## Abstract (arXiv)

This paper studies the problem of globally optimizing a variable of interest that is part of a causal model in which a sequence of interventions can be performed. This problem arises in biology, operational research, communications and, more generally, in all fields where the goal is to optimize an output metric of a system of interconnected nodes. Our approach combines ideas from causal inference, uncertainty quantification and sequential decision making. In particular, it generalizes Bayesian optimization, which treats the input variables of the objective function as independent, to scenarios where causal information is available. We show how knowing the causal graph significantly improves the ability to reason about optimal decision making strategies decreasing the optimization cost while avoiding suboptimal solutions. We propose a new algorithm called Causal Bayesian Optimization (CBO). CBO automatically balances two trade-offs: the classical exploration-exploitation and the new observation-intervention, which emerges when combining real interventional data with the estimated intervention effects computed via do-calculus. We demonstrate the practical benefits of this method in a synthetic setting and in two real-world applications.