# Constrained Causal Bayesian Optimization

arXiv: https://arxiv.org/abs/2305.20011 · HTML: https://mlsanity.com/paper/2305.20011/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 50 references that are in the map.
- First posted on arXiv 31 May 2023.

## Builds on (most cited first, 19 of 19)

- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [Bayesian Optimization with Unknown Constraints](https://mlsanity.com/paper/1403.5607/) (2014)
- [Constrained Bayesian Optimization with Noisy Experiments](https://mlsanity.com/paper/1706.07094/) (2017)
- [Causal Bandits: Learning Good Interventions via Causal Inference](https://mlsanity.com/paper/1606.03203/) (2016)
- [Efficient Model-Based Reinforcement Learning through Optimistic Policy Search and Planning](https://mlsanity.com/paper/2006.08684/) (2020)
- [Scalable Constrained Bayesian Optimization](https://mlsanity.com/paper/2002.08526/) (2020)
- [Stagewise Safe Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1806.07555/) (2018)
- [Safe Controller Optimization for Quadrotors with Gaussian Processes](https://mlsanity.com/paper/1509.01066/) (2015)
- [Adaptive and Safe Bayesian Optimization in High Dimensions via One-Dimensional Subspaces](https://mlsanity.com/paper/1902.03229/) (2019)
- [Interventions, Where and How? Experimental Design for Causal Models at Scale](https://mlsanity.com/paper/2203.02016/) (2022)
- [Causal Bayesian Optimization](https://mlsanity.com/paper/2005.11741/) (2020)
- [Bayesian optimization under mixed constraints with a slack-variable augmented Lagrangian](https://mlsanity.com/paper/1605.09466/) (2016)
- [Model-based Causal Bayesian Optimization](https://mlsanity.com/paper/2211.10257/) (2022)
- [A Bayesian approach to constrained single- and multi-objective optimization](https://mlsanity.com/paper/1510.00503/) (2015)
- [Constrained Bayesian Optimization for Automatic Chemical Design](https://mlsanity.com/paper/1709.05501/) (2017)
- [Causal Entropy Optimization](https://mlsanity.com/paper/2208.10981/) (2022)
- [JUMBO: Scalable Multi-task Bayesian Optimization using Offline Data](https://mlsanity.com/paper/2106.00942/) (2021)
- [Learning to search efficiently for causally near-optimal treatments](https://mlsanity.com/paper/2007.00973/) (2020)

## Built on by (most cited first, 6 of 6)

- [CAnDOIT: Causal Discovery with Observational and Interventional Data from Time-Series](https://mlsanity.com/paper/2410.02844/) (2024)
- [Multi-Objective Causal Bayesian Optimization](https://mlsanity.com/paper/2502.14755/) (2025)
- [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)
- [Causal Bayesian Optimization with Unknown Graphs](https://mlsanity.com/paper/2503.19554/) (2025)
- [Transferring Information Across Interventions in Causal Bayesian Optimization](https://mlsanity.com/paper/2606.01457/) (2026)

## Abstract (arXiv)

We propose constrained causal Bayesian optimization (cCBO), an approach for finding interventions in a known causal graph that optimize a target variable under some constraints. cCBO first reduces the search space by exploiting the graph structure and, if available, an observational dataset; and then solves the restricted optimization problem by modelling target and constraint quantities using Gaussian processes and by sequentially selecting interventions via a constrained expected improvement acquisition function. We propose different surrogate models that enable to integrate observational and interventional data while capturing correlation among effects with increasing levels of sophistication. We evaluate cCBO on artificial and real-world causal graphs showing successful trade off between fast convergence and percentage of feasible interventions.