# Model-based Causal Bayesian Optimization

arXiv: https://arxiv.org/abs/2211.10257 · HTML: https://mlsanity.com/paper/2211.10257/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 24 references that are in the map.
- First posted on arXiv 18 Nov 2022.

## Builds on (most cited first, 12 of 12)

- [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)
- [Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimization](https://mlsanity.com/paper/1706.00090/) (2017)
- [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)
- [Causal Bandits for Linear Structural Equation Models](https://mlsanity.com/paper/2208.12764/) (2022)
- [Bayesian Optimization for Cascade-type Multi-stage Processes](https://mlsanity.com/paper/2111.08330/) (2021)
- [Multi-task Causal Learning with Gaussian Processes](https://mlsanity.com/paper/2009.12821/) (2020)
- [Causal Entropy Optimization](https://mlsanity.com/paper/2208.10981/) (2022)
- [BoGraph: Structured Bayesian Optimization From Logs for Expensive Systems with Many Parameters](https://mlsanity.com/paper/2112.08774/) (2021)

## Built on by (most cited first, 26 of 26)

- [Optimistic Active Exploration of Dynamical Systems](https://mlsanity.com/paper/2306.12371/) (2023)
- [Efficient Exploration in Continuous-time Model-based Reinforcement Learning](https://mlsanity.com/paper/2310.19848/) (2023)
- [Intervention Generalization: A View from Factor Graph Models](https://mlsanity.com/paper/2306.04027/) (2023)
- [Causal Bandits with General Causal Models and Interventions](https://mlsanity.com/paper/2403.00233/) (2024)
- [SOMBRL: Scalable and Optimistic Model-Based RL](https://mlsanity.com/paper/2511.20066/) (2025)
- [Constrained Causal Bayesian Optimization](https://mlsanity.com/paper/2305.20011/) (2023)
- [Functional Causal Bayesian Optimization](https://mlsanity.com/paper/2306.06409/) (2023)
- [Challenges and Considerations in the Evaluation of Bayesian Causal Discovery](https://mlsanity.com/paper/2406.03209/) (2024)
- [Linear Causal Bandits: Unknown Graph and Soft Interventions](https://mlsanity.com/paper/2411.02383/) (2024)
- [BONSAI: Structure-exploiting robust Bayesian optimization for networked black-box systems under uncertainty](https://mlsanity.com/paper/2510.03893/) (2025)
- [CO-BED: Information-Theoretic Contextual Optimization via Bayesian Experimental Design](https://mlsanity.com/paper/2302.14015/) (2023)
- [Adversarial Causal Bayesian Optimization](https://mlsanity.com/paper/2307.16625/) (2023)
- [Robust Causal Bandits for Linear Models](https://mlsanity.com/paper/2310.19794/) (2023)
- [NeoRL: Efficient Exploration for Nonepisodic RL](https://mlsanity.com/paper/2406.01175/) (2024)
- [Causal Bayesian Optimization via Exogenous Distribution Learning](https://mlsanity.com/paper/2402.02277/) (2024)
- [No-Regret Learning of Nash Equilibrium for Black-Box Games via Gaussian Processes](https://mlsanity.com/paper/2405.08318/) (2024)
- [Multi-Objective Causal Bayesian Optimization](https://mlsanity.com/paper/2502.14755/) (2025)
- [Contextual Causal Bayesian Optimisation](https://mlsanity.com/paper/2301.12412/) (2023)
- [Improved Bound for Robust Causal Bandits with Linear Models](https://mlsanity.com/paper/2405.07795/) (2024)
- [Asymmetric Graph Error Control with Low Complexity in Causal Bandits](https://mlsanity.com/paper/2408.11240/) (2024)
- [Bayesian Optimization of Expensive Nested Grey-Box Functions](https://mlsanity.com/paper/2306.05150/) (2023)
- [Graph Agnostic Causal Bayesian Optimisation](https://mlsanity.com/paper/2411.03028/) (2024)
- [Optimal Observation-Intervention Trade-Off in Optimisation Problems with Causal Structure](https://mlsanity.com/paper/2309.02287/) (2023)
- [Causal Bayesian Optimization with Unknown Graphs](https://mlsanity.com/paper/2503.19554/) (2025)
- [Online Identification of IT Systems through Active Causal Learning](https://mlsanity.com/paper/2509.02130/) (2025)
- [Joint Parameter and State-Space Bayesian Optimization: Using Process Expertise to Accelerate Manufacturing Optimization](https://mlsanity.com/paper/2602.17679/) (2026)

## Abstract (arXiv)

How should we intervene on an unknown structural equation model to maximize a downstream variable of interest? This setting, also known as causal Bayesian optimization (CBO), has important applications in medicine, ecology, and manufacturing. Standard Bayesian optimization algorithms fail to effectively leverage the underlying causal structure. Existing CBO approaches assume noiseless measurements and do not come with guarantees. We propose the model-based causal Bayesian optimization algorithm (MCBO) that learns a full system model instead of only modeling intervention-reward pairs. MCBO propagates epistemic uncertainty about the causal mechanisms through the graph and trades off exploration and exploitation via the optimism principle. We bound its cumulative regret, and obtain the first non-asymptotic bounds for CBO. Unlike in standard Bayesian optimization, our acquisition function cannot be evaluated in closed form, so we show how the reparameterization trick can be used to apply gradient-based optimizers. The resulting practical implementation of MCBO compares favorably with state-of-the-art approaches empirically.