# Causal Entropy Optimization

arXiv: https://arxiv.org/abs/2208.10981 · HTML: https://mlsanity.com/paper/2208.10981/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 84 references that are in the map.
- First posted on arXiv 23 Aug 2022.

## Builds on (most cited first, 28 of 28)

- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Maximizing acquisition functions for Bayesian optimization](https://mlsanity.com/paper/1805.10196/) (2018)
- [Causal Bandits: Learning Good Interventions via Causal Inference](https://mlsanity.com/paper/1606.03203/) (2016)
- [Permutation-based Causal Inference Algorithms with Interventions](https://mlsanity.com/paper/1705.10220/) (2017)
- [Characterizing and Learning Equivalence Classes of Causal DAGs under Interventions](https://mlsanity.com/paper/1802.06310/) (2018)
- [ABCD-Strategy: Budgeted Experimental Design for Targeted Causal Structure Discovery](https://mlsanity.com/paper/1902.10347/) (2019)
- [Interventions, Where and How? Experimental Design for Causal Models at Scale](https://mlsanity.com/paper/2203.02016/) (2022)
- [Cost-Optimal Learning of Causal Graphs](https://mlsanity.com/paper/1703.02645/) (2017)
- [Artificial Intelligence and Statistics](https://mlsanity.com/paper/1712.03779/) (2017)
- [Causal Bayesian Optimization](https://mlsanity.com/paper/2005.11741/) (2020)
- [Budgeted Experiment Design for Causal Structure Learning](https://mlsanity.com/paper/1709.03625/) (2017)
- [Active Invariant Causal Prediction: Experiment Selection through Stability](https://mlsanity.com/paper/2006.05690/) (2020)
- [Causal Bandits with Unknown Graph Structure](https://mlsanity.com/paper/2106.02988/) (2021)
- [Active Bayesian Causal Inference](https://mlsanity.com/paper/2206.02063/) (2022)
- [Partition MCMC for inference on acyclic digraphs](https://mlsanity.com/paper/1504.05006/) (2015)
- [Entropic Causal Inference](https://mlsanity.com/paper/1611.04035/) (2016)
- [Jointly interventional and observational data: estimation of interventional Markov equivalence classes of directed acyclic graphs](https://mlsanity.com/paper/1303.3216/) (2013)
- [Differentiable Causal Discovery Under Latent Interventions](https://mlsanity.com/paper/2203.02336/) (2022)
- [Optimal experimental design via Bayesian optimization: active causal structure learning for Gaussian process networks](https://mlsanity.com/paper/1910.03962/) (2019)
- [Dynamic Causal Bayesian Optimization](https://mlsanity.com/paper/2110.13891/) (2021)
- [Gaussian Process Networks](https://mlsanity.com/paper/1301.3857/) (2013)
- [Multi-task Causal Learning with Gaussian Processes](https://mlsanity.com/paper/2009.12821/) (2020)
- [Observational-Interventional Priors for Dose-Response Learning](https://mlsanity.com/paper/1605.01573/) (2016)
- [Bayesian Optimal Experimental Design for Inferring Causal Structure](https://mlsanity.com/paper/2103.15229/) (2021)
- [Bayesian Model Averaging for Causality Estimation and its Approximation based on Gaussian Scale Mixture Distributions](https://mlsanity.com/paper/2103.08195/) (2021)
- [Gaussian Process Structural Equation Models with Latent Variables](https://mlsanity.com/paper/1408.2042/) (2014)
- [Learning to search efficiently for causally near-optimal treatments](https://mlsanity.com/paper/2007.00973/) (2020)

## Built on by (most cited first, 13 of 13)

- [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)
- [CEBoosting: Online Sparse Identification of Dynamical Systems with Regime Switching by Causation Entropy Boosting](https://mlsanity.com/paper/2304.07863/) (2023)
- [Constrained Causal Bayesian Optimization](https://mlsanity.com/paper/2305.20011/) (2023)
- [Bayesian Active Learning in the Presence of Nuisance Parameters](https://mlsanity.com/paper/2310.14968/) (2023)
- [Multi-Objective Causal Bayesian Optimization](https://mlsanity.com/paper/2502.14755/) (2025)
- [Causal Layering via Conditional Entropy](https://mlsanity.com/paper/2401.10495/) (2024)
- [Graph Agnostic Causal Bayesian Optimisation](https://mlsanity.com/paper/2411.03028/) (2024)
- [Learning Relevant Contextual Variables Within Bayesian Optimization](https://mlsanity.com/paper/2305.14120/) (2023)
- [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)
- [Transferring Information Across Interventions in Causal Bayesian Optimization](https://mlsanity.com/paper/2606.01457/) (2026)
- [SAGE: Surrogate-gradient Adaptation via Attention-Guided Entropy for Spiking Transformers](https://mlsanity.com/paper/2608.13702/) (2026)

## Abstract (arXiv)

We study the problem of globally optimizing the causal effect on a target variable of an unknown causal graph in which interventions can be performed. This problem arises in many areas of science including biology, operations research and healthcare. We propose Causal Entropy Optimization (CEO), a framework that generalizes Causal Bayesian Optimization (CBO) to account for all sources of uncertainty, including the one arising from the causal graph structure. CEO incorporates the causal structure uncertainty both in the surrogate models for the causal effects and in the mechanism used to select interventions via an information-theoretic acquisition function. The resulting algorithm automatically trades-off structure learning and causal effect optimization, while naturally accounting for observation noise. For various synthetic and real-world structural causal models, CEO achieves faster convergence to the global optimum compared with CBO while also learning the graph. Furthermore, our joint approach to structure learning and causal optimization improves upon sequential, structure-learning-first approaches.