# Dynamic Causal Bayesian Optimization

arXiv: https://arxiv.org/abs/2110.13891 · HTML: https://mlsanity.com/paper/2110.13891/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 58 references that are in the map.
- First posted on arXiv 26 Oct 2021.

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

- [Counterfactual Multi-Agent Policy Gradients](https://mlsanity.com/paper/1705.08926/) (2017)
- [Explainable Reinforcement Learning Through a Causal Lens](https://mlsanity.com/paper/1905.10958/) (2019)
- [Multi-armed Bandit Models for the Optimal Design of Clinical Trials: Benefits and Challenges](https://mlsanity.com/paper/1507.08025/) (2015)
- [Causal Bandits: Learning Good Interventions via Causal Inference](https://mlsanity.com/paper/1606.03203/) (2016)
- [Woulda, Coulda, Shoulda: Counterfactually-Guided Policy Search](https://mlsanity.com/paper/1811.06272/) (2018)
- [Time-Varying Gaussian Process Bandit Optimization](https://mlsanity.com/paper/1601.06650/) (2016)
- [Causal Discovery and Forecasting in Nonstationary Environments with State-Space Models](https://mlsanity.com/paper/1905.10857/) (2019)
- [From Ordinary Differential Equations to Structural Causal Models: the deterministic case](https://mlsanity.com/paper/1408.2063/) (2014)
- [Causal Bayesian Optimization](https://mlsanity.com/paper/2005.11741/) (2020)
- [Deconfounding Reinforcement Learning in Observational Settings](https://mlsanity.com/paper/1812.10576/) (2018)
- [Causal models for dynamical systems](https://mlsanity.com/paper/2001.06208/) (2020)
- [From Deterministic ODEs to Dynamic Structural Causal Models](https://mlsanity.com/paper/1608.08028/) (2016)
- [Directed Cyclic Graphical Representations of Feedback Models](https://mlsanity.com/paper/1302.4982/) (2013)
- [Learning Contextual Bandits in a Non-stationary Environment](https://mlsanity.com/paper/1805.09365/) (2018)
- [Multi-task Causal Learning with Gaussian Processes](https://mlsanity.com/paper/2009.12821/) (2020)
- [Bayesian Optimization for Dynamic Problems](https://mlsanity.com/paper/1803.03432/) (2018)
- [Identifying Independencies in Causal Graphs with Feedback](https://mlsanity.com/paper/1302.3595/) (2013)
- [Causal Inference using Gaussian Processes with Structured Latent Confounders](https://mlsanity.com/paper/2007.07127/) (2020)
- [Gaussian Process Structural Equation Models with Latent Variables](https://mlsanity.com/paper/1408.2042/) (2014)

## Built on by (most cited first, 17 of 17)

- [Developing Optimal Causal Cyber-Defence Agents via Cyber Security Simulation](https://mlsanity.com/paper/2207.12355/) (2022)
- [Causal Deep Learning](https://mlsanity.com/paper/2303.02186/) (2023)
- [Inroads into Autonomous Network Defence using Explained Reinforcement Learning](https://mlsanity.com/paper/2306.09318/) (2023)
- [Causal Entropy Optimization](https://mlsanity.com/paper/2208.10981/) (2022)
- [Finding Counterfactually Optimal Action Sequences in Continuous State Spaces](https://mlsanity.com/paper/2306.03929/) (2023)
- [Generative Adversarial Model-Based Optimization via Source Critic Regularization](https://mlsanity.com/paper/2402.06532/) (2024)
- [Functional Causal Bayesian Optimization](https://mlsanity.com/paper/2306.06409/) (2023)
- [Adversarial Causal Bayesian Optimization](https://mlsanity.com/paper/2307.16625/) (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)
- [Bayesian Optimization of Expensive Nested Grey-Box Functions](https://mlsanity.com/paper/2306.05150/) (2023)
- [Causal Discovery via Bayesian Optimization](https://mlsanity.com/paper/2501.14997/) (2025)
- [Chronological Causal Bandits](https://mlsanity.com/paper/2112.01819/) (2021)
- [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)
- [Neural Nonmyopic Bayesian Optimization in Dynamic Cost Settings](https://mlsanity.com/paper/2601.06505/) (2026)

## Abstract (arXiv)

This paper studies the problem of performing a sequence of optimal interventions in a causal dynamical system where both the target variable of interest and the inputs evolve over time. This problem arises in a variety of domains e.g. system biology and operational research. Dynamic Causal Bayesian Optimization (DCBO) brings together ideas from sequential decision making, causal inference and Gaussian process (GP) emulation. DCBO is useful in scenarios where all causal effects in a graph are changing over time. At every time step DCBO identifies a local optimal intervention by integrating both observational and past interventional data collected from the system. We give theoretical results detailing how one can transfer interventional information across time steps and define a dynamic causal GP model which can be used to quantify uncertainty and find optimal interventions in practice. We demonstrate how DCBO identifies optimal interventions faster than competing approaches in multiple settings and applications.