Contextual Causal Bayesian Optimisation
Vahan Arsenyan, Antoine Grosnit, Haitham Bou-Ammar, Arnak Dalalyan
TL;DR
CoCa-BO introduces a unified Contextual-Causal Bayesian Optimisation framework that jointly searches over mixed policy scopes compatible with a given causal graph and contextual information. It combines POMPS selection via MAB-UCB with HEBO-based Gaussian-process BO inside the chosen scope, and provides worst-case and instance-dependent regret bounds leveraging maximum information gain. The approach demonstrates sublinear regret and improved sample efficiency over CaBO and CoBO across diverse, high-dimensional environments, while remaining robust to moderate noise and scalable via parallelizable policy-scope enumeration. The work advances practical policy learning in settings with causal structure and observable context, enabling more efficient intervention design in complex systems. A public, implementation-ready pipeline supports reproducibility and benchmarking across tasks with varying context and intervention richness.
Abstract
We introduce a unified framework for contextual and causal Bayesian optimisation, which aims to design intervention policies maximising the expectation of a target variable. Our approach leverages both observed contextual information and known causal graph structures to guide the search. Within this framework, we propose a novel algorithm that jointly optimises over policies and the sets of variables on which these policies are defined. This thereby extends and unifies two previously distinct approaches: Causal Bayesian Optimisation and Contextual Bayesian Optimisation, while also addressing their limitations in scenarios that yield suboptimal results. We derive worst-case and instance-dependent high-probability regret bounds for our algorithm. We report experimental results across diverse environments, corroborating that our approach achieves sublinear regret and reduces sample complexity in high-dimensional settings.