Title: Contextual Causal Bayesian Optimisation
Primary area: optimization
Keywords: Bayesian Optimization, Causality, Optimal Control

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.

TL;DR: We extend causal Bayesin optimization to contextual scenarios and provide the first upper bound on the regret of causal BO methods that covers both contextual and context free setups.