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.

翻译：本文提出了一个统一的上下文与因果贝叶斯优化框架，旨在设计能够最大化目标变量期望的干预策略。我们的方法同时利用观测到的上下文信息以及已知的因果图结构来指导搜索。在此框架内，我们提出了一种新颖的算法，该算法联合优化策略及其所定义的变量集合。由此，本工作扩展并统一了先前两种独立的范式——因果贝叶斯优化与上下文贝叶斯优化，同时解决了它们在可能导致次优结果的场景中的局限性。我们为所提算法推导了最坏情况与实例依赖的高概率遗憾界。我们在多种环境中报告了实验结果，证实了我们的方法能够实现次线性遗憾，并在高维设置中降低了样本复杂度。