Contextual Causal Bayesian Optimisation
Vahan Arsenyan, Antoine Grosnit, Haitham Bou-Ammar, Arnak Dalalyan
TL;DR
This paper presents a unified framework for contextual and causal Bayesian optimisation that leverages causal graphs and contextual information to design intervention policies with improved sample efficiency and regret bounds.
Contribution
It introduces a novel algorithm that jointly optimizes policies and variable sets, unifying and extending causal and contextual Bayesian optimisation approaches.
Findings
Achieves sublinear regret in diverse environments
Reduces sample complexity in high-dimensional settings
Provides theoretical regret bounds
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…
Peer Reviews
Decision·ICLR 2026 Poster
- The paper presents a clean framework that truly unifies causal scope selection with contextual action choice and identifies precise failure modes of CaBO/CoBO. - The authors also provide sound theory with practical knobs. That is, there are clear regret guarantees with interpretable dependence on info gain; the approach also uses well-known GP-UCB machinery. - Scope-as-arms with HEBO inside each arm is sensible and parallelisable; - The paper is careful about the acquisition mismatch in con
- The approach requires known causal structure; while standard in CaBO, many real tasks need robustness to graph misspecification or partial knowledge. (They defer discovery to future work.) - Computing the POMPS set can be exponential in |V| (albeit parallelisable). For very large graphs, this may become the bottleneck. -The MAB over scopes uses historical acquisition values; bandit feedback is influenced by the within-scope BO’s learning speed and noise, which may cause slow scope identificati
The paper presents an extensive theoretical analysis of the proposed method. In addition, the authors use real-world examples to illustrate and support the proposed method.
Although the paper provides thorough theoretical results on the regret bounds, several important aspects require further clarification and experimental validation: (1) Missing Baselines. The experimental evaluation lacks comparisons with several relevant baselines, such as existing causal Bayesian optimization (CaBO) methods — e.g., CBO (Aglietti et al., 2020) and MCBO (Sussex et al., 2023). Even though the proposed framework targets a specific problem setting, existing CBO methods could poten
Summary The paper proposes CoCa-BO, a framework that unifies causal and contextual Bayesian optimisation by integrating the concept of Mixed Policy Scopes (MPSs) from causal inference with Bayesian optimisation (BO) methods. The algorithm operates in two layers: (i) a multi-armed bandit (MAB) mechanism that adaptively selects among possibly-optimal mixed policy scopes (POMPSs), and (ii) a Gaussian-process-based BO routine that optimises interventions within each chosen scope. Theoretical analysi
Weaknesses Limited empirical validation Experiments are mostly synthetic or semi-realistic; no real-world dataset or ablation studies. The runtime overhead of managing multiple scopes is not quantified. Independence across scopes Each POMPS maintains a separate GP, which may underutilise shared structure among overlapping interventions. Discussion on potential information sharing (e.g., multitask GPs or shared hyperpriors) would be valuable. Algorithmic detail gaps Algorithm 1 is schemati
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Taxonomy
TopicsAdvanced Bandit Algorithms Research · Bayesian Modeling and Causal Inference