Graph Agnostic Causal Bayesian Optimisation

Abstract: We study the problem of globally optimising a target variable of an unknown causal graph on which a sequence of soft or hard interventions can be performed. The problem of optimising the target variable associated with a causal graph is formalised as Causal Bayesian Optimisation (CBO). We study the CBO problem under the cumulative regret objective with unknown causal graphs for two settings, namely structural causal models with hard interventions and function networks with soft interventions. We propose Graph Agnostic Causal Bayesian Optimisation (GACBO), an algorithm that actively discovers the causal structure that contributes to achieving optimal rewards. GACBO seeks to balance exploiting the actions that give the best rewards against exploring the causal structures and functions. To the best of our knowledge, our work is the first to study causal Bayesian optimization with cumulative regret objectives in scenarios where the graph is unknown or partially known. We show our proposed algorithm outperforms baselines in simulated experiments and real-world applications.