Contextual Causal Bayesian Optimisation

Abstract: Causal Bayesian optimisation (CaBO) combines causality with Bayesian optimisation (BO) and shows that there are situations where the optimal reward is not achievable if causal knowledge is ignored. While CaBO exploits causal relations to determine the set of controllable variables to intervene on, it does not exploit purely observational variables and marginalises them. We show that, in general, utilising a subset of observational variables as a context to choose the values of interventional variables leads to lower cumulative regrets. We propose a general framework of contextual causal Bayesian optimisation that efficiently searches through combinations of controlled and contextual variables, known as policy scopes, and identifies the one yielding the optimum. We highlight the difficulties arising from the application of the causal acquisition function currently used in CaBO to select the policy scope in contextual settings and propose a multi-armed bandits based selection mechanism. We analytically show that well-established methods, such as contextual BO (CoBO) or CaBO, are not able to achieve the optimum in some cases, and empirically show that the proposed method achieves sub-linear regret in various environments and under different configurations.