  We propose constrained causal Bayesian optimization (cCBO), an approach for
finding interventions in a known causal graph that optimize a target variable
under some constraints. cCBO first reduces the search space by exploiting the
graph structure and, if available, an observational dataset; and then solves
the restricted optimization problem by modelling target and constraint
quantities using Gaussian processes and by sequentially selecting interventions
via a constrained expected improvement acquisition function. We propose
different surrogate models that enable to integrate observational and
interventional data while capturing correlation among effects with increasing
levels of sophistication. We evaluate cCBO on artificial and real-world causal
graphs showing successful trade off between fast convergence and percentage of
feasible interventions.
