  This paper studies the problem of globally optimizing a variable of interest
that is part of a causal model in which a sequence of interventions can be
performed. This problem arises in biology, operational research, communications
and, more generally, in all fields where the goal is to optimize an output
metric of a system of interconnected nodes. Our approach combines ideas from
causal inference, uncertainty quantification and sequential decision making. In
particular, it generalizes Bayesian optimization, which treats the input
variables of the objective function as independent, to scenarios where causal
information is available. We show how knowing the causal graph significantly
improves the ability to reason about optimal decision making strategies
decreasing the optimization cost while avoiding suboptimal solutions. We
propose a new algorithm called Causal Bayesian Optimization (CBO). CBO
automatically balances two trade-offs: the classical exploration-exploitation
and the new observation-intervention, which emerges when combining real
interventional data with the estimated intervention effects computed via
do-calculus. We demonstrate the practical benefits of this method in a
synthetic setting and in two real-world applications.
