  We study the problem of globally optimizing the causal effect on a target
variable of an unknown causal graph in which interventions can be performed.
This problem arises in many areas of science including biology, operations
research and healthcare. We propose Causal Entropy Optimization (CEO), a
framework that generalizes Causal Bayesian Optimization (CBO) to account for
all sources of uncertainty, including the one arising from the causal graph
structure. CEO incorporates the causal structure uncertainty both in the
surrogate models for the causal effects and in the mechanism used to select
interventions via an information-theoretic acquisition function. The resulting
algorithm automatically trades-off structure learning and causal effect
optimization, while naturally accounting for observation noise. For various
synthetic and real-world structural causal models, CEO achieves faster
convergence to the global optimum compared with CBO while also learning the
graph. Furthermore, our joint approach to structure learning and causal
optimization improves upon sequential, structure-learning-first approaches.
