  Determining the causal structure of a set of variables is critical for both
scientific inquiry and decision-making. However, this is often challenging in
practice due to limited interventional data. Given that randomized experiments
are usually expensive to perform, we propose a general framework and theory
based on optimal Bayesian experimental design to select experiments for
targeted causal discovery. That is, we assume the experimenter is interested in
learning some function of the unknown graph (e.g., all descendants of a target
node) subject to design constraints such as limits on the number of samples and
rounds of experimentation. While it is in general computationally intractable
to select an optimal experimental design strategy, we provide a tractable
implementation with provable guarantees on both approximation and optimization
quality based on submodularity. We evaluate the efficacy of our proposed method
on both synthetic and real datasets, thereby demonstrating that our method
realizes considerable performance gains over baseline strategies such as random
sampling.
