Budgeted Experiment Design for Causal Structure Learning

We study the problem of causal structure learning when the experimenter is limited to perform at most $k$ non-adaptive experiments of size $1$. We formulate the problem of finding the best intervention target set as an optimization problem, which aims to maximize the average number of edges whose directions are resolved. We prove that the objective function is submodular and a greedy algorithm is a $(1-\frac{1}{e})$-approximation algorithm for the problem. We further present an accelerated variant of the greedy algorithm, which can lead to orders of magnitude performance speedup. We validate our proposed approach on synthetic and real graphs. The results show that compared to the purely observational setting, our algorithm orients majority of the edges through only a small number of interventions.