Active causal structure learning with advice

We introduce the problem of active causal structure learning with advice. In the typical well-studied setting, the learning algorithm is given the essential graph for the observational distribution and is asked to recover the underlying causal directed acyclic graph (DAG) G* while minimizing the number of interventions made. In our setting, we are additionally given side information about G* as advice, e.g. a DAG G purported to be G*. We ask whether the learning algorithm can benefit from the advice when it is close to being correct, while still having worst-case guarantees even when the advice is arbitrarily bad. Our work is in the same space as the growing body of research on algorithms with predictions. When the advice is a DAG G, we design an adaptive search algorithm to recover G* whose intervention cost is at most O(max{1, log psi}) times the cost for verifying G*; here, psi is a distance measure between G and G* that is upper bounded by the number of variables n, and is exactly 0 when G = G*. Our approximation factor matches the state-of-the-art for the advice-less setting.