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.