  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.
