Active causal structure learning with advice
(2305.19588)Abstract
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.
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