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.

翻译：我们提出了带有建议的主动因果结构学习问题。在典型的已被充分研究的设定中，学习算法被赋予观测分布的 essential 图，并被要求恢复底层的因果有向无环图 (DAG) $G^*$，同时最小化所做的干预次数。在我们的设定中，我们额外获得关于 $G^*$ 的边信息作为建议，例如一个声称是 $G^*$ 的 DAG $G$。我们探究当建议接近正确时，学习算法能否从中获益，同时即便建议非常糟糕，仍能保证最坏情况下的性能。我们的工作与日益增长的带预测算法研究处于同一领域。当建议是一个 DAG $G$ 时，我们设计了一种自适应搜索算法来恢复 $G^*$，其干预成本最多是验证 $G^*$ 成本的 $O(\max\{1, \log \psi\})$ 倍；这里，$\psi$ 是 $G$ 与 $G^*$ 之间的距离度量，其上限为变量数 $n$，且当 $G=G^*$ 时恰好为 0。我们的近似因子与无建议设定下的最新结果相匹配。