Recovering causal relationships from data is an important problem. Using observational data, one can typically only recover causal graphs up to a Markov equivalence class and additional assumptions or interventional data are needed for complete recovery. In this work, under some standard assumptions, we study causal graph discovery via adaptive interventions with node-dependent interventional costs. For this setting, we show that no algorithm can achieve an approximation guarantee that is asymptotically better than linear in the number of vertices with respect to the verification number; a well-established benchmark for adaptive search algorithms. Motivated by this negative result, we define a new benchmark that captures the worst-case interventional cost for any search algorithm. Furthermore, with respect to this new benchmark, we provide adaptive search algorithms that achieve logarithmic approximations under various settings: atomic, bounded size interventions and generalized cost objectives.

翻译：从数据中恢复因果关系是一个重要问题。利用观测数据，通常只能恢复至马尔可夫等价类别的因果图，而完整恢复需要额外假设或干预数据。在本研究中，在若干标准假设下，我们研究了通过具有节点相关干预成本的自适应干预进行因果图发现的问题。针对此设定，我们证明：对于验证数（自适应搜索算法的经典基准），任何算法都无法实现渐近优于顶点数线性关系的近似保证。受这一负面结果的启发，我们定义了一个捕捉任意搜索算法最坏情况干预成本的新基准。进一步，基于此新基准，我们提供了在原子干预、有界规模干预及广义成本目标等多种设定下达到对数近似效果的自适应搜索算法。