Causal discovery aims to uncover cause-and-effect relationships encoded in causal graphs by leveraging observational, interventional data, or their combination. The majority of existing causal discovery methods are developed assuming infinite interventional data. We focus on data interventional efficiency and formalize causal discovery from the perspective of online learning, inspired by pure exploration in bandit problems. A graph separating system, consisting of interventions that cut every edge of the graph at least once, is sufficient for learning causal graphs when infinite interventional data is available, even in the worst case. We propose a track-and-stop causal discovery algorithm that adaptively selects interventions from the graph separating system via allocation matching and learns the causal graph based on sampling history. Given any desired confidence value, the algorithm determines a termination condition and runs until it is met. We analyze the algorithm to establish a problem-dependent upper bound on the expected number of required interventional samples. Our proposed algorithm outperforms existing methods in simulations across various randomly generated causal graphs. It achieves higher accuracy, measured by the structural hamming distance (SHD) between the learned causal graph and the ground truth, with significantly fewer samples.

翻译：因果发现旨在通过利用观测数据、干预数据或其组合来揭示因果图中编码的因果关系。现有的大多数因果发现方法都是在假设拥有无限干预数据的前提下开发的。我们关注数据干预效率，并从在线学习的角度形式化因果发现，其灵感来源于赌博机问题中的纯探索。一个图分离系统——由至少切断图中每条边一次的干预组成——即使在最坏情况下，当有无限干预数据可用时，也足以学习因果图。我们提出了一种跟踪-停止因果发现算法，该算法通过分配匹配自适应地从图分离系统中选择干预，并基于采样历史学习因果图。给定任何期望的置信度值，该算法确定一个终止条件并运行直到满足该条件。我们分析了该算法，为所需干预样本的期望数量建立了一个与问题相关的上界。我们提出的算法在各种随机生成的因果图的模拟中优于现有方法。它以显著更少的样本，实现了更高的准确度，该准确度通过学习到的因果图与真实图之间的结构汉明距离来衡量。