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、干预数据或二者的组合，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均假设可使用无限量的干预数据。我们聚焦于干预数据的效率问题，并受赌博机问题中纯探索思想的启发，从在线学习的视角对因果发现进行了形式化表述。一个由能够至少切断图中每条边一次的干预构成的图分离系统，即使在最坏情况下，当拥有无限干预数据时也足以学习因果图。我们提出了一种追踪并终止的因果发现算法，该算法通过分配匹配从图分离系统中自适应地选择干预，并基于采样历史学习因果图。给定任意期望的置信度，该算法确定一个终止条件并运行直至满足该条件。我们对算法进行了分析，建立了所需干预样本期望数的问题相关上界。在多种随机生成的因果图模拟中，我们提出的算法性能优于现有方法。它能够以显著更少的样本实现更高的准确度，该准确度通过所学因果图与真实图之间的结构汉明距离（SHD）来衡量。