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编码在因果图中的因果关系。现有大多数因果发现方法均假设存在无限干预数据进行开发。受多臂赌博机问题中纯探索策略的启发，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问题。图分离系统——由至少切断图中每条边一次的干预措施组成——即使在最坏情况下，当可获得无限干预数据时，也足以学习因果图。我们提出一种跟踪-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措施，并基于采样历史学习因果图。给定任意期望置信度值，该算法确定终止条件并持续运行直至满足条件。我们通过分析算法，建立了所需干预样本数量的期望值问题相关上界。在各种随机生成的因果图模拟中，我们提出的算法优于现有方法。通过比较学习到的因果图与真实图之间的结构汉明距离（SHD），该算法以显著更少的样本实现了更高的准确度。