  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.
