We study the causal bandit problem when the causal graph is unknown and develop an efficient algorithm for finding the parent node of the reward node using atomic interventions. We derive the exact equation for the expected number of interventions performed by the algorithm and show that under certain graphical conditions it could perform either logarithmically fast or, under more general assumptions, slower but still sublinearly in the number of variables. We formally show that our algorithm is optimal as it meets the universal lower bound we establish for any algorithm that performs atomic interventions. Finally, we extend our algorithm to the case when the reward node has multiple parents. Using this algorithm together with a standard algorithm from bandit literature leads to improved regret bounds.

翻译：我们研究了当因果图未知时的因果Bandit问题，并开发了一种高效算法，通过原子干预寻找奖励节点的父节点。我们推导了该算法执行干预次数的精确期望公式，并证明在特定图条件下其收敛速度可达到对数级别，或在更一般假设下虽然较慢但仍为关于变量数量的亚线性。我们严格证明了该算法的最优性——它达到了我们为所有执行原子干预的算法建立的通用下界。最后，我们将算法扩展至奖励节点存在多父节点的情况。将本算法与Bandit文献中的标准算法结合，可得到改进的遗憾界。