  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.
