The increasing complexity of IT environments urgently requires the use of analytical approaches and automated problem resolution for more efficient delivery of IT services. In this paper, we model the automation recommendation procedure of IT automation services as a contextual bandit problem with dependent arms, where the arms are in the form of hierarchies. Intuitively, different automations in IT automation services, designed to automatically solve the corresponding ticket problems, can be organized into a hierarchy by domain experts according to the types of ticket problems. We introduce a novel hierarchical multi-armed bandit algorithms leveraging the hierarchies, which can match the coarse-to-fine feature space of arms. Empirical experiments on a real large-scale ticket dataset have demonstrated substantial improvements over the conventional bandit algorithms. In addition, a case study of dealing with the cold-start problem is conducted to clearly show the merits of our proposed algorithms.