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Digital library as one of the most important ways in helping students acquire professional knowledge and improve their professional level has gained great attention in recent years. However, its large collection (especially the book resources) hinders students from finding the resources that they are interested in. To overcome this challenge, many researchers have already turned to recommendation algorithms. Compared with traditional recommendation tasks, in the digital library, there are two challenges in book recommendation problems. The first is that users may borrow books that they are not interested in (i.e., noisy borrowing behaviours), such as borrowing books for classmates. The second is that the number of books in a digital library is usually very large, which means one student can only borrow a small set of books in history (i.e., data sparsity issue). As the noisy interactions in students' borrowing sequences may harm the recommendation performance of a book recommender, we focus on refining recommendations via filtering out data noises. Moreover, due to the the lack of direct supervision information, we treat noise filtering in sequences as a decision-making process and innovatively introduce a reinforcement learning method as our recommendation framework. Furthermore, to overcome the sparsity issue of students' borrowing behaviours, a clustering-based reinforcement learning algorithm is further developed. Experimental results on two real-world datasets demonstrate the superiority of our proposed method compared with several state-of-the-art recommendation methods. [ABSTRACT FROM AUTHOR]