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We show in this work that reinforcement learning can be successfully applied to decoding short to moderate length sparse graph-based channel codes. Specifically, we focus on low-density parity check (LDPC) codes, which for example have been standardized in the context of 5G cellular communication systems due to their excellent error correcting performance. These codes are typically decoded via belief propagation iterative decoding on the corresponding bipartite (Tanner) graph of the code via flooding, i.e., all check and variable nodes in the Tanner graph are updated at once. In contrast, in this paper we utilize a sequential update policy which selects the optimum check node (CN) scheduling in order to improve decoding performance. In particular, we model the CN update process as a multi-armed bandit process with dependent arms and employ a Q-learning scheme for optimizing the CN scheduling policy. In order to reduce the learning complexity, we propose a novel graph-induced CN clustering approach to partition the state space in such a way that dependencies between clusters are minimized. Our results show that compared to other decoding approaches from the literature, the proposed reinforcement learning scheme not only significantly improves the decoding performance, but also reduces the decoding complexity dramatically once the scheduling policy is learned.