In this work, we consider the decoding of short sparse graph-based channel codes via reinforcement learning (RL). 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. LDPC codes are typically decoded via belief propagation 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. We model the node-wise sequential LDPC scheduling scheme as a Markov decision process (MDP), and obtain optimized check node (CN) scheduling policies via RL to improve sequential decoding performance as compared to flooding. In each RL step, an agent decides which CN to schedule next by observing a reward associated with each choice. Repeated scheduling enables the agent to discover the optimized CN scheduling policy which is later incorporated in our RL-based sequential LDPC decoder. In order to reduce RL complexity, we propose a novel graph-induced CN clustering approach to partition the state space of the MDP in such a way that dependencies between clusters are minimized. Compared to standard decoding approaches from the literature, some of our proposed RL schemes not only improve the decoding performance, but also reduce the decoding complexity dramatically once the scheduling policy is learned. By concatenating an outer Hamming code with an inner LDPC code which is decoded based on our learned policy, we demonstrate significant improvements in the decoding performance compared to other LDPC decoding policies.