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Hierarchical reinforcement learning facilitates learning in large and complex domains by exploiting subtasks and creating hierarchical structures using these subtasks. Subtasks are usually defined through finding subgoals of the problem. Providing mechanisms for autonomous subgoal discovery and skill acquisition is a challenging issue in reinforcement learning. Among the proposed algorithms, a few of them are successful both in performance and also efficiency in terms of the running time of the algorithm. In this paper, we study four methods for subgoal discovery which are based on graph partitioning. The idea behind the methods proposed in this paper is that if we partition the transition...