Abstraction of Markov Decision Processes is a useful tool for solving complex problems, as it can ignore unimportant aspects of an environment, simplifying the process of learning an optimal policy. In this paper, we propose a new algorithm for finding abstract MDPs in environments with continuous state spaces. It is based on MDP homomorphisms, a structure-preserving mapping between MDPs. We demonstrate our algorithm's ability to learn abstractions from collected experience and show how to reuse the abstractions to guide exploration in new tasks the agent encounters. Our novel task transfer method outperforms baselines based on a deep Q-network in the majority of our experiments. The source code is at https://github.com/ondrejba/aamas_19.
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