Regret Bounds for Reinforcement Learning via Markov Chain Concentration

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Ronald Ortner


We give a simple optimistic algorithm for which it is easy to derive regret bounds of O(sqrt{t-mix SAT}) steps in uniformly ergodic Markov decision processes with S states, A actions, and mixing time parameter t-mix. These bounds are the first regret bounds in the general, non-episodic setting with an optimal dependence on all given parameters. They could only be improved by using an alternative mixing time parameter.

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