Square-root regret bounds for continuous-time episodic Markov decision processes
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We study reinforcement learning for continuous-time Markov decision processes (MDPs) in the finite-horizon episodic setting. We present a learning algorithm based on the methods of value iteration and upper confidence bound. We derive an upper bound on the worst-case expected regret for the proposed algorithm, and establish a worst-case lower bound, both bounds are of the order of square-root on the number of episodes. Finally, we conduct simulation experiments to illustrate the performance of our algorithm.
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