Metrics for Markov Decision Processes with Infinite State Spaces

07/04/2012 ∙ by Norman Ferns, et al. ∙ 0

We present metrics for measuring state similarity in Markov decision processes (MDPs) with infinitely many states, including MDPs with continuous state spaces. Such metrics provide a stable quantitative analogue of the notion of bisimulation for MDPs, and are suitable for use in MDP approximation. We show that the optimal value function associated with a discounted infinite horizon planning task varies continuously with respect to our metric distances.

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