Metrics for Markov decision processes with infinite state spaces
arXiv preprint arXiv:1207.1386, 2012•arxiv.org
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.
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.
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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