Metrics for Markov Decision Processes with Infinite State Spaces
Norman Ferns, Prakash Panangaden, Doina Precup
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.
PDF Link: /papers/05/p201-ferns.pdf
AUTHOR = "Norman Ferns
and Prakash Panangaden and Doina Precup",
TITLE = "Metrics for Markov Decision Processes with Infinite State Spaces",
BOOKTITLE = "Proceedings of the Twenty-First Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-05)",
PUBLISHER = "AUAI Press",
ADDRESS = "Arlington, Virginia",
YEAR = "2005",
PAGES = "201--208"