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Symbolic dynamic programming for continuous state and observation POMDPs

: Zamani, Z.; Sanner, S.; Poupart, P.; Kersting, K.

Neural Information Processing Systems -NIPS- Foundation:
Advances in Neural Information Processing Systems 25. 26th Annual Conference on Neural Information Processing Systems 2012. Vol.2 : December 3 - 6, 2012, Lake Tahoe, Nevada, USA
Red Hook, NY: Curran, 2013
ISBN: 978-1-62748-003-1
Annual Conference on Neural Information Processing Systems (NIPS) <26, 2012, Lake Tahoe/Nev.>
Fraunhofer IAIS ()

Point-based value iteration (PBVI) methods have proven extremely effective for finding (approximately) optimal dynamic programming solutions to partially-observable Markov decision processes (POMDPs) when a set of initial belief states is known. However, no PBVI work has provided exact point-based backups for both continuous state and observation spaces, which we tackle in this paper. Our key insight is that while there may be an infinite number of observations, there are only a finite number of continuous observation partitionings that are relevant for optimal decision-making when a finite, fixed set of reachable belief states is considered. To this end, we make two important contributions: (1) we show how previous exact symbolic dynamic programming solutions for continuous state MDPs can be generalized to continuous state POMDPs with discrete observations, and (2) we show how recently developed symbolic integration methods allow this solution to be extended to PBVI fo r continuous state and observation POMDPs with potentially correlated, multivariate continuous observation spaces.