POMDPs under probabilistic semantics Journal Article

Author(s): Chatterjee, Krishnendu; Chmelík, Martin
Article Title: POMDPs under probabilistic semantics
Affiliation IST Austria
Abstract: We consider partially observable Markov decision processes (POMDPs) with limit-average payoff, where a reward value in the interval [0,1] is associated with every transition, and the payoff of an infinite path is the long-run average of the rewards. We consider two types of path constraints: (i) a quantitative constraint defines the set of paths where the payoff is at least a given threshold λ1ε(0,1]; and (ii) a qualitative constraint which is a special case of the quantitative constraint with λ1=1. We consider the computation of the almost-sure winning set, where the controller needs to ensure that the path constraint is satisfied with probability 1. Our main results for qualitative path constraints are as follows: (i) the problem of deciding the existence of a finite-memory controller is EXPTIME-complete; and (ii) the problem of deciding the existence of an infinite-memory controller is undecidable. For quantitative path constraints we show that the problem of deciding the existence of a finite-memory controller is undecidable. We also present a prototype implementation of our EXPTIME algorithm and experimental results on several examples.
Keywords: Almost-sure winning; Limit-average objectives; POMDPs
Journal Title: Artificial Intelligence
Volume: 221
ISSN: 0004-3702
Publisher: Elsevier  
Date Published: 2015-04-01
Start Page: 46
End Page: 72
DOI: 10.1016/j.artint.2014.12.009
Open access: yes (repository)
IST Austria Authors
  1. Martin Chmelik
    23 Chmelik