Author(s):

Chatterjee, Krishnendu; Chmelík, Martin

Title: 
POMDPs under probabilistic semantics

Affiliation 
IST Austria 
Abstract: 
We consider partially observable Markov decision processes (POMDPs) with limitaverage payoff, where a reward value in the interval [0,1] is associated to every transition, and the payoff of an infinite path is the longrun average of the rewards. We consider two types of path constraints: (i) quantitative constraint defines the set of paths where the payoff is at least a given threshold λ ∈ (0, 1]; and (ii) qualitative constraint which is a special case of quantitative constraint with λ = 1. We consider the computation of the almostsure winning set, where the controller needs to ensure that the path constraint is satisfied with probability 1. Our main results for qualitative path constraint are as follows: (i) the problem of deciding the existence of a finitememory controller is EXPTIMEcomplete; and (ii) the problem of deciding the existence of an infinitememory controller is undecidable. For quantitative path constraint we show that the problem of deciding the existence of a finitememory controller is undecidable.

Conference Title:

UAI: Uncertainty in Artificial Intelligence

Volume: 
221

Conference Dates:

July 1115, 2013

Conference Location:

Bellevue, Washington, USA

Publisher:

AUAI Press

Date Published:

20150401

Start Page: 
46

End Page:

72

URL: 

DOI: 
10.1016/j.artint.2014.12.009

Notes: 
We thank anonymous reviewers for several important suggestions that helped us to improve the presentation of the paper.

Open access: 
yes (repository) 