10.1016/j.artint.2014.12.009
Chatterjee, Krishnendu
Krishnendu
Chatterjee0000-0002-4561-241X
Chmelik, Martin
Martin
Chmelik
POMDPs under probabilistic semantics
Elsevier
2015
2018-12-11T11:54:28Z
2019-08-02T12:37:29Z
journal_article
https://research-explorer.app.ist.ac.at/record/1873
https://research-explorer.app.ist.ac.at/record/1873.json
1408.2058
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.