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# Optimal cost almost-sure reachability in POMDPs

1 Anonymous, 2 Anonymous, 3 Anonymous, 4 Anonymous, Optimal Cost Almost-Sure Reachability in POMDPs, IST Austria, 2014.

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*Technical Report*|

*Published*|

*English*

**Scopus indexed**

Author

Anonymous, 1;
Anonymous, 2;
Anonymous, 3;
Anonymous, 4

Series Title

IST Austria Technical Report

Abstract

We consider partially observable Markov decision processes (POMDPs) with a set of target states and every transition is associated with an integer cost. The optimization objective we study asks to minimize the expected total cost till the target set is reached, while ensuring that the target set is reached almost-surely (with probability 1). We show that for integer costs approximating the optimal cost is undecidable. For positive costs, our results are as follows: (i) we establish matching lower and upper bounds for the optimal cost and the bound is double exponential; (ii) we show that the problem of approximating the optimal cost is decidable and present approximation algorithms developing on the existing algorithms for POMDPs with finite-horizon objectives. While the worst-case running time of our algorithm is double exponential, we also present efficient stopping criteria for the algorithm and show experimentally that it performs well in many examples of interest.

Publishing Year

Date Published

2014-09-09

Page

22

ISSN

IST-REx-ID

### Cite this

Anonymous 1, Anonymous 2, Anonymous 3, Anonymous 4.

*Optimal Cost Almost-Sure Reachability in POMDPs*. IST Austria; 2014.Anonymous, 1, Anonymous, 2, Anonymous, 3, & Anonymous, 4. (2014).

*Optimal cost almost-sure reachability in POMDPs*. IST Austria.Anonymous, 1, 2 Anonymous, 3 Anonymous, and 4 Anonymous.

*Optimal Cost Almost-Sure Reachability in POMDPs*. IST Austria, 2014.1 Anonymous, 2 Anonymous, 3 Anonymous, and 4 Anonymous,

*Optimal cost almost-sure reachability in POMDPs*. IST Austria, 2014.Anonymous 1, Anonymous 2, Anonymous 3, Anonymous 4. 2014. Optimal cost almost-sure reachability in POMDPs, IST Austria, 22p.

Anonymous, 1, et al.

*Optimal Cost Almost-Sure Reachability in POMDPs*. IST Austria, 2014.**All files available under the following license(s):**

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