We study countably infinite Markov decision processes with B\"uchi objectives, which ask to visit a given subset of states infinitely often. A question left open by T.P. Hill in 1979 is whether there always exist ε-optimal Markov strategies, i.e., strategies that base decisions only on the current state and the number of steps taken so far. We provide a negative answer to this question by constructing a non-trivial counterexample. On the other hand, we show that Markov strategies with only 1 bit of extra memory are sufficient.
Cite
@article{arxiv.1904.11573,
title = {B\"uchi Objectives in Countable MDPs},
author = {Stefan Kiefer and Richard Mayr and Mahsa Shirmohammadi and Patrick Totzke},
journal= {arXiv preprint arXiv:1904.11573},
year = {2019}
}
Comments
full version of an ICALP'19 paper. This update only fixes some typesetting issues