Büchi Objectives in Countable MDPs



Kiefer, Stefan, Mayr, Richard, Shirmohammadi, Mahsa and Totzke, Patrick ORCID: 0000-0001-5274-8190
(2019) Büchi Objectives in Countable MDPs. .

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Abstract

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 $\varepsilon$-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.

Item Type: Conference or Workshop Item (Unspecified)
Additional Information: full version of an ICALP'19 paper. This update only fixes some typesetting issues
Uncontrolled Keywords: math.PR, math.PR, cs.FL, math.OC
Depositing User: Symplectic Admin
Date Deposited: 21 Aug 2019 08:38
Last Modified: 29 Sep 2021 18:36
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3051509