No good Markov strategies for Büchi objectives in countable MDPs

Journal article

We study countably infinite Markov decision processes with Büchi objectives, which ask to visit a given subset of states infinitely often. A question left open by T.P. Hill (1979) is whether there always exist ε$$\varepsilon $$-optimal Markov strategies, i.e., strategies that base decisions only on the current state and on the clock (the number of steps taken so far). We provide a negative answer to this question by constructing a non-trivial counterexample.

Authors: Kiefer, S; Mayr, R; Shirmohammadi, M; Totzke, P

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Annals of Operations Research
• Pages: 1-16
• Publication date: 2026-05-09
• Acceptance date: 2026-04-09
• DOI: 10.1007/s10479-026-07226-6
• EISSN: 1572-9338
• ISSN: 0254-5330
• Language: English
• Keywords: State (computer science); Markov chain; Base (topology); Markov process; Ask price; Markov decision process; Theory of computation; Countable set