Work

No good Markov strategies for Büchi objectives in countable MDPs

Year: 2026

Type: article

Abstract: 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 $$\varepsilon $$ ε -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.

Source: Annals of Operations Research

DOI: 10.1007/s10479-026-07226-6

Authors: Stefan Kiefer, Richard Mayr, Mahsa Shirmohammadi, Patrick Totzke

Institutions: University of Oxford, University of Edinburgh, Centre National de la Recherche Scientifique, Institut de Recherche en Informatique Fondamentale, University of Liverpool

Language: English

Topic: Formal Methods in Verification

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Agence Nationale de la Recherche, Engineering and Physical Sciences Research Council