How to Play in Infinite MDPs (Invited Talk)

Authors Stefan Kiefer, Richard Mayr, Mahsa Shirmohammadi, Patrick Totzke, Dominik Wojtczak

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Author Details

Stefan Kiefer
  • Department of Computer Science, University of Oxford, United Kingdom
Richard Mayr
  • School of Informatics, University of Edinburgh, United Kingdom
Mahsa Shirmohammadi
  • CNRS & IRIF, Université de Paris, France
Patrick Totzke
  • Department of Computer Science, University of Liverpool, United Kingdom
Dominik Wojtczak
  • Department of Computer Science, University of Liverpool, United Kingdom

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Stefan Kiefer, Richard Mayr, Mahsa Shirmohammadi, Patrick Totzke, and Dominik Wojtczak. How to Play in Infinite MDPs (Invited Talk). In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 3:1-3:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Markov decision processes (MDPs) are a standard model for dynamic systems that exhibit both stochastic and nondeterministic behavior. For MDPs with finite state space it is known that for a wide range of objectives there exist optimal strategies that are memoryless and deterministic. In contrast, if the state space is infinite, optimal strategies may not exist, and optimal or ε-optimal strategies may require (possibly infinite) memory. In this paper we consider qualitative objectives: reachability, safety, (co-)Büchi, and other parity objectives. We aim at giving an introduction to a collection of techniques that allow for the construction of strategies with little or no memory in countably infinite MDPs.

Subject Classification

ACM Subject Classification
  • Theory of computation → Random walks and Markov chains
  • Mathematics of computing → Probability and statistics
  • Markov decision processes


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