Finite-Memory Strategies for Almost-Sure Energy-MeanPayoff Objectives in MDPs

Authors Mohan Dantam, Richard Mayr

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Mohan Dantam
  • School of Informatics, University of Edinburgh, UK
Richard Mayr
  • School of Informatics, University of Edinburgh, UK

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Mohan Dantam and Richard Mayr. Finite-Memory Strategies for Almost-Sure Energy-MeanPayoff Objectives in MDPs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 133:1-133:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


We consider finite-state Markov decision processes with the combined Energy-MeanPayoff objective. The controller tries to avoid running out of energy while simultaneously attaining a strictly positive mean payoff in a second dimension. We show that finite memory suffices for almost surely winning strategies for the Energy-MeanPayoff objective. This is in contrast to the closely related Energy-Parity objective, where almost surely winning strategies require infinite memory in general. We show that exponential memory is sufficient (even for deterministic strategies) and necessary (even for randomized strategies) for almost surely winning Energy-MeanPayoff. The upper bound holds even if the strictly positive mean payoff part of the objective is generalized to multidimensional strictly positive mean payoff. Finally, it is decidable in pseudo-polynomial time whether an almost surely winning strategy exists.

Subject Classification

ACM Subject Classification
  • Theory of computation → Random walks and Markov chains
  • Mathematics of computing → Probability and statistics
  • Markov decision processes
  • energy
  • mean payoff
  • parity
  • strategy complexity


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