License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2023.10
URN: urn:nbn:de:0030-drops-185448
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18544/
Go to the corresponding LIPIcs Volume Portal

Akian, Marianne ; Gaubert, Stéphane ; Naepels, Ulysse ; Terver, Basile

Solving Irreducible Stochastic Mean-Payoff Games and Entropy Games by Relative Krasnoselskii-Mann Iteration

pdf-format:
LIPIcs-MFCS-2023-10.pdf (0.8 MB)

Abstract

We analyse an algorithm solving stochastic mean-payoff games, combining the ideas of relative value iteration and of Krasnoselskii-Mann damping. We derive parameterized complexity bounds for several classes of games satisfying irreducibility conditions. We show in particular that an ε-approximation of the value of an irreducible concurrent stochastic game can be computed in a number of iterations in O(|log(ε)|) where the constant in the O(⋅) is explicit, depending on the smallest non-zero transition probabilities. This should be compared with a bound in O(ε^{-1}|log(ε)|) obtained by Chatterjee and Ibsen-Jensen (ICALP 2014) for the same class of games, and to a O(ε^{-1}) bound by Allamigeon, Gaubert, Katz and Skomra (ICALP 2022) for turn-based games. We also establish parameterized complexity bounds for entropy games, a class of matrix multiplication games introduced by Asarin, Cervelle, Degorre, Dima, Horn and Kozyakin. We derive these results by methods of variational analysis, establishing contraction properties of the relative Krasnoselskii-Mann iteration with respect to Hilbert’s semi-norm.

BibTeX - Entry

@InProceedings{akian_et_al:LIPIcs.MFCS.2023.10,
  author =	{Akian, Marianne and Gaubert, St\'{e}phane and Naepels, Ulysse and Terver, Basile},
  title =	{{Solving Irreducible Stochastic Mean-Payoff Games and Entropy Games by Relative Krasnoselskii-Mann Iteration}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{10:1--10:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18544},
  URN =		{urn:nbn:de:0030-drops-185448},
  doi =		{10.4230/LIPIcs.MFCS.2023.10},
  annote =	{Keywords: Stochastic mean-payoff games, concurrent games, entropy games, relative value iteration, Krasnoselskii-Mann fixed point algorithm, Hilbert projective metric}
}

Keywords: Stochastic mean-payoff games, concurrent games, entropy games, relative value iteration, Krasnoselskii-Mann fixed point algorithm, Hilbert projective metric
Collection: 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)
Issue Date: 2023
Date of publication: 21.08.2023

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI