A Generic Strategy Improvement Method for Simple Stochastic Games

Authors David Auger, Xavier Badin de Montjoye, Yann Strozecki



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Author Details

David Auger
  • Université Paris Saclay, UVSQ, DAVID, France
Xavier Badin de Montjoye
  • Université Paris Saclay, UVSQ, DAVID, France
Yann Strozecki
  • Université Paris Saclay, UVSQ, DAVID, France

Acknowledgements

The authors want to thank Pierre Coucheney for many interesting discussions on SSGs.

Cite AsGet BibTex

David Auger, Xavier Badin de Montjoye, and Yann Strozecki. A Generic Strategy Improvement Method for Simple Stochastic Games. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 12:1-12:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.MFCS.2021.12

Abstract

We present a generic strategy improvement algorithm (GSIA) to find an optimal strategy of simple stochastic games (SSG). We prove the correctness of GSIA, and derive a general complexity bound, which implies and improves on the results of several articles. First, we remove the assumption that the SSG is stopping, which is usually obtained by a polynomial blowup of the game. Second, we prove a tight bound on the denominator of the values associated to a strategy, and use it to prove that all strategy improvement algorithms are in fact fixed parameter tractable in the number r of random vertices. All known strategy improvement algorithms can be seen as instances of GSIA, which allows to analyze the complexity of converge from below by Condon [Condon, 1993] and to propose a class of algorithms generalising Gimbert and Horn’s algorithm [Gimbert and Horn, 2008; Gimbert and Horn, 2009]. These algorithms terminate in at most r! iterations, and for binary SSGs, they do less iterations than the current best deterministic algorithm given by Ibsen-Jensen and Miltersen [Ibsen-Jensen and Miltersen, 2012].

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory
Keywords
  • Simple Stochastic Games
  • Strategy Improvement
  • Parametrized Complexity
  • Stopping
  • Meta Algorithm
  • f-strategy

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