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Solving Simple Stochastic Games with Few Random Nodes Faster Using Bland’s Rule

Authors David Auger, Pierre Coucheney, Yann Strozecki

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David Auger
  • DAVID laboratory, University of Versailles Saint-Quentin-en-Yvelines, France
Pierre Coucheney
  • DAVID laboratory, University of Versailles Saint-Quentin-en-Yvelines, France
Yann Strozecki
  • DAVID laboratory, University of Versailles Saint-Quentin-en-Yvelines, France

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David Auger, Pierre Coucheney, and Yann Strozecki. Solving Simple Stochastic Games with Few Random Nodes Faster Using Bland’s Rule. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 9:1-9:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.STACS.2019.9

Abstract

The best algorithm so far for solving Simple Stochastic Games is Ludwig’s randomized algorithm [Ludwig, 1995] which works in expected 2^{O(sqrt{n})} time. We first give a simpler iterative variant of this algorithm, using Bland’s rule from the simplex algorithm, which uses exponentially less random bits than Ludwig’s version. Then, we show how to adapt this method to the algorithm of Gimbert and Horn [Gimbert and Horn, 2008] whose worst case complexity is O(k!), where k is the number of random nodes. Our algorithm has an expected running time of 2^{O(k)}, and works for general random nodes with arbitrary outdegree and probability distribution on outgoing arcs.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory
Keywords
  • simple stochastic games
  • randomized algorithm
  • parametrized complexity
  • strategy improvement
  • Bland’s rule

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