Approximative Methods for Monotone Systems of Min-Max-Polynomial Equations

  • Javier Esparza
  • Thomas Gawlitza
  • Stefan Kiefer
  • Helmut Seidl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5125)


A monotone system of min-max-polynomial equations (min-max-MSPE) over the variables X 1,...,X n has for every i exactly one equation of the form X i  = f i (X 1,...,X n ) where each f i (X 1,...,X n ) is an expression built up from polynomials with non-negative coefficients, minimum- and maximum-operators. The question of computing least solutions of min-max-MSPEs arises naturally in the analysis of recursive stochastic games [5,6,14]. Min-max-MSPEs generalize MSPEs for which convergence speed results of Newton’s method are established in [11,3]. We present the first methods for approximatively computing least solutions of min-max-MSPEs which converge at least linearly. Whereas the first one converges faster, a single step of the second method is cheaper. Furthermore, we compute ε-optimal positional strategies for the player who wants to maximize the outcome in a recursive stochastic game.


Approximative Method Markov Decision Process Strategy Iteration Stochastic Game Linear Convergence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Javier Esparza
    • 1
  • Thomas Gawlitza
    • 1
  • Stefan Kiefer
    • 1
  • Helmut Seidl
    • 1
  1. 1.Institut für InformatikTechnische Universität MünchenGermany

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