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Strong polynomiality of the Gass-Saaty shadow-vertex pivoting rule for controlled random walks

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  • Guy Even
  • Alexander Zadorojniy

Abstract

We consider the subclass of linear programs that formulate Markov Decision Processes ( mdps). We show that the Simplex algorithm with the Gass-Saaty shadow-vertex pivoting rule is strongly polynomial for a subclass of mdps, called controlled random walks (CRWs); the running time is O(|S| 3 ⋅|U| 2 ), where |S| denotes the number of states and |U| denotes the number of actions per state. This result improves the running time of Zadorojniy et al. (Mathematics of Operations Research 34(4):992–1007, 2009 ) algorithm by a factor of |S|. In particular, the number of iterations needed by the Simplex algorithm for CRWs is linear in the number of states and does not depend on the discount factor. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Guy Even & Alexander Zadorojniy, 2012. "Strong polynomiality of the Gass-Saaty shadow-vertex pivoting rule for controlled random walks," Annals of Operations Research, Springer, vol. 201(1), pages 159-167, December.
    • Handle: RePEc:spr:annopr:v:201:y:2012:i:1:p:159-167:10.1007/s10479-012-1199-x
    DOI: 10.1007/s10479-012-1199-x
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    References listed on IDEAS

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