The Simplex Method is Strongly Polynomial for the Markov Decision Problem with a Fixed Discount Rate

@inproceedings{Ye2010TheSM,
  title={The Simplex Method is Strongly Polynomial for the Markov Decision Problem with a Fixed Discount Rate},
  author={Yinyu Ye},
  year={2010}
}
In this short paper we prove that the classic simplex method with the mostnegative-reduced-cost pivoting rule (Dantzig 1947) for solving the Markov decision problem (MDP) with a fixed discount rate is a strongly polynomial-time algorithm. The result seems surprising since this very pivoting rule was shown to be exponential for solving a general linear programming (LP) problem, and the simplex (or simple policy iteration) method with the smallest-index pivoting rule was shown to be exponential… CONTINUE READING

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