The Simplex Method is Strongly Polynomial for Deterministic Markov Decision Processes

  title={The Simplex Method is Strongly Polynomial for Deterministic Markov Decision Processes},
  author={Ian Post and Yinyu Ye},
  booktitle={Mathematics of Operations Research},
  • Ian PostY. Ye
  • Published in
    Mathematics of Operations…
    24 August 2012
  • Mathematics
We prove that the simplex method with the highest gain/most-negative-reduced cost pivoting rule converges in strongly polynomial time for deterministic Markov decision processes (MDPs) regardless of the discount factor. For a deterministic MDP with n states and m actions, we prove the simplex method runs in O(n3m2 log2 n) iterations if the discount factor is uniform and O(n5m3 log2 n) iterations if each action has a distinct discount factor. Previously the simplex method was known to run in… 

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