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The Simplex Method is Strongly Polynomial for Deterministic Markov Decision Processes

2015
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Mathematics of Operations Research
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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(n 3 m 2 log 2 n) iterations if the discount factor is uniform and O(n 5 m 3 log 2 n) iterations if each action has a distinct discount factor. Previously the simplex method was known to

doi:10.1287/moor.2014.0699
fatcat:oerirap3nfbwrorlark5b3hcl4