Modified policy iteration algorithms are not strongly polynomial for discounted dynamic programming

Eugene A. Feinberg 1 Jefferson Huang 1 Bruno Scherrer 2
1 SBU - Stony Brook University [The State University of New York]
2 MAIA - Autonomous intelligent machine
Inria Nancy - Grand Est, LORIA - AIS - Department of Complex Systems, Artificial Intelligence & Robotics
Abstract : This note shows that the number of arithmetic operations required by any member of a broad class of optimistic policy iteration algorithms to solve a deterministic discounted dynamic programming problem with three states and four actions may grow arbitrarily. Therefore any such algorithm is not strongly polynomial. In particular, the modified policy iteration and $\lambda$-policy iteration algorithms are not strongly polynomial.
Keywords : Markov decision process Modified policy iteration Strongly polynomial Policy Algorithm
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Submitted on : Friday, December 5, 2014 - 11:48:44 AM
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Eugene A. Feinberg, Jefferson Huang, Bruno Scherrer. Modified policy iteration algorithms are not strongly polynomial for discounted dynamic programming. Operations Research Letters, Elsevier, 2014, 42, pp.429 - 431. ⟨10.1016/j.orl.2014.07.006⟩. ⟨hal-01091370⟩

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