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Policy Iteration (PI) is a widely used family of algorithms to computeoptimal policies for Markov Decision Problems (MDPs). We derive upper bounds onthe running time of PI on Deterministic MDPs (DMDPs): the class of MDPs inwhich every state-action pair has a unique next state. Our results include anon-trivial upper bound that applies to the entire family of PI algorithms;another to all "max-gain" switching variants; and affirmation that a conjectureregarding Howard's PI on MDPs is true for DMDPs. Our analysis is based oncertain graph-theoretic results, which may be of independent interest.

Upper Bounds for All and Max-gain Policy Iteration Algorithms on Deterministic MDPs