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This note provides upper bounds on the number of operations required tocompute by value iterations a nearly optimal policy for an infinite-horizondiscounted Markov decision process with a finite number of states and actions.For a given discount factor, magnitude of the reward function, and desiredcloseness to optimality, these upper bounds are strongly polynomial in thenumber of state-action pairs, and one of the provided upper bounds has theproperty that it is a non-decreasing function of the value of the discountfactor.

Strong Polynomiality of the Value Iteration Algorithm for Computing Nearly Optimal Policies for Discounted Dynamic Programming