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This note provides a simple example demonstrating that, if exact computationsare allowed, the number of iterations required for the value iterationalgorithm to find an optimal policy for discounted dynamic programming problemsmay grow arbitrarily quickly with the size of the problem. In particular, thenumber of iterations can be exponential in the number of actions. Thus, unlikepolicy iterations, the value iteration algorithm is not strongly polynomial fordiscounted dynamic programming.

The Value Iteration Algorithm is Not Strongly Polynomial for Discounted Dynamic Programming