Finite-State Approximations to Denumerable-State Dynamic Programs.

by Bennett L. Fox

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Description of a sequence of policies for essentially finite-state dynamic programs with applications to Air Force inventory control problems. This work considers the case in dynamic programming where the domain and range is the space of denumerable sequences. To obtain a sequence of finite-state approximations, the problem is expressed in a manner essentially equivalent to that of an [n]-state problem, achieved by "cutting off the tail" of the original problem. Policies are defined for essentially finite-state dynamic programs such that the corresponding vector of optimal returns converges pointwise to that of a denumerable-state dynamic program. This result implies that when the number of states in the approximating program is large, the exact number does not matter significantly, say, in determining supply and stockage policies. A corresponding result is also given for stochastic games. 20 pp. Ref

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