On the Class of Closed Dynamic Programs

This paper considers a class of general dynamic programs which satisfies the mono tonicity and contraction assumption, and in which the sets of cost functions and policies are closed under the monotone contraction operators. This class of dynamic programs includes, piecewise linear, affine dynamic programs, partially observable Markov decision processes, and many sequential decision processes under uncertainty such as machine maintenance control models and search problems with incomplete infOImation. An algorithm based on generalized policy improvement has the property that it only generates cost functions and policies belonging to distinguished subsets of cost functions and policies, respectively.