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We introduce a framework that represents a dynamic program as a family ofoperators acting on a partially ordered set. We provide an optimality theorybased only on order-theoretic assumptions and show how applications acrossalmost all subfields of dynamic programming fit into this framework. Theserange from traditional dynamic programs to those involving nonlinear recursivepreferences, desire for robustness, function approximation, Monte Carlosampling and distributional dynamic programs. We apply the framework toestablish new optimality and algorithmic results for specific applications.

Dynamic Programs on Partially Ordered Sets