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Dynamic Programs on Partially Ordered Sets

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arxiv 2308.02148 v4 pith:TW32TMAW submitted 2023-08-04 math.OC

Thomas J. Sargent , John Stachurski This is my paper · ORCID
classification math.OC
keywords dynamicframeworkprogramsapplicationsoptimalityorderedpartiallyacross
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We introduce a framework that represents a dynamic program as a family of operators acting on a partially ordered set. We provide an optimality theory based only on order-theoretic assumptions and show how applications across almost all subfields of dynamic programming fit into this framework. These range from traditional dynamic programs to those involving nonlinear recursive preferences, desire for robustness, function approximation, Monte Carlo sampling and distributional dynamic programs. We apply the framework to establish new optimality and algorithmic results for specific applications.

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Cited by 1 Pith paper

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  1. History-Dependent Recursive Preferences in Markov Decision Processes

    math.OC 2026-07 conditional novelty 6.0 of 10

    History-dependent recursive preferences have a canonical minimal preference-augmented state and Bellman recursion when certainty-equivalent richness and separability axioms hold.

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