Dynamic Programs on Partially Ordered Sets
Optimization and Control
2025-01-07 v4
Abstract
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.
Cite
@article{arxiv.2308.02148,
title = {Dynamic Programs on Partially Ordered Sets},
author = {Thomas J. Sargent and John Stachurski},
journal= {arXiv preprint arXiv:2308.02148},
year = {2025}
}