DYNAMIC PROGRAMS ON PARTIALLY ORDERED SETS

Thomas J. Sargent; John Stachurski

doi:10.1137/24M1696159

DYNAMIC PROGRAMS ON PARTIALLY ORDERED SETS

Thomas J. Sargent, John Stachurski

Research output: Contribution to journal › Article › peer-review

Abstract

We represent a dynamic program as a family of operators acting on a partially ordered set. We provide an optimality theory based on order-theoretic assumptions and show how many applications 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 our framework to establish new optimality and algorithmic results for specific applications.

Original language	English (US)
Pages (from-to)	778-795
Number of pages	18
Journal	SIAM Journal on Control and Optimization
Volume	63
Issue number	2
DOIs	https://doi.org/10.1137/24M1696159
State	Published - 2025

Keywords

Bellman equation
dynamic programming
partial orders

ASJC Scopus subject areas

Control and Optimization
Applied Mathematics

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10.1137/24M1696159

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abstract = "We represent a dynamic program as a family of operators acting on a partially ordered set. We provide an optimality theory based on order-theoretic assumptions and show how many applications 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 our framework to establish new optimality and algorithmic results for specific applications.",

keywords = "Bellman equation, dynamic programming, partial orders",

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AB - We represent a dynamic program as a family of operators acting on a partially ordered set. We provide an optimality theory based on order-theoretic assumptions and show how many applications 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 our framework to establish new optimality and algorithmic results for specific applications.

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KW - partial orders

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DYNAMIC PROGRAMS ON PARTIALLY ORDERED SETS

Abstract

Keywords

ASJC Scopus subject areas

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