Relaxations of Weakly Coupled Stochastic Dynamic Programs

We consider a broad class of stochastic dynamic programming problems that are amenable to relaxation via decomposition. These problems comprise multiple subproblems that are independent of each other except for a collection of coupling constraints on the action space. We fit an additively separable...

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Bibliographic Details
Published in:Operations research Vol. 56; no. 3; pp. 712 - 727
Main Authors: Adelman, Daniel, Mersereau, Adam J
Format: Journal Article
Language:English
Published: Linthicum, MD INFORMS 01.05.2008
Institute for Operations Research and the Management Sciences
Subjects:
Algorithms
Analysis
Applied sciences
approximate dynamic programming
Approximation
column generation
discounted infinite horizon
Dynamic programming
dynamic programming/optimal control
Exact sciences and technology
Integer programming
Integers
Lagrange multiplier
Lagrangian function
Lagrangian optimization
Learning models (Stochastic processes)
Linear programming
Mathematical functions
Mathematical programming
Numberings
Operational research and scientific management
Operational research. Management science
Optimal solutions
Optimization algorithms
Problem sets
Problem solving
Stochastic models
Studies
United States
dynamic programming/optimal control: approximate dynamic programming
Lagrangian
Discount
Lagrangian optimization
Tolerance
Linear programming
Function approximation
Optimization
Stochastic programming
Separation method
Column generation
Lagrange multiplier
Optimal control
discounted infinite horizon; linear programming: column generation
Relaxation method
Infinite horizon
Dynamic programming
ISSN:0030-364X, 1526-5463
Online Access:Get full text
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Summary:We consider a broad class of stochastic dynamic programming problems that are amenable to relaxation via decomposition. These problems comprise multiple subproblems that are independent of each other except for a collection of coupling constraints on the action space. We fit an additively separable value function approximation using two techniques, namely, Lagrangian relaxation and the linear programming (LP) approach to approximate dynamic programming. We prove various results comparing the relaxations to each other and to the optimal problem value. We also provide a column generation algorithm for solving the LP-based relaxation to any desired optimality tolerance, and we report on numerical experiments on bandit-like problems. Our results provide insight into the complexity versus quality trade-off when choosing which of these relaxations to implement.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0030-364X
1526-5463
DOI:10.1287/opre.1070.0445