The Shift-Function Approach for Markov Decision Processes with Unbounded Returns.

Abstract

We study a discrete-time Markov decision process with general state and action space. The objective is to maximize the expected total return over a finite or infinite horizon. The transition probability measure is allowed to be defective, so that the model includes discounting, state-and action-dependent transition times (semi-Markov decision processes), and stopping problems. With applications to control of queues and inventory systems as a motivation, we develop a set of conditions on the one-period return function, the transition probabilities and the terminal value function that guarantee uniform convergence (with respect to the sup norm) of the finite-horizon optimal value functions to the infinite-horizon optimal value function (successive approximations). These conditions are substantially weaker and more realistic for the applications we have in mind than those of the classical, discounted bounded model. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1981
Accession Number
ADA109774

Entities

People

  • Jo Van Nunen
  • Shaler Stidham Jr.

Organizations

  • Stanford University

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Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Banach Space
  • Contracts
  • Convergence
  • Equations
  • Inventory
  • Inventory Control
  • Mathematics
  • Military Research
  • Operations Research
  • Probability
  • Probability Distributions
  • Random Variables
  • Random Walk
  • Stochastic Processes
  • Terminals
  • United States
  • United States Government

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  • Mathematical Modeling and Probability Theory.

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  • Space