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Foundations of average-cost nonhomog...

Cao, Xi-Ren.

Foundations of average-cost nonhomogeneous controlled Markov chains

Record Type:	Electronic resources : Monograph/item
Title/Author:	Foundations of average-cost nonhomogeneous controlled Markov chainsby Xi-Ren Cao.
Author:	Cao, Xi-Ren.
Published:	Cham :Springer International Publishing :2021.
Description:	viii, 120 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Markov processes.
Online resource:	https://doi.org/10.1007/978-3-030-56678-4
ISBN:	9783030566784$q(electronic bk.)

Foundations of average-cost nonhomogeneous controlled Markov chains
Cao, Xi-Ren.

Foundations of average-cost nonhomogeneous controlled Markov chains[electronic resource] /by Xi-Ren Cao. - Cham :Springer International Publishing :2021. - viii, 120 p. :ill., digital ;24 cm. - SpringerBriefs in electrical and computer engineering, Control, automation and robotics,2192-6786. - SpringerBriefs in electrical and computer engineering.Control, automation and robotics..

Chapter 1. Introduction -- Chapter 2. Confluencity and State Classification -- Chapter 3. Optimization of Average Rewards and Bias: Single Class -- Chapter 4. Optimization of Average Rewards: Multi-Chains -- Chapter 5. The Nth-Bias and Blackwell Optimality.

This Springer brief addresses the challenges encountered in the study of the optimization of time-nonhomogeneous Markov chains. It develops new insights and new methodologies for systems in which concepts such as stationarity, ergodicity, periodicity and connectivity do not apply. This brief introduces the novel concept of confluencity and applies a relative optimization approach. It develops a comprehensive theory for optimization of the long-run average of time-nonhomogeneous Markov chains. The book shows that confluencity is the most fundamental concept in optimization, and that relative optimization is more suitable for treating the systems under consideration than standard ideas of dynamic programming. Using confluencity and relative optimization, the author classifies states as confluent or branching and shows how the under-selectivity issue of the long-run average can be easily addressed, multi-class optimization implemented, and Nth biases and Blackwell optimality conditions derived. These results are presented in a book for the first time and so may enhance the understanding of optimization and motivate new research ideas in the area.

ISBN: 9783030566784$q(electronic bk.)

Standard No.: 10.1007/978-3-030-56678-4doiSubjects--Topical Terms:

181910
Markov processes.

LC Class. No.: QA274.7 / .C36 2021

Dewey Class. No.: 519.233

Foundations of average-cost nonhomogeneous controlled Markov chains
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505 0 $a Chapter 1. Introduction -- Chapter 2. Confluencity and State Classification -- Chapter 3. Optimization of Average Rewards and Bias: Single Class -- Chapter 4. Optimization of Average Rewards: Multi-Chains -- Chapter 5. The Nth-Bias and Blackwell Optimality.
520 $a This Springer brief addresses the challenges encountered in the study of the optimization of time-nonhomogeneous Markov chains. It develops new insights and new methodologies for systems in which concepts such as stationarity, ergodicity, periodicity and connectivity do not apply. This brief introduces the novel concept of confluencity and applies a relative optimization approach. It develops a comprehensive theory for optimization of the long-run average of time-nonhomogeneous Markov chains. The book shows that confluencity is the most fundamental concept in optimization, and that relative optimization is more suitable for treating the systems under consideration than standard ideas of dynamic programming. Using confluencity and relative optimization, the author classifies states as confluent or branching and shows how the under-selectivity issue of the long-run average can be easily addressed, multi-class optimization implemented, and Nth biases and Blackwell optimality conditions derived. These results are presented in a book for the first time and so may enhance the understanding of optimization and motivate new research ideas in the area.
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