Foundations of Average-Cost Nonhomogeneous Controlled Markov Chains / by Xi-Ren Cao

By:

Cao, Xi-Ren [VerfasserIn]

Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: SpringerBriefs in Control, Automation and RoboticsPublisher: Cham : Springer International Publishing, 2021Publisher: Cham : Imprint: Springer, 2021Edition: 1st ed. 2021Description: 1 Online-Ressource(VIII, 120 p. 36 illus., 3 illus. in color.)ISBN:

9783030566784

Subject(s):

Additional physical formats: 9783030566777 | 9783030566791 | Erscheint auch als: 9783030566777 Druck-Ausgabe | Erscheint auch als: 9783030566791 Druck-AusgabeDOI: DOI: 10.1007/978-3-030-56678-4Online resources:

Summary: 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.Summary: 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.PPN: PPN: 1734642300Package identifier: Produktsigel: ZDB-2-INR | ZDB-2-SEB | ZDB-2-SXIT

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