Foundations of Average-Cost Nonhomogeneous Controlled Markov Chains
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Beschreibung
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.
Presents a comprehensive methodology for the performance optimization of time-nonhomogeneous Markov chains Introduces the concept of confluencity, showing how it is fundamental to performance optimization and state classification Tackles various long-standing issues related to time-nonhomogeneous Markov chains. Motivates new research ideas future work in Markov system optimization
Autor*in
Xi-Ren Cao
Themen in »Foundations of Average-Cost Nonhomogeneous Controlled Markov Chains«
Markov Decision Processes Blackwell Optimality Branching States Confluencity Multi-Class Optimization Nth-Bias Optimality Performance Potentials State Classification Time-Nonhomogeneous Markov Chain Markov Chains
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“The book presents a complete and interesting analysis for the optimization of TNHMCs with long-run average performance.” (Raúl Montes-de-Oca, Mathematical Reviews, March, 2022)
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