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Turnpike phenomenon for markov decis...

Zaslavski, Alexander J.

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Turnpike phenomenon for markov decision processes

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Turnpike phenomenon for markov decision processes / by Alexander J. Zaslavski.
作者:	Zaslavski, Alexander J.
出版者:	Cham :Springer Nature Switzerland : : 2025.,
面頁冊數:	x, 133 p. :ill., digital ;24 cm.
內容註:	1. Introduction -- 2. Uniqueness and stability of optimal policies -- 3. Existence of an overtaking optimal policy -- 4. A weak turnpike property -- 5. Convex Markov decision processes -- 6. Turnpike properties for MDPs with perturbations -- 7. Controllability properties -- 8. Optimal control problems with singleton-turnpikes -- 9. Conclusions.
Contained By:	Springer Nature eBook
標題:	Markov processes. -
電子資源:	https://doi.org/10.1007/978-3-032-00854-1
ISBN:	9783032008541

Turnpike phenomenon for markov decision processes
Zaslavski, Alexander J.

Turnpike phenomenon for markov decision processes [electronic resource] /by Alexander J. Zaslavski. - Cham :Springer Nature Switzerland :2025. - x, 133 p. :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8201. - SpringerBriefs in mathematics..

1. Introduction -- 2. Uniqueness and stability of optimal policies -- 3. Existence of an overtaking optimal policy -- 4. A weak turnpike property -- 5. Convex Markov decision processes -- 6. Turnpike properties for MDPs with perturbations -- 7. Controllability properties -- 8. Optimal control problems with singleton-turnpikes -- 9. Conclusions.

This book provides a comprehensive examination of the structure of approximate optimal policies in Markov decision processes (MDPs) with finite state spaces, as well as approximate optimal solutions for deterministic discrete-time optimal control problems. At its core, the monograph delves into the turnpike property, a concept introduced by P. Samuelson, which suggests that optimal solutions are largely determined by the objective function, independent of interval length or endpoint conditions. Key concepts include the uniqueness and stability of minimizing Markov actions, the existence of overtaking optimal policies, and the asymptotic and weak turnpike properties. The authors meticulously examine these phenomena across various classes of MDPs, employing a Baire category approach to demonstrate the generic nature of these properties. The book also addresses the impact of perturbations on cost functions, ensuring the stability of turnpike properties. This monograph is an essential resource for researchers and scholars in the fields of operations research, applied mathematics, and control theory. It provides valuable insights into the intricate dynamics of MDPs and optimal control systems, making it a must-read for anyone seeking to deepen their understanding of these complex topics.

ISBN: 9783032008541

Standard No.: 10.1007/978-3-032-00854-1doiSubjects--Topical Terms:

532104
Markov processes.

LC Class. No.: QA274.7

Dewey Class. No.: 519.233

Turnpike phenomenon for markov decision processes
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505 0 $a 1. Introduction -- 2. Uniqueness and stability of optimal policies -- 3. Existence of an overtaking optimal policy -- 4. A weak turnpike property -- 5. Convex Markov decision processes -- 6. Turnpike properties for MDPs with perturbations -- 7. Controllability properties -- 8. Optimal control problems with singleton-turnpikes -- 9. Conclusions.
520 $a This book provides a comprehensive examination of the structure of approximate optimal policies in Markov decision processes (MDPs) with finite state spaces, as well as approximate optimal solutions for deterministic discrete-time optimal control problems. At its core, the monograph delves into the turnpike property, a concept introduced by P. Samuelson, which suggests that optimal solutions are largely determined by the objective function, independent of interval length or endpoint conditions. Key concepts include the uniqueness and stability of minimizing Markov actions, the existence of overtaking optimal policies, and the asymptotic and weak turnpike properties. The authors meticulously examine these phenomena across various classes of MDPs, employing a Baire category approach to demonstrate the generic nature of these properties. The book also addresses the impact of perturbations on cost functions, ensuring the stability of turnpike properties. This monograph is an essential resource for researchers and scholars in the fields of operations research, applied mathematics, and control theory. It provides valuable insights into the intricate dynamics of MDPs and optimal control systems, making it a must-read for anyone seeking to deepen their understanding of these complex topics.
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