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Stochastic approximation = a dynamical systems viewpoint /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Stochastic approximation/ by Vivek S. Borkar.
其他題名:	a dynamical systems viewpoint /
作者:	Borkar, Vivek S.
出版者:	Singapore :Springer Nature Singapore : : 2023.,
面頁冊數:	xv, 273 p. :ill., digital ;24 cm.
內容註:	1. Introduction -- 2. Convergence Analysis -- 3. Finite Time Bounds and Traps -- 4. Stability Criteria -- 5. Stochastic Recursive Inclusions -- 6. Asynchronous Schemes -- 7. A Limit Theorem for Fluctuations -- 8. Multiple Timescales -- 9. Constant Stepsize Algorithms -- 10. General Noise Models -- 11. Stochastic Gradient Schemes -- 12. Liapunov and Related Systems -- 13. Appendix A: Topics in Analysis -- 14. Appendix B: Ordinary Differential Equations -- 15. Appendix C: Topics in Probability -- Bibliography -- Index.
Contained By:	Springer Nature eBook
標題:	Stochastic approximation. -
電子資源:	https://doi.org/10.1007/978-981-99-8277-6
ISBN:	9789819982776

Stochastic approximation = a dynamical systems viewpoint /
Borkar, Vivek S.

Stochastic approximationa dynamical systems viewpoint /[electronic resource] :by Vivek S. Borkar. - Second edition. - Singapore :Springer Nature Singapore :2023. - xv, 273 p. :ill., digital ;24 cm. - Texts and readings in mathematics,v. 482366-8725 ;. - Texts and readings in mathematics ;v. 48..

1. Introduction -- 2. Convergence Analysis -- 3. Finite Time Bounds and Traps -- 4. Stability Criteria -- 5. Stochastic Recursive Inclusions -- 6. Asynchronous Schemes -- 7. A Limit Theorem for Fluctuations -- 8. Multiple Timescales -- 9. Constant Stepsize Algorithms -- 10. General Noise Models -- 11. Stochastic Gradient Schemes -- 12. Liapunov and Related Systems -- 13. Appendix A: Topics in Analysis -- 14. Appendix B: Ordinary Differential Equations -- 15. Appendix C: Topics in Probability -- Bibliography -- Index.

This book serves as an advanced text for a graduate course on stochastic algorithms for the students of probability and statistics, engineering, economics and machine learning. This second edition gives a comprehensive treatment of stochastic approximation algorithms based on the ordinary differential equation (ODE) approach which analyses the algorithm in terms of a limiting ODE. It has a streamlined treatment of the classical convergence analysis and includes several recent developments such as concentration bounds, avoidance of traps, stability tests, distributed and asynchronous schemes, multiple time scales, general noise models, etc., and a category-wise exposition of many important applications. It is also a useful reference for researchers and practitioners in the field.

ISBN: 9789819982776

Standard No.: 10.1007/978-981-99-8277-6doiSubjects--Topical Terms:

699701
Stochastic approximation.

LC Class. No.: QA274.2

Dewey Class. No.: 519.2

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505 0 $a 1. Introduction -- 2. Convergence Analysis -- 3. Finite Time Bounds and Traps -- 4. Stability Criteria -- 5. Stochastic Recursive Inclusions -- 6. Asynchronous Schemes -- 7. A Limit Theorem for Fluctuations -- 8. Multiple Timescales -- 9. Constant Stepsize Algorithms -- 10. General Noise Models -- 11. Stochastic Gradient Schemes -- 12. Liapunov and Related Systems -- 13. Appendix A: Topics in Analysis -- 14. Appendix B: Ordinary Differential Equations -- 15. Appendix C: Topics in Probability -- Bibliography -- Index.
520 $a This book serves as an advanced text for a graduate course on stochastic algorithms for the students of probability and statistics, engineering, economics and machine learning. This second edition gives a comprehensive treatment of stochastic approximation algorithms based on the ordinary differential equation (ODE) approach which analyses the algorithm in terms of a limiting ODE. It has a streamlined treatment of the classical convergence analysis and includes several recent developments such as concentration bounds, avoidance of traps, stability tests, distributed and asynchronous schemes, multiple time scales, general noise models, etc., and a category-wise exposition of many important applications. It is also a useful reference for researchers and practitioners in the field.
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