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Stochastic Approximation: A Dynamical Systems Viewpoint de Vivek S. Borkar

Stochastic Approximation: A Dynamical Systems Viewpoint

Autor Vivek S. Borkar
en Limba Engleză Paperback – feb 2025
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.
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Paperback (1) 49149 lei  38-44 zile
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  Springer Nature Singapore – feb 2024 67901 lei  3-5 săpt.
  Cambridge University Press – 31 aug 2008 45335 lei  6-8 săpt.

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Specificații

ISBN-13: 9789819982790
ISBN-10: 9819982790
Pagini: 292
Dimensiuni: 155 x 235 x 15 mm
Greutate: 0.5 kg
Ediția:Second Edition 2023
Editura: Springer

Cuprins

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.               

Notă biografică

Vivek Shripad Borkar is Professor at the Department of Electrical Engineering, Indian Institute of Technology (IIT) Bombay, Powai, Mumbai, India. Earlier, he held positions at the TIFR Centre for Applicable Mathematics and Indian Institute of Science in Bengaluru; Indian Institute of Science, Bengaluru; Tata Institute of Fundamental Research and Indian Institute of Technology Bombay in Mumbai. He also held visiting positions at the Massachusetts Institute of Technology (MIT), the University of Maryland at College Park, the University of California at Berkeley, and the University of Illinois at Urbana-Champaign, USA. 

Professor Borkar obtained his B.Tech. (Electrical Engineering) from the IIT Bombay in 1976, MS (Systems and Control Engineering) from Case Western Reserve University in 1977, and Ph.D. (Electrical Engineering and Computer Sciences) from the University of California, Berkeley, USA, in 1980. He is Fellow of American Mathematical Society, IEEE, and the World Academy of Sciences, and of various science and engineering academies in India. He has won several awards and honours in India and was an invited speaker at the ICM 2006 in Madrid. He has authored/co-authored six books and several archival publications. His primary research interests are in stochastic optimization and control, covering theory and algorithms.

Textul de pe ultima copertă

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.

Caracteristici

Presents a comprehensive view of the ODE-based approach for the analysis of stochastic approximation algorithms Discusses important themes on stability tests, concentration bounds, and avoidance of traps Covers very recent developments with copious pointers to related literature

Recenzii

'I highly recommend [this book] to all readers interested in the theory of recursive algorithms and its applications in practice.' Mathematical Reviews
'This simple compact toolkit for designing and analyzing stochastic approximation algorithms requires only basic literacy in probability and differential equations … Ideal for graduate students, researchers and practitioners in electrical engineering and computer science, especially those working in control, communications, signal processing and machine learning, this book is also relevant to economics, probability and statistics.' L'Enseignement Mathématique