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Stochastic Approximation: A Dynamical Systems Viewpoint

Vivek S. Borkar (Autor)

Buch | Softcover

268 Seiten

2024 | 2nd ed. 2024
Springer Verlag, Singapore
978-981-99-8273-8 (ISBN)

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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.

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.

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.

Erscheint lt. Verlag	22.1.2024
Reihe/Serie	Texts and Readings in Mathematics
Zusatzinfo	XII, 268 p.
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
	Wirtschaft ► Betriebswirtschaft / Management
Schlagworte	Adaptive Algorithms • Artificial Intelligence • Control Theory • dynamical systems view of algorithms • Game Theory • Learning Algorithms • ODE approach to stochastic approximation • Probability Theory • sequential statistical methods • stochastic approximation
ISBN-10	981-99-8273-1 / 9819982731
ISBN-13	978-981-99-8273-8 / 9789819982738
Zustand	Neuware