Stochastic Approximation: A Dynamical Systems Viewpoint

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.

List of contents

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.               

Product details

• Authors: Vivek S Borkar, Vivek S. Borkar
• Publisher: Springer, Berlin
• Original title: Stochastic Approximation. A Dynamical Systems Viewpoint
• Languages: English
• Product format: Paperback / Softback
• Released: 01.02.2025
• EAN: 9789819982790
• ISBN: 978-981-9982-79-0
• No. of pages: 273
• Dimensions: 155 mm x 13 mm x 235 mm
• Weight: 500 g
• Illustrations: XV, 273 p. 2 illus.
• Series: Texts and Readings in Mathematics
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics