## Texts and Readings in Mathematics

Stochastic Approximation: A Dynamical Systems View Point

Vivek S. Borkar

Stochastic approximation algorithms form a cornerstone of statistical computation, signal processing and machine learning. This book provides a simple and compact approach to the dynamical systems viewpoint of stochastic approximation algorithms. This viewpoint treats the algorithm as a noisy discretization of an ordinary differential equation and uses the known qualitative behaviour of the latter in order to study the algorithm. This provides a valuable toolkit for both designing and analyzing such algorithms.

The book also covers several novel issues such as finite time behaviour, multiple time scales and asynchronous implementations. In a separate chapter, it gives a variety of potential applications, with many concrete examples arising from engineering. Three appendices give a self-contained summary of the background material needed from probability theory and differential equations. The book should interest students and researchers in probability and statistics, control engineering, communications engineering, machine learning and economic modelling.

Contents

1. Introduction2. Basic convergence analysis

3. Stability criteria

4. Lock-in probability

5. Stochastic recursive inclusions

6. Multiple timescales

7. Asynchronous schemes

8. A limit theorem for fluctuations

9. Constant stepsize algorithms

10. Applications

11. Appendices

Reference, Index.

Texts and Readings in Mathematics/ 48

2008‚ 9788185931852‚ 176 pages‚ hard cover‚ Out of Print

2008‚ 9788185931852‚ 176 pages‚ hard cover‚ Out of Print