Stochastic Recursive Algorithms for Optimization

1. Front Matter

   Pages 1-15

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2. Introduction to Stochastic Recursive Algorithms

   1. Front Matter

      Pages 1-2

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   2. Introduction

      • S. Bhatnagar, H. Prasad, L. Prashanth

      Pages 3-12

   3. Deterministic Algorithms for Local Search

      • S. Bhatnagar, H. Prasad, L. Prashanth

      Pages 13-15

   4. Stochastic Approximation Algorithms

      • S. Bhatnagar, H. Prasad, L. Prashanth

      Pages 17-28

3. Gradient Estimation Schemes

   1. Front Matter

      Pages 29-30

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   2. Kiefer-Wolfowitz Algorithm

      • S. Bhatnagar, H. Prasad, L. Prashanth

      Pages 31-39

   3. Gradient Schemes with Simultaneous Perturbation Stochastic Approximation

      • S. Bhatnagar, H. Prasad, L. Prashanth

      Pages 41-76

   4. Smoothed Functional Gradient Schemes

      • S. Bhatnagar, H. Prasad, L. Prashanth

      Pages 77-102

4. Hessian Estimation Schemes

   1. Front Matter

      Pages 103-104

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   2. Newton-Based Simultaneous Perturbation Stochastic Approximation

      • S. Bhatnagar, H. Prasad, L. Prashanth

      Pages 105-131

   3. Newton-Based Smoothed Functional Algorithms

      • S. Bhatnagar, H. Prasad, L. Prashanth

      Pages 133-148

5. Variations to the Basic Scheme

   1. Front Matter

      Pages 149-150

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   2. Discrete Parameter Optimization

      • S. Bhatnagar, H. Prasad, L. Prashanth

      Pages 151-166

   3. Algorithms for Constrained Optimization

      • S. Bhatnagar, H. Prasad, L. Prashanth

      Pages 167-186

   4. Reinforcement Learning

      • S. Bhatnagar, H. Prasad, L. Prashanth

      Pages 187-220

6. Applications

   1. Front Matter

      Pages 221-223

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   2. Service Systems

      • S. Bhatnagar, H. Prasad, L. Prashanth

      Pages 225-241

   3. Road Traffic Control

      • S. Bhatnagar, H. Prasad, L. Prashanth

      Pages 243-255

   4. Communication Networks

      • S. Bhatnagar, H. Prasad, L. Prashanth

      Pages 257-280

Stochastic Recursive Algorithms for Optimization presents algorithms for constrained and unconstrained optimization and for reinforcement learning. Efficient perturbation approaches form a thread unifying all the algorithms considered. Simultaneous perturbation stochastic approximation and smooth fractional estimators for gradient- and Hessian-based methods are presented. These algorithms:
• are easily implemented;
• do not require an explicit system model; and
• work with real or simulated data.
Chapters on their application in service systems, vehicular traffic control and communications networks illustrate this point. The book is self-contained with necessary mathematical results placed in an appendix.
The text provides easy-to-use, off-the-shelf algorithms that are given detailed mathematical treatment so the material presented will be of significant interest to practitioners, academic researchers and graduate students alike. The breadth of applications makes the book appropriate for reader from similarly diverse backgrounds: workers in relevant areas of computer science, control engineering, management science, applied mathematics, industrial engineering and operations research will find the content of value.

• Gradient Estimation
• Hessian Estimation
• Optimization Techniques
• Simultaneous Perturbation Methods
• Stochastic Algorithms

From the reviews:

“The book under review summarizes the recent research on simultaneously perturbation problems. … The book provides a coverage of the known material in stochastic optimizations, such that both researchers and practitioners should find it useful. The text is well understandable, the book is clearly written and impressively printed. Theorems and algorithms are emphasized in coloured frames. Therefore, the book can be used as material for lectures dedicated to master students. … There are references at the end of every chapter.” (Werner H. Schmidt, Zentralblatt MATH, Vol. 1260, 2013)

• , Department of Computer Science, Indian Institute of Science, Bangalore, India

  S. Bhatnagar, H.L. Prasad, L.A. Prashanth

All three authors have been extensively working in the area of stochastic control and optimization. S. Bhatnagar has worked for nearly 20 years in this area and has published extensively in both journals and conferences. This book in many ways summarizes the various strands of research that S.Bhatnagar has been involved in over the last decade. H.L.Prasad and Prashanth L.A. have been working in this area for over five years now and have been actively involved in various aspects of the research reported here. The entire book, in many ways, is a collection of the various strands of the research that has been primarily carried out by the authors themselves during the course of the last several years.

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