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Look Inside Stochastic Approximation

Stochastic Approximation
A Dynamical Systems Viewpoint


  • Author: Vivek S. Borkar, Tata Institute of Fundamental Research, Mumbai, India
  • Date Published: September 2008
  • availability: Available
  • format: Hardback
  • isbn: 9780521515924

£ 57.99

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About the Authors
  • This simple, compact toolkit for designing and analyzing stochastic approximation algorithms requires only basic literacy in probability and differential equations. Yet these algorithms have powerful applications in control and communications engineering, artificial intelligence and economic modelling. The dynamical systems viewpoint treats an algorithm as a noisy discretization of a limiting differential equation and argues that, under reasonable hypotheses, it tracks the asymptotic behaviour of the differential equation with probability one. The differential equation, which can usually be obtained by inspection, is easier to analyze. Novel topics include finite-time behaviour, multiple timescales and asynchronous implementation. There is a useful taxonomy of applications, with concrete examples from engineering and economics. Notably it covers variants of stochastic gradient-based optimization schemes, fixed-point solvers, which are commonplace in learning algorithms for approximate dynamic programming, and some models of collective behaviour. Three appendices give background on differential equations and probability.

    • Simple, compact, cohesive
    • Motivated by modern applications and implementation
    • Discussion of current topics: finite-time behaviour, multiple timescales, asynchronous implementation
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    Reviews & endorsements

    '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

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    Product details

    • Date Published: September 2008
    • format: Hardback
    • isbn: 9780521515924
    • length: 176 pages
    • copublisher: Hindustan Book Agency
    • dimensions: 233 x 157 x 17 mm
    • weight: 0.38kg
    • availability: Available
  • Table of Contents

    1. Introduction
    2. 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

  • Author

    Vivek S. Borkar, Tata Institute of Fundamental Research, Mumbai, India
    Vivek S. Borkar is dean of the School of Technology and Computer Science at the Tata Institute of Fundamental Research. A distinguished researcher in stochastic and adaptive control, he distils his deep knowledge and broad experience in this motivating book.

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