Approximate Iterative Algorithms

Name: Approximate Iterative Algorithms
Brand: Taylor & Francis Ltd
Price: 211.75 AUD
Availability: BackOrder

By: Anthony Louis Almudevar

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Hardcover | 18 February 2014 | Edition Number 1

At a Glance

Hardcover
372 Pages

Dimensions(cm)
24.6 x 17.4 x 2.54

Hardcover

RRP $242.00

$211.75

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Algorithms are usually classified based on their convergence order - linear, quadratic, etc - and their convergence rate, defined as a bound as the number of iterates goes to infinity. The rate is calculated with respect to the number of steps (iterates) an algorithm takes to converge, with no thought on how much effort is applied at each iterate.
This volume demonstrates that the use of partial information, refined at each new iteration of the algorithm, can increase the efficiency of the algorithm, while guaranteeing convergence to the optimal solution, provided that the rate of refinement is carefully chosen. Based on approximate algorithms for problem solving, the authors present a new theory, which serves as a general framework for the problem, and consider general and particularly Markov Decision processes. A more suitable definition of the convergence rate with respect to the computational effort is derived for the proposed class of approximate iterative algorithms. In addition, an optimal refinement strategy is derived, which maximizes the rate of convergence with respect to the computation effort of this class of algorithms. Hence, a class of algorithms is derived that makes optimal use of the computational resources available. With a given, fixed amount of computation time, the proposed class of algorithms gets closer to the solution than any other algorithm, including the classical (exact) algorithm. Many numerical examples are included for illustration.
This volume is intended for mathematicians, engineers and computer scientists, who work on learning processes in numerical analysis and are involved with optimization, optimal control, decision analysis and machine learning.

Industry Reviews

"This is an excellent book on dynamic programming and Markov decision processes. Dynamic programming, invented by the late Richard Bellman, has created a new field of optimality and approximation theory. The author has divided his book into three parts: I: Mathematical background with 8 chapters, II: General theory of approximate iterative algorithms with 3 chapters, and III: Application to Markov decision processes with 6 chapters. [...] The author has elaborated the theory in the application to online parameter estimation and exploration schedule." Nirode C. Mohanty (Huntington Beach), Zentralblatt MATH 1297-1 "Many real-life processes and program optimization tasks require approximations for their analysis and execution, as well asbeing recursive and requiring multiple iterations to achieve workable approximations. This rather dense and mathematically beautiful text provides the nexcessary background for the construction and development of algorithms to handle such tasks. [...] Thorough and mathematically rigorous throughout, the book will be useful to both pure mathematicians and programmers working in diverse fields from error analysis to machine learning." 2014 Ringgold, Inc., Portland, OR, USA

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