Learning automata and stochastic optimization
This book is a meager contribution to the field of learning automata and stochastic optimization in spite of the excessive number of theorems and lemmas contained in it. The book consists of five chapters, each chapter with its own references. The authors duplicate their previously published work with little new insight while repeatedly citing themselves throughout. The authors seem to selectively ignore previous work. For instance, the use of Robbins and Siegmund martingale theorem to prove convergence, which is heavily used throughout the book, was pioneered by \textit{Y. M. El-Fattah} and \textit{C. Foulard} [Learning systems: Decision, simulation, and control. Lect. Notes Control Inf. Sci. 9 (1978; Zbl 0415.68050)]. The normalization procedure claimed by the authors was also used by \textit{Y. M. El-Fattah} [Adv. Appl. Probab. 13, 778-803 (1981; Zbl 0475.60051)] in the context of Markov chains and learning automata. The authors claim to show in Chapter 1 how learning automata can be used to solve efficiently various stochastic optimization problems. The chapter, and the book as a whole, however offers no precise statement of what is meant by efficiency and how learning automata compare to alternative methods with respect to efficiency. The other chapters of the book are entitled: on learning automata, unconstrained optimization problems, constrained optimization problems, and optimization of nonstationary functions. Contrary to the authors' opinions, the book does not offer guidance to the systematic use of learning automata concepts in stochastic optimization problems; rather, it is misleading to readers who are new to this area of research. However, the book may offer some value to theorists and researchers actively involved in the learning automata area.
scientific article; zbMATH DE number 1010944
scientific article