Approximate Iterative Algorithms

by Anthony Louis Almudevar

Overview

Iterative algorithms often rely on approximate evaluation techniques, which may include statistical estimation, computer simulation or functional approximation. This volume presents methods for the study of approximate iterative algorithms, providing tools for the derivation of error bounds and convergence rates, and for the optimal design of such algorithms. Techniques of functional analysis are used to derive analytical relationships between approximation methods and convergence properties for general classes of algorithms. This work provides the necessary background in functional analysis and probability theory. Extensive applications to Markov decision processes are presented.

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.

Product Details

ISBN-13:	9780367378882
Publisher:	CRC Press
Publication date:	10/10/2019
Pages:	372
Product dimensions:	6.88(w) x 9.69(h) x (d)

About the Author

Dr. Almudevar was born in Halifax and raised in Ontario, Canada. He completed a PhD in Statistics at the University of Toronto, and is currently a faculty member in the Department of Biostatistics and Computational Biology at the University of Rochester. He has a wide range of interests, which include biological network modeling, analysis of genetic data, immunological modeling and clinical applications of technological home monitoring. He has a more general interest in optimization and control theory, with an emphasis on the computational issues associated with Markov decision processes.

Table of Contents

1. Introduction. PART I Mathematical background: 2. Real analysis and linear algebra 3. Background – measure theory 4. Background – probability theory 5. Background – stochastic processes 6. Functional analysis 7. Fixed point equations 8. The distribution of a maximum. PART II General theory of approximate iterative algorithms: 9. Background – linear convergence 10. A general theory of approximate iterative algorithms (AIA) 11. Selection of approximation schedules for coarse-to-fine AIAs. PART III Application to Markov decision processes: 12. Markov decision processes (MDP) – background 13. Markov decision processes – value iteration 14. Model approximation in dynamic programming – general theory 15. Sampling based approximation methods 16. Approximate value iteration by truncation 17. Grid approximations of MDPs with continuous state/action spaces 18. Adaptive control of MDPs.

Editorial 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

From the Publisher