Approximate Iterative Algorithms

ISBN-13: 9780367378882 / Angielski / Miękka / 2019 / 372 str.

Anthony Louis Almudevar

Opis

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. The volume provides the necessary background in functional analysis and probability theory and presents extensive applications to Markov decision processes.

Spis treści

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.

O autorze

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.