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Almudevar A. Approximate Iterative Algorithms

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Almudevar A. Approximate Iterative Algorithms
Leiden: CRC Press, 2014. - 359p.
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 analys.
Content:
Introduction.
Mathematical background.
Real analysis and linear algebra.
Background - measure theory.
Background - probability theory.
Background - stochastic processes.
Functional analysis.
Fixed point equations.
The distribution of a maximum.
General theory of approximate iterative algorithms.
Background - linear convergence.
A general theory of approximate iterative algorithms (AIA).
Selection of approximation schedules for coarse-to-fine AIAs.
Application to Markov decision processes.
Markov decision processes (MDP) - background.
Markov decision processes - value iteration.
Model approximation in dynamic programming - general theory.
Sampling based approximation methods.
Approximate value iteration by truncation.
Grid approximations of MDPs with continuous state/action spaces.
Adaptive control of MDPs.
Bibliography.
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