by Dimitri P. Bertsekas
ISBN: 1-886529-42-6, 978-1-886529-42-7
Publication: April 2013, 256 pages, hardcover
Table of Contents and Preface,
A research monograph providing a synthesis of research on the foundations of dynamic programming that started nearly 50 years ago, with the modern theory of approximate dynamic programming and the new class of semicontractive models.
It aims at a unified and economical development of the core theory and algorithms of total cost sequential decision problems, based on the strong connections of the subject with fixed point theory. The analysis focuses on the abstract mapping that underlies dynamic programming and defines the mathematical character of the associated problem. The discussion centers on two fundamental properties that this mapping may have: monotonicity and (weighted sup-norm) contraction. It turns out that the nature of the analytical and algorithmic DP theory is determined primarily by the presence or absence of these two properties, and the rest of the problem's structure is largely inconsequential. New research is focused on two areas: 1) The ramifications of these properties in the context of algorithms for approximate dynamic programming, and 2) The new class of semicontractive models, exemplified by stochastic shortest path problems, where some but not all policies are contractive.
The book is an excellent supplement to several of our books: Dynamic Programming and Optimal Control (Athena Scientific, 2012), and Neuro-Dynamic Programming (Athena Scientific, 1996).
Among its features, the book:
develops the algorithmic foundations of approximate dynamic programming within an abstract unifying framework
discusses algorithms for approximate dynamic programming within a broadly applicable setting
develops the connections of dynamic programming with fixed point theory
contains significant new research
Dimitri P. Bertsekas is McAfee Professor of Engineering at the Massachusetts Institute of Technology and a member of the prestigious United States National Academy of Engineering. He is the recipient of the 2001 A. R. Raggazini ACC education award and the 2009 INFORMS expository writing award.
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