Abstract Dynamic Programming

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9781886529427: Abstract Dynamic Programming

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.

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About the Author:

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 AACC education award, the 2009 INFORMS expository writing award, the 2014 Kachiyan Prize, the 2014 AACC Bellman Heritage Award, and the 2015 George B. Dantzig prize.

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Dimitri P. Bertsekas
Published by Athena Scientific (2013)
ISBN 10: 1886529426 ISBN 13: 9781886529427
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Dimitri P. Bertsekas
Published by Athena Scientific (2013)
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