The research monograph "Abstract Dynamic Programming," published in 2013, may be ordered in hardcover from the publishing company, Athena Scientific, or from Amazon.com.
The research monograph provides 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:
Click here to visit the book's web site at Athena Scientific for contents, preface, Chapter 1, slides, videos, and other instructional material, or to order the book directly from the publisher for faster service.
The following documents have a strong connection to the book, and amplify on the analysis and the range of applications of the semicontractive models of Chapters 3 and 4:
The 2nd edition of the research monograph "Abstract Dynamic Programming," may be downloaded from here. The print version will become available from the publishing company, Athena Scientific, in early 2018.
The 2nd edition aims primarily to amplify the presentation of the semicontractive models of Chapter 3 and Chapter 4 (see above), and to supplement it with a broad spectrum of research results that I obtained and published in journals and reports since the first edition was written (see above). As a result, the size of this material more than doubled, and the size of the book increased by nearly 40%.
Contents and Preface, 2ND EDITION
Chapter 1, 2ND EDITION, Introduction
Chapter 2, 2ND EDITION, Contractive Models
Chapter 3, 2ND EDITION, Semicontractive Models
Chapter 4, 2ND EDITION, Noncontractive Models
Appendixes and References, 2ND EDITION
In addition to the changes in Chapters 3, and 4, I have also eliminated from the second edition the material of the first edition that deals with restricted policies and Borel space models (Chapter 5 and Appendix C). These models are motivated in part by the complex measurability questions that arise in mathematically rigorous theories of stochastic optimal control involving continuous probability spaces. The restricted policies framework aims primarily to extend abstract DP ideas to Borel space models. Since this material is fully covered in Chapter 6 of the 1978 monograph by Bertsekas and Shreve, and followup research on the subject has been limited, I decided to omit Chapter 5 and Appendix C of the first edition from the second edition and just post them below.
Chapter 5 of 1st Edition
Appendix C of 1st Edition