Abstract Dynamic Programming
by Dimitri P.
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:
The ramifications of these properties in the context of algorithms for approximate dynamic programming.
The new class of semicontractive models, exemplified by stochastic shortest path problems, where some but not all policies are contractive.
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:
D. P. Bertsekas, "Regular Policies in Abstract Dynamic Programming", Lab. for Information and Decision
Systems Report LIDS-P-3173, MIT, May 2015 (revised August, 2016) (Related Lecture Slides); (Related Video Lectures).
D. P. Bertsekas, "Value and Policy Iteration in Deterministic Optimal Control and Adaptive Dynamic Programming", Lab. for Information and Decision
Systems Report LIDS-P-3174, MIT, May 2015 (revised Sept. 2015); to appear in IEEE Transactions on Neural Networks and Learning Systems.
D. P. Bertsekas and H. Yu, "Stochastic Shortest Path Problems Under Weak Conditions", Lab. for Information and Decision
Systems Report LIDS-P-2909, MIT, January 2016; to appear in Math. of OR.
D. P. Bertsekas, "Robust Shortest Path Planning and Semicontractive Dynamic Programming", Lab. for Information and Decision
Systems Report LIDS-P-2915, MIT, Jan. 2016; revised in June 2016; to appear in Naval Research Logistics.
D. P. Bertsekas, "Affine Monotonic and Risk-Sensitive Models in Dynamic Programming", Lab. for Information and Decision
Systems Report LIDS-3204, MIT, June 2016.
D. P. Bertsekas, "Stable Optimal Control and Semicontractive Dynamic Programming", Lab. for Information and Decision
Systems Report LIDS-3506, MIT, May 2017.
An updated version of Chapter 4 and a new Appendix B, of the author's Dynamic Programming book, Vol. II, which incorporate recent research on a variety of undiscounted problems and abstract DP topics;
(Related Lecture Slides).
UPDATED CHAPTERS 3 AND 4
Drafts of the two updated chapters of the Abstract Dynamic Programming monograph, which incorporate the most recent research, are posted here: Chapter 3 and Chapter 4.
They will be updated periodically.