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Click here to download lecture slides for the MIT course "Dynamic Programming and Stochastic Control (6.231), Dec. 2015. The last six lectures cover a lot of the approximate dynamic programming material. Click here to download research papers and other material on Dynamic Programming and Approximate Dynamic Programming. Abstract Dynamic Programming, 3rd Edition, 2022 by Dimitri P. Bertsekas The 3rd edition of the book is available as an Ebook from Google Books.The print version of the 3rd edition of the book is available from the publishing company, Athena Scientific. This research monograph provides a synthesis of old research on the foundations of dynamic programming (DP), with the modern theory of approximate DP and new research on 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 DP 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 DP, and 2) The new class of semicontractive models, exemplified by stochastic shortest path problems, where some but not all policies are contractive.
The 3rd edition is very similar to the 2nd edition, except for the addition of a new 40-page Chapter 5, which introduces a contractive abstract DP framework and related policy iteration algorithms, specifically designed for sequential zero-sum games and minimax problems with a general structure, and based on a recent paper by the author. Aside from greater generality, the advantage of our algorithms over alternatives is that they resolve some long-standing convergence difficulties of the natural PI algorithm, which have been known since the Pollatschek and Avi-Itzhak method for finite-state Markov games. Mathematically, this natural algorithm is a form of Newton's method for solving Bellman's equation, but Newton's method, contrary to the case of single-player DP problems, is not globally convergent in the case of a minimax problem, because of an additional difficulty: the Bellman operator may have components that are neither convex nor concave.The algorithms address this difficulty by introducing alternating player choices, and by using a policy-dependent mapping with a uniform sup-norm contraction property, similar to earlier works by Bertsekas and Yu, which is described in part in Chapter 2. Moreover, our algorithms allow a convergent and highly parallelizable implementation, which is based on state space partitioning, and distributed asynchronous policy evaluation and policy improvement operations within each set of the partition. They are also suitable for approximations based on an aggregation approach. The book can be downloaded and used freely for noncommercial purposes:Abstract Dynamic Programming, 3RD EDITION, Complete 2b1af7f3a8