By Martin L. Puterman
An up to date, unified and rigorous therapy of theoretical, computational and utilized study on Markov choice procedure types. Concentrates on infinite-horizon discrete-time types. Discusses arbitrary kingdom areas, finite-horizon and continuous-time discrete-state types. additionally covers transformed coverage new release, multichain versions with regular gift criterion and delicate optimality. contains a wealth of figures which illustrate examples and an in depth bibliography.
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Extra resources for Markov decision processes: discrete stochastic dynamic programming
1 MODEL FORMULAHON The Role of Model Assumptions The model in Sec. 2 provides a focus for discussing the role of assumptions about S and A,. Suppose first that S is a Borel measurable subset of Euclidean space. rr = ( d , ) E IIMDand suppose d,(s) = a. 1) becomes if the density p,(uls, a) exists. 1) may be represented by the Lebesgue-Stieltjes integral v(u)p,(duls,a). For the above expressions to be meaningful requires that u ( . ) p , ( * ( sa, ) be Lebesgue integrable, or u ( * ) be Lebesgue-Stieljes integrable with respect to p,(du(s,a ) for each s E S and a E A,.
The primary focus of this book will be models with discrete T . A particular continuous time model (a semi-Markov decision process) will be discussed (Chapter 11). 2 State and Action Sets At each decision epoch, the system occupies a sfate. If, at some decision epoch, the decision maker observes the system in state s E S, he may choose action a from the set of allowable actions in state s, A,. Let A = U S E ,A, (Fig. ) Note we assume that S and A, do not vary with t . We expand on this point below.
Upon substitution’of d,, it becomes ss For analyzing multi-period models we require this to be a measurable and integrable function on S. This necessitates imposing assumptions on rl(s, . ), p,(uls, ), and d,( 1. At a minimum we require d,(s) to be a measurable function from S to A , which means that we must restrict the set of admissible decision rules to include only measurable functions. To identify measurable functions requires a topology on A. In Sec. 4). For discrete S, d* E D,,since D,consisted of the set of all functions from S to A , but, as discussed above, we require that d* be measurable.