New PDF release: Optimized Bayesian Dynamic Advising: Theory and Algorithms

By Miroslav Karny

ISBN-10: 1846282543

ISBN-13: 9781846282546

ISBN-10: 1852339284

ISBN-13: 9781852339289

A cutting-edge study monograph delivering constant therapy of supervisory keep an eye on, through one of many world’s major teams within the region of Bayesian id, regulate, and determination making. An accompanying CD illustrates the book’s underlying idea.

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Extra info for Optimized Bayesian Dynamic Advising: Theory and Algorithms (Advanced Information and Knowledge Processing)

Example text

9 (Bellman function; loss-to-go) The function V(·) occurring in dynamic programming is called the Bellman function. 24) is also called the optimal loss-to-go. 2 Fully probabilistic design A specific design that expresses losses fully in probabilistic terms is formulated and solved here. It is systematically used in the body of the text. Moreover, it is believed to form a bridge between optimal and practically optimal designs. The notion of the Kullback–Leibler divergence [37] that measures well proximity of a pair of pdfs is widely used.

4 (Dominated rules; strictly isotonic expectation) Let a loss function Z measure the quality of the behavior. The decision rule R : Q∗ → a∗ is called dominated iff (if and only if) there is another de˜ : Q∗ → a∗ such that cision rule R ZR (Υ ) ≥ ZR˜ (Υ ) ⇔ Z(QR , Υ ) ≥ Z(QR˜ , Υ ), ∀Υ ∈ Υ ∗ . 3) is strict. 2) is said to be strictly isotonic if for a decision ˜ it holds rule R, strictly dominated by a decision rule R, E˜R [ZR ] > E˜R˜ [ZR˜ ]. We take the dominated decision rules as those to be surely avoided.

16) min ∗ {Rt : Pa∗∗ →a∗ t} t t<˚ t E ∗ min E[V(Pa˚∗ )|a˚ t , Pa˚ ] . 18). The following step becomes min ∗ {Rt : Pa∗∗ →a∗ t} t t<˚ t E V(Pa˚∗ ) . 4 Dynamic design 27 We face the identical situation as above with the horizon decreased by one. Thus, the procedure can be repeated until the initial optimal rule oR1 is constructed. The optimization relies on our ability to evaluate the expectations E[V(Pa∗t+1 )|at , Pa∗t ] = V(Pa∗t , at , ∆t )f (∆t |at , Pa∗t ) d∆t , ∀t ∈ t∗ . The introduced innovation ∆t contains those observable quantities that can be used for the choice at+1 but not for the choice of at .

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Optimized Bayesian Dynamic Advising: Theory and Algorithms (Advanced Information and Knowledge Processing) by Miroslav Karny


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