By Warren B. Powell

Praise for the First Edition

"Finally, a e-book dedicated to dynamic programming and written utilizing the language of operations study (OR)! this gorgeous publication fills a spot within the libraries of OR experts and practitioners."
Computing Reviews

This new version showcases a spotlight on modeling and computation for complicated sessions of approximate dynamic programming problems

Understanding approximate dynamic programming (ADP) is essential in an effort to improve useful and high quality suggestions to complicated business difficulties, relatively whilst these difficulties contain making judgements within the presence of uncertainty. Approximate Dynamic Programming, moment version uniquely integrates 4 certain disciplines—Markov selection procedures, mathematical programming, simulation, and statistics—to reveal find out how to effectively process, version, and remedy quite a lot of real-life difficulties utilizing ADP.

The booklet keeps to bridge the distance among laptop technology, simulation, and operations examine and now adopts the notation and vocabulary of reinforcement studying in addition to stochastic seek and simulation optimization. the writer outlines the fundamental algorithms that function a place to begin within the layout of functional ideas for actual difficulties. the 3 curses of dimensionality that effect complicated difficulties are brought and specified assurance of implementation demanding situations is supplied. The Second Edition additionally features:

  • A new bankruptcy describing 4 primary periods of rules for operating with assorted stochastic optimization difficulties: myopic regulations, look-ahead guidelines, coverage functionality approximations, and regulations in keeping with worth functionality approximations

  • A new bankruptcy on coverage seek that brings jointly stochastic seek and simulation optimization suggestions and introduces a brand new classification of optimum studying strategies

  • Updated assurance of the exploration exploitation challenge in ADP, now together with a lately built strategy for doing energetic studying within the presence of a actual country, utilizing the concept that of the data gradient

  • A new series of chapters describing statistical equipment for approximating worth capabilities, estimating the price of a hard and fast coverage, and cost functionality approximation whereas looking for optimum policies

The provided insurance of ADP emphasizes types and algorithms, concentrating on comparable functions and computation whereas additionally discussing the theoretical part of the subject that explores proofs of convergence and expense of convergence. A similar web site good points an ongoing dialogue of the evolving fields of approximation dynamic programming and reinforcement studying, in addition to extra readings, software program, and datasets.

Requiring just a uncomplicated figuring out of facts and likelihood, Approximate Dynamic Programming, moment variation is a superb ebook for business engineering and operations learn classes on the upper-undergraduate and graduate degrees. It additionally serves as a worthy reference for researchers and execs who make the most of dynamic programming, stochastic programming, and keep an eye on conception to resolve difficulties of their daily work.

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Extra info for Approximate Dynamic Programming: Solving the Curses of Dimensionality, 2nd Edition (Wiley Series in Probability and Statistics)

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One hundred eighty 6. eight. 1 a few probabilistic preliminaries . . . . . . . . . . . . . . . . . . . . . 181 6. eight. 2 An older evidence 6. eight. three A extra smooth facts . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 6. eight. four facts of theorem 6. five. 1 . . . . . . . . . . . . . . . . . . . . . . . . . . a hundred ninety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 Bibliographic notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 6. nine. 1 Stochastic approximation literature . . . . . . . . . . . . . . . . . . . 193 6. nine. 2 Stepsizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 7 Discrete, finite horizon difficulties 198 7. 1 functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 7. 2 pattern types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 hundred 7. three 7. four 7. 2. 1 The shortest course challenge . . . . . . . . . . . . . . . . . . . . . . . . 2 hundred 7. 2. 2 Getting via university . . . . . . . . . . . . . . . . . . . . . . . . . . 204 7. 2. three The taxi challenge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 7. 2. four promoting an asset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 innovations for finite horizon difficulties . . . . . . . . . . . . . . . . . . . . . . 208 7. three. 1 price new release utilizing a post-decision country variable . . . . . . . . . . . 208 7. three. 2 worth new release utilizing a pre-decision country variable . . . . . . . . . . . 210 7. three. three Q-learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 Temporal distinction studying . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 7. four. 1 the fundamental notion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 7. four. 2 adaptations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 7. five Monte Carlo price and coverage new release . . . . . . . . . . . . . . . . . . . . . 218 7. 6 coverage new release . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 7. 7 nation sampling thoughts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 7. 7. 1 Sampling all states . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 7. 7. 2 Tree seek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 7. 7. three Rollout heuristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 CONTENTS vi 7. eight A taxonomy of approximate dynamic programming ideas . . . . . . . . 225 7. nine yet does it paintings? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 7. nine. 1 Convergence of temporal distinction studying . . . . . . . . . . . . . . 227 7. nine. 2 Convergence of Q-learning . . . . . . . . . . . . . . . . . . . . . . . . 227 7. 10 Why does it work** . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 7. eleven Bibliographic notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 eight endless horizon difficulties 230 eight. 1 Approximate dynamic programming for countless horizon difficulties . . . . . . 231 eight. 2 Algorithmic recommendations for discrete worth features . . . . . . . . . . . . . . . 231 eight. three price generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 eight. four Approximate coverage new release . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 eight. five TD studying with discrete price features . . . . . . . . . . . . . . . . . . . . 235 eight. 6 Q-learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 eight. 7 Why does it paintings? ** . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 eight. eight Bibliographic notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 nine price functionality approximations 240 nine. 1 easy aggregation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 nine. 2 The case of biased estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 nine. three a number of degrees of aggregation . . . . . . . . . . . . . . . . . . . . . . . . . . 249 nine. four nine. five nine. three. 1 Combining a number of records . . . . . . . . . . . . . . . . . . . . . . 250 nine. three. 2 the matter of correlated information . . . . . . . . . . . . . . . . . . .

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