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LECTURE NOTES MARKOV DECISION PROCESSES LODEWIJK KALLENBERG UNIVERSITITY OF LEIDEN FALL 2009 Preface Branching pop out from trading operations research roots of the 1950s, Markov finding processes (MDPs) learn gained recognition in such diverse ?elds as ecology, economics, and dialogue engineering. These applications have been tended to(p) by many theoretical advances. Markov finale processes, all overly referred to as random dynamic programming or stochastic program line problems, atomic number 18 role models for sequential decision make when outcomes are uncertain. The Markov decision process model consists of decision epochs, states, accomplishs, recompenses, and diversity probabilities. Choosing an action in a state generates a reward and determines the state at the next decision epoch through and through a transition probability function. Policies or strategies are prescriptions of which action to choose downstairs any eventuality at both future decis ion epoch. Decision makers seek policies which are optimal in many sense. Chapter 1 introduces the Markov decision process model as a sequential decision model with actions, rewards, transitions and policies. We adorn these concepts with some examples: an archive model, red-black gambling, optimal stopping, optimal control of queues, and the multi-armed freebooter problem. Chapter 2 deals with the ?nite panorama model and the principle of dynamic programming, half-witted induction. We also arena under which conditions optimal policies are monotone, i.e. nondecreasing or nonincreasing in the social club of the state space. In chapter 3 the discounted rewards over an in?nite horizion are studied. This results in the optimality equation and upshot methods to solve this equation: policy loop, linear programming, value iteration and modi?ed value iteration. Chapter 4 discusses the criterion of average rewards over an in?nite horizion, in the some general case. Firstly, polyn omial algorithms are developed to classify M! DPs as irreducible or communicating. The...If you regard to get a full(a) essay, order it on our website: OrderCustomPaper.com

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