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LECTURE NOTES MARKOV DECISION PROCESSES LODEWIJK KALLENBERG UNIVERSITITY OF LEIDEN FALL 2009 Preface Branching egress from trading operations research roots of the 1950s, Markov finding processes (MDPs) postulate gained recognition in such diverse ?elds as ecology, economics, and colloquy engineering. These applications have been tended to(p) by many theoretical advances. Markov finale processes, similarly referred to as random dynamic programming or stochastic program line problems, are gravels for sequential decision devising when outcomes are uncertain. The Markov decision process model consists of decision epochs, states, body processs, give backs, and variety probabilities. Choosing an action in a state generates a reward and determines the state at the next decision epoch finished a transition probability function. Policies or strategies are prescriptions of which action to choose downstairs any eventuality at any future decision epoch. Decision mak ers seek policies which are best in many sense. Chapter 1 introduces the Markov decision process model as a sequential decision model with actions, rewards, transitions and policies. We instance these concepts with some examples: an archive model, red-black gambling, optimal stopping, optimal control of queues, and the multi-armed marauder problem.

Chapter 2 deals with the ?nite panorama model and the principle of dynamic programming, rearward 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 everyplace an in?nit! e horizion are studied. This results in the optimality equation and termination methods to solve this equation: policy grummet, 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, polynomial algorithms are developed to classify MDPs as irreducible or communicating. The...If you deficiency to get a full(a) essay, order it on our website: OrderCustomPaper.com

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