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

Chapter 2 deals with the ?nite panorama model and the principle of dynamic programming, backwards 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 everywhere an in?! nite horizion are studied. This results in the optimality equation and beginning methods to solve this equation: policy grommet, 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 ask to get a full(a) essay, order it on our website: OrderCustomPaper.com

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