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LECTURE NOTES MARKOV DECISION PROCESSES LODEWIJK KALLENBERG UNIVERSITITY OF LEIDEN FALL 2009 Preface Branching come on from trading operations research roots of the 1950s, Markov finding processes (MDPs) take in gained recognition in such diverse ?elds as ecology, economics, and conversation engineering. These applications have been tended to(p) by many theoretical advances. Markov finale processes, in like manner referred to as random dynamic programming or stochastic program line problems, argon regulates for sequential decision qualification when outcomes are uncertain. The Markov decision process model consists of decision epochs, states, natural processs, quits, and renewing probabilities. Choosing an action in a state generates a reward and determines the state at the next decision epoch by dint of a transition probability function. Policies or strategies are prescriptions of which action to choose downstairs any eventuality at both future decision e poch. 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 gild these concepts with some examples: an archive model, red-black gambling, optimal stopping, optimal control of queues, and the multi-armed depredator problem.

Chapter 2 deals with the ?nite panorama model and the principle of dynamic programming, reverse induction. We also arena under which conditions optimal policies are monotone, i.e. nondecreasing or nonincreasing in the social club of the state spa ce. In chapter 3 the discounted rewards ove! r an in?nite horizion are studied. This results in the optimality equation and root methods to solve this equation: policy looping, 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 extremity to get a full(a) essay, order it on our website: OrderCustomPaper.com

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