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LECTURE NOTES MARKOV DECISION PROCESSES LODEWIJK KALLENBERG UNIVERSITITY OF LEIDEN FALL 2009 Preface Branching kayoed from trading operations research roots of the 1950s, Markov finding processes (MDPs) concur 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, also referred to as random dynamic programming or stochastic program line problems, ar mannikins for sequential decision qualification when outcomes are uncertain. The Markov decision process model consists of decision epochs, states, achieves, returns, and novelty probabilities. Choosing an action in a state generates a reward and determines the state at the next decision epoch through with(predicate) a transition probability function. Policies or strategies are prescriptions of which action to choose downstairs any eventuality at both future decision epoch. Decisi on 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 expound these concepts with some examples: an archive model, red-black gambling, optimal stopping, optimal control of queues, and the multi-armed plunderer problem.

Chapter 2 deals with the ?nite panorama model and the principle of dynamic programming, retrograde 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 firmness 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, polynomial algorithms are developed to classify MDPs as irreducible or communicating. The...If you want to get a full(a) essay, order it on our website: OrderCustomPaper.com

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