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Finite Stage Continuous Time Markov Decision Processes With An Infinite Planning Horizon
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Book Synopsis Finite Stage Continuous Time Markov Decision Processes with an Infinite Planning Horizon by : Bruce L. Miller
Download or read book Finite Stage Continuous Time Markov Decision Processes with an Infinite Planning Horizon written by Bruce L. Miller and published by . This book was released on 1967 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: The system considered may be in one of n states at any point in time; its probability law is a Markov process that depends on the policy (control) chosen. The return to the system over a given planning horizon is the integral over that horizon of a return rate that depends on both the policy and the sample path of the process. The objective is to find a policy that maximizes the expected discounted return as the planning horizon tends to infinity. The case where the discount factor goes to zero is also considered. In all cases it is shown that there is a stationary policy that is optimal, and an algorithm is given to obtain that policy. (Author).
Book Synopsis Finite State Continuous Time Markov Decision Processes with an Infinite Planning Horizon by : Bruce L Miller
Download or read book Finite State Continuous Time Markov Decision Processes with an Infinite Planning Horizon written by Bruce L Miller and published by . This book was released on 1967 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite State Continuous Time Markov Decision Processes with a Finite Planning Horizon by : Bruce Leonard Miller
Download or read book Finite State Continuous Time Markov Decision Processes with a Finite Planning Horizon written by Bruce Leonard Miller and published by . This book was released on 1967 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: The system considered may be in one of n states at any point in time and its probability law is a Markov process which depends on the policy (control) chosen. The return to the system over a given planning horizon is the integral (over that horizon) of a return rate which depends on both the policy and the sample path of the process. The objective is to find a policy which maximizes the expected return over the given planning horizon. A necessary and sufficient condition for optimality is obtained, and a constructive proof is given that there is a piecewise constant policy which is optimal. A bound on the number of switches (points where the piecewise constant policy jumps) is obtained for the case where there are two states. (Author).
Book Synopsis Continuous-Time Markov Decision Processes by : Xianping Guo
Download or read book Continuous-Time Markov Decision Processes written by Xianping Guo and published by Springer Science & Business Media. This book was released on 2009-09-18 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuous-time Markov decision processes (MDPs), also known as controlled Markov chains, are used for modeling decision-making problems that arise in operations research (for instance, inventory, manufacturing, and queueing systems), computer science, communications engineering, control of populations (such as fisheries and epidemics), and management science, among many other fields. This volume provides a unified, systematic, self-contained presentation of recent developments on the theory and applications of continuous-time MDPs. The MDPs in this volume include most of the cases that arise in applications, because they allow unbounded transition and reward/cost rates. Much of the material appears for the first time in book form.
Book Synopsis Markov Decision Processes with Applications to Finance by : Nicole Bäuerle
Download or read book Markov Decision Processes with Applications to Finance written by Nicole Bäuerle and published by Springer Science & Business Media. This book was released on 2011-06-06 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Markov decision processes focuses on controlled Markov chains in discrete time. The authors establish the theory for general state and action spaces and at the same time show its application by means of numerous examples, mostly taken from the fields of finance and operations research. By using a structural approach many technicalities (concerning measure theory) are avoided. They cover problems with finite and infinite horizons, as well as partially observable Markov decision processes, piecewise deterministic Markov decision processes and stopping problems. The book presents Markov decision processes in action and includes various state-of-the-art applications with a particular view towards finance. It is useful for upper-level undergraduates, Master's students and researchers in both applied probability and finance, and provides exercises (without solutions).
Book Synopsis Continuous-Time Markov Decision Processes by : Alexey Piunovskiy
Download or read book Continuous-Time Markov Decision Processes written by Alexey Piunovskiy and published by Springer Nature. This book was released on 2020-11-09 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a systematic and rigorous treatment of continuous-time Markov decision processes, covering both theory and possible applications to queueing systems, epidemiology, finance, and other fields. Unlike most books on the subject, much attention is paid to problems with functional constraints and the realizability of strategies. Three major methods of investigations are presented, based on dynamic programming, linear programming, and reduction to discrete-time problems. Although the main focus is on models with total (discounted or undiscounted) cost criteria, models with average cost criteria and with impulsive controls are also discussed in depth. The book is self-contained. A separate chapter is devoted to Markov pure jump processes and the appendices collect the requisite background on real analysis and applied probability. All the statements in the main text are proved in detail. Researchers and graduate students in applied probability, operational research, statistics and engineering will find this monograph interesting, useful and valuable.
Book Synopsis Markov Decision Processes by : Martin L. Puterman
Download or read book Markov Decision Processes written by Martin L. Puterman and published by John Wiley & Sons. This book was released on 2014-08-28 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. "This text is unique in bringing together so many results hitherto found only in part in other texts and papers. . . . The text is fairly self-contained, inclusive of some basic mathematical results needed, and provides a rich diet of examples, applications, and exercises. The bibliographical material at the end of each chapter is excellent, not only from a historical perspective, but because it is valuable for researchers in acquiring a good perspective of the MDP research potential." —Zentralblatt fur Mathematik ". . . it is of great value to advanced-level students, researchers, and professional practitioners of this field to have now a complete volume (with more than 600 pages) devoted to this topic. . . . Markov Decision Processes: Discrete Stochastic Dynamic Programming represents an up-to-date, unified, and rigorous treatment of theoretical and computational aspects of discrete-time Markov decision processes." —Journal of the American Statistical Association
Book Synopsis Examples in Markov Decision Processes by : A. B. Piunovskiy
Download or read book Examples in Markov Decision Processes written by A. B. Piunovskiy and published by World Scientific. This book was released on 2013 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book provides approximately eighty examples illustrating the theory of controlled discrete-time Markov processes. Except for applications of the theory to real-life problems like stock exchange, queues, gambling, optimal search etc, the main attention is paid to counter-intuitive, unexpected properties of optimization problems. Such examples illustrate the importance of conditions imposed in the theorems on Markov Decision Processes. Many of the examples are based upon examples published earlier in journal articles or textbooks while several other examples are new. The aim was to collect them together in one reference book which should be considered as a complement to existing monographs on Markov decision processes. The book is self-contained and unified in presentation. The main theoretical statements and constructions are provided, and particular examples can be read independently of others. Examples in Markov Decision Processes is an essential source of reference for mathematicians and all those who apply the optimal control theory to practical purposes. When studying or using mathematical methods, the researcher must understand what can happen if some of the conditions imposed in rigorous theorems are not satisfied. Many examples confirming the importance of such conditions were published in different journal articles which are often difficult to find. This book brings together examples based upon such sources, along with several new ones. In addition, it indicates the areas where Markov decision processes can be used. Active researchers can refer to this book on applicability of mathematical methods and theorems. It is also suitable reading for graduate and research students where they will better understand the theory.
Book Synopsis Markov Chains and Decision Processes for Engineers and Managers by : Theodore J. Sheskin
Download or read book Markov Chains and Decision Processes for Engineers and Managers written by Theodore J. Sheskin and published by CRC Press. This book was released on 2016-04-19 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recognized as a powerful tool for dealing with uncertainty, Markov modeling can enhance your ability to analyze complex production and service systems. However, most books on Markov chains or decision processes are often either highly theoretical, with few examples, or highly prescriptive, with little justification for the steps of the algorithms u
Book Synopsis Finite State Continuous Time Markov Processes with a Finite Planning Horizon by : Bruce L. Miller
Download or read book Finite State Continuous Time Markov Processes with a Finite Planning Horizon written by Bruce L. Miller and published by . This book was released on 1967 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Markov Decision Processes by : Martin L. Puterman
Download or read book Markov Decision Processes written by Martin L. Puterman and published by Wiley-Interscience. This book was released on 1994-04-29 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date, unified and rigorous treatment of theoretical, computational and applied research on Markov decision process models. Concentrates on infinite-horizon discrete-time models. Discusses arbitrary state spaces, finite-horizon and continuous-time discrete-state models. Also covers modified policy iteration, multichain models with average reward criterion and sensitive optimality. Features a wealth of figures which illustrate examples and an extensive bibliography.
Book Synopsis Selected Topics on Continuous-time Controlled Markov Chains and Markov Games by : Tomas Prieto-Rumeau
Download or read book Selected Topics on Continuous-time Controlled Markov Chains and Markov Games written by Tomas Prieto-Rumeau and published by World Scientific. This book was released on 2012 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concerns continuous-time controlled Markov chains, also known as continuous-time Markov decision processes. They form a class of stochastic control problems in which a single decision-maker wishes to optimize a given objective function. This book is also concerned with Markov games, where two decision-makers (or players) try to optimize their own objective function. Both decision-making processes appear in a large number of applications in economics, operations research, engineering, and computer science, among other areas. An extensive, self-contained, up-to-date analysis of basic optimality criteria (such as discounted and average reward), and advanced optimality criteria (e.g., bias, overtaking, sensitive discount, and Blackwell optimality) is presented. A particular emphasis is made on the application of the results herein: algorithmic and computational issues are discussed, and applications to population models and epidemic processes are shown. This book is addressed to students and researchers in the fields of stochastic control and stochastic games. Moreover, it could be of interest also to undergraduate and beginning graduate students because the reader is not supposed to have a high mathematical background: a working knowledge of calculus, linear algebra, probability, and continuous-time Markov chains should suffice to understand the contents of the book.
Book Synopsis Finite State Continuous-time Markov Decision Processes, with Applications to a Class of Optimization Problems in Queueing Theory by : Bruce L. Miller
Download or read book Finite State Continuous-time Markov Decision Processes, with Applications to a Class of Optimization Problems in Queueing Theory written by Bruce L. Miller and published by . This book was released on 1967 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Markov Processes and Controlled Markov Chains by : Zhenting Hou
Download or read book Markov Processes and Controlled Markov Chains written by Zhenting Hou and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general theory of stochastic processes and the more specialized theory of Markov processes evolved enormously in the second half of the last century. In parallel, the theory of controlled Markov chains (or Markov decision processes) was being pioneered by control engineers and operations researchers. Researchers in Markov processes and controlled Markov chains have been, for a long time, aware of the synergies between these two subject areas. However, this may be the first volume dedicated to highlighting these synergies and, almost certainly, it is the first volume that emphasizes the contributions of the vibrant and growing Chinese school of probability. The chapters that appear in this book reflect both the maturity and the vitality of modern day Markov processes and controlled Markov chains. They also will provide an opportunity to trace the connections that have emerged between the work done by members of the Chinese school of probability and the work done by the European, US, Central and South American and Asian scholars.
Book Synopsis Constrained Markov Decision Processes by : Eitan Altman
Download or read book Constrained Markov Decision Processes written by Eitan Altman and published by CRC Press. This book was released on 1999-03-30 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unified approach for the study of constrained Markov decision processes with a finite state space and unbounded costs. Unlike the single controller case considered in many other books, the author considers a single controller with several objectives, such as minimizing delays and loss, probabilities, and maximization of throughputs. It is desirable to design a controller that minimizes one cost objective, subject to inequality constraints on other cost objectives. This framework describes dynamic decision problems arising frequently in many engineering fields. A thorough overview of these applications is presented in the introduction. The book is then divided into three sections that build upon each other. The first part explains the theory for the finite state space. The author characterizes the set of achievable expected occupation measures as well as performance vectors, and identifies simple classes of policies among which optimal policies exist. This allows the reduction of the original dynamic into a linear program. A Lagranian approach is then used to derive the dual linear program using dynamic programming techniques. In the second part, these results are extended to the infinite state space and action spaces. The author provides two frameworks: the case where costs are bounded below and the contracting framework. The third part builds upon the results of the first two parts and examines asymptotical results of the convergence of both the value and the policies in the time horizon and in the discount factor. Finally, several state truncation algorithms that enable the approximation of the solution of the original control problem via finite linear programs are given.
Book Synopsis Relative Optimization of Continuous-Time and Continuous-State Stochastic Systems by : Xi-Ren Cao
Download or read book Relative Optimization of Continuous-Time and Continuous-State Stochastic Systems written by Xi-Ren Cao and published by Springer Nature. This book was released on 2020-05-13 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph applies the relative optimization approach to time nonhomogeneous continuous-time and continuous-state dynamic systems. The approach is intuitively clear and does not require deep knowledge of the mathematics of partial differential equations. The topics covered have the following distinguishing features: long-run average with no under-selectivity, non-smooth value functions with no viscosity solutions, diffusion processes with degenerate points, multi-class optimization with state classification, and optimization with no dynamic programming. The book begins with an introduction to relative optimization, including a comparison with the traditional approach of dynamic programming. The text then studies the Markov process, focusing on infinite-horizon optimization problems, and moves on to discuss optimal control of diffusion processes with semi-smooth value functions and degenerate points, and optimization of multi-dimensional diffusion processes. The book concludes with a brief overview of performance derivative-based optimization. Among the more important novel considerations presented are: the extension of the Hamilton–Jacobi–Bellman optimality condition from smooth to semi-smooth value functions by derivation of explicit optimality conditions at semi-smooth points and application of this result to degenerate and reflected processes; proof of semi-smoothness of the value function at degenerate points; attention to the under-selectivity issue for the long-run average and bias optimality; discussion of state classification for time nonhomogeneous continuous processes and multi-class optimization; and development of the multi-dimensional Tanaka formula for semi-smooth functions and application of this formula to stochastic control of multi-dimensional systems with degenerate points. The book will be of interest to researchers and students in the field of stochastic control and performance optimization alike.
Book Synopsis OPTIMIZATION AND OPERATIONS RESEARCH – Volume IV by : Ulrich Derigs
Download or read book OPTIMIZATION AND OPERATIONS RESEARCH – Volume IV written by Ulrich Derigs and published by EOLSS Publications. This book was released on 2009-04-15 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization and Operations Research is a component of Encyclopedia of Mathematical Sciences in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty one Encyclopedias. The Theme on Optimization and Operations Research is organized into six different topics which represent the main scientific areas of the theme: 1. Fundamentals of Operations Research; 2. Advanced Deterministic Operations Research; 3. Optimization in Infinite Dimensions; 4. Game Theory; 5. Stochastic Operations Research; 6. Decision Analysis, which are then expanded into multiple subtopics, each as a chapter. These four volumes are aimed at the following five major target audiences: University and College students Educators, Professional Practitioners, Research Personnel and Policy Analysts, Managers, and Decision Makers and NGOs.
