Continuous Time Markov Decision Processes

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Continuous Time Markov Decision Processes

Author : Xianping Guo
ISBN : 9783642025471
Genre : Mathematics
File Size : 58.24 MB
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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.
Category: Mathematics

Continuous Time Markov Decision Processes

Author : Alexey Piunovskiy
ISBN : 9783030549879
Genre : Mathematics
File Size : 75.51 MB
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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.
Category: Mathematics

Average Optimality For Continuous Time Markov Decision Processes Under Weak Continuity Conditions

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ISBN : OCLC:1051368412
Genre :
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Abstract : This paper considers the average optimality for a continuous-time Markov decision process in Borel state and action spaces, and with an arbitrarily unbounded nonnegative cost rate. The existence of a deterministic stationary optimal policy is proved under the conditions that allow the following; the controlled process can be explosive, the transition rates are weakly continuous, and the multifunction defining the admissible action spaces can be neither compact-valued nor upper semicontinuous.

Selected Topics On Continuous Time Controlled Markov Chains And Markov Games

Author : Tomás Prieto-Rumeau
ISBN : 9781848168480
Genre : Mathematics
File Size : 77.87 MB
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This book concerns continuous-time controlled Markov chains and Markov games. The former, which are also known as continuous-time Markov decision processes, form a class of stochastic control problems in which a single decision-maker has a wish to optimize a given objective function. In contrast, there are two or more decision-makers (or players, or controllers) trying to optimize its own objective function in a Markov game. Both decision-making processes appear in a large number of applications in economics, operations research, engineering, and computer science among other areas. The main features of the control and game models studied in the book are the continuous time variable, the denumerable state space, and that the control (or action) sets are Borel spaces. Moreover, the transition and reward rates of the dynamical system may be unbounded. The authors are interested in some aspects of controlled Markov chains and Markov games such as characterizing the optimal reward functions, and determining optimal policies for each of the optimality criteria studied here. The main focus is on advanced optimality criteria (such as, bias, variance, sensitive discount, and Blackwell optimality), though they also deal with the basic optimality criteria (discounted and average reward). A particular emphasis is made on the application of the results presented in this book. One of the main concerns is to propose assumptions on the control and game models that are easily verifiable (and verified) in practice. Moreover, algorithmic and computational issues are also analyzed. In particular, the authors propose approximation results that allow precise numerical approximations of the solution to some problems of practical interest. Applications to population models and epidemic processes are also shown.
Category: Mathematics

Markov Decision Processes In Practice

Author : Richard J. Boucherie
ISBN : 9783319477664
Genre : Business & Economics
File Size : 77.81 MB
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This book presents classical Markov Decision Processes (MDP) for real-life applications and optimization. MDP allows users to develop and formally support approximate and simple decision rules, and this book showcases state-of-the-art applications in which MDP was key to the solution approach. The book is divided into six parts. Part 1 is devoted to the state-of-the-art theoretical foundation of MDP, including approximate methods such as policy improvement, successive approximation and infinite state spaces as well as an instructive chapter on Approximate Dynamic Programming. It then continues with five parts of specific and non-exhaustive application areas. Part 2 covers MDP healthcare applications, which includes different screening procedures, appointment scheduling, ambulance scheduling and blood management. Part 3 explores MDP modeling within transportation. This ranges from public to private transportation, from airports and traffic lights to car parking or charging your electric car . Part 4 contains three chapters that illustrates the structure of approximate policies for production or manufacturing structures. In Part 5, communications is highlighted as an important application area for MDP. It includes Gittins indices, down-to-earth call centers and wireless sensor networks. Finally Part 6 is dedicated to financial modeling, offering an instructive review to account for financial portfolios and derivatives under proportional transactional costs. The MDP applications in this book illustrate a variety of both standard and non-standard aspects of MDP modeling and its practical use. This book should appeal to readers for practitioning, academic research and educational purposes, with a background in, among others, operations research, mathematics, computer science, and industrial engineering.
Category: Business & Economics

Continuous Time Markov Chains And Applications

Author : G. George Yin
ISBN : 9781461443469
Genre : Mathematics
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This book gives a systematic treatment of singularly perturbed systems that naturally arise in control and optimization, queueing networks, manufacturing systems, and financial engineering. It presents results on asymptotic expansions of solutions of Komogorov forward and backward equations, properties of functional occupation measures, exponential upper bounds, and functional limit results for Markov chains with weak and strong interactions. To bridge the gap between theory and applications, a large portion of the book is devoted to applications in controlled dynamic systems, production planning, and numerical methods for controlled Markovian systems with large-scale and complex structures in the real-world problems. This second edition has been updated throughout and includes two new chapters on asymptotic expansions of solutions for backward equations and hybrid LQG problems. The chapters on analytic and probabilistic properties of two-time-scale Markov chains have been almost completely rewritten and the notation has been streamlined and simplified. This book is written for applied mathematicians, engineers, operations researchers, and applied scientists. Selected material from the book can also be used for a one semester advanced graduate-level course in applied probability and stochastic processes.
Category: Mathematics

Markov Decision Processes With Their Applications

Author : Qiying Hu
ISBN : 9780387369518
Genre : Business & Economics
File Size : 44.42 MB
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Put together by two top researchers in the Far East, this text examines Markov Decision Processes - also called stochastic dynamic programming - and their applications in the optimal control of discrete event systems, optimal replacement, and optimal allocations in sequential online auctions. This dynamic new book offers fresh applications of MDPs in areas such as the control of discrete event systems and the optimal allocations in sequential online auctions.
Category: Business & Economics

Discrete Time Markov Chains

Author : G. George Yin
ISBN : 9780387268712
Genre : Mathematics
File Size : 88.42 MB
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This book focuses on two-time-scale Markov chains in discrete time. Our motivation stems from existing and emerging applications in optimization and control of complex systems in manufacturing, wireless communication, and ?nancial engineering. Much of our e?ort in this book is devoted to designing system models arising from various applications, analyzing them via analytic and probabilistic techniques, and developing feasible compu- tionalschemes. Ourmainconcernistoreducetheinherentsystemcompl- ity. Although each of the applications has its own distinct characteristics, all of them are closely related through the modeling of uncertainty due to jump or switching random processes. Oneofthesalientfeaturesofthisbookistheuseofmulti-timescalesin Markovprocessesandtheirapplications. Intuitively,notallpartsorcom- nents of a large-scale system evolve at the same rate. Some of them change rapidly and others vary slowly. The di?erent rates of variations allow us to reduce complexity via decomposition and aggregation. It would be ideal if we could divide a large system into its smallest irreducible subsystems completely separable from one another and treat each subsystem indep- dently. However, this is often infeasible in reality due to various physical constraints and other considerations. Thus, we have to deal with situations in which the systems are only nearly decomposable in the sense that there are weak links among the irreducible subsystems, which dictate the oc- sional regime changes of the system. An e?ective way to treat such near decomposability is time-scale separation. That is, we set up the systems as if there were two time scales, fast vs. slow. xii Preface Followingthetime-scaleseparation,weusesingularperturbationmeth- ology to treat the underlying systems.
Category: Mathematics

Modern Trends In Controlled Stochastic Processes

Author : Alexey B. Piunovskiy
ISBN : 9781905986309
Genre : Mathematics
File Size : 79.66 MB
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World leading experts give their accounts of the modern mathematical models in the field: Markov Decision Processes, controlled diffusions, piece-wise deterministic processes etc, with a wide range of performance functionals. One of the aims is to give a general view on the state-of-the-art. The authors use Dynamic Programming, Convex Analytic Approach, several numerical methods, index-based approach and so on. Most chapters either contain well developed examples, or are entirely devoted to the application of the mathematical control theory to real life problems from such fields as Insurance, Portfolio Optimization and Information Transmission. The book will enable researchers, academics and research students to get a sense of novel results, concepts, models, methods, and applications of controlled stochastic processes.
Category: Mathematics

Markov Decision Processes

Author : Martin L. Puterman
ISBN : 9781118625873
Genre : Mathematics
File Size : 35.45 MB
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The Wiley-Interscience Paperback Series consists of selected booksthat have been made more accessible to consumers in an effort toincrease global appeal and general circulation. With these newunabridged softcover volumes, Wiley hopes to extend the lives ofthese works by making them available to future generations ofstatisticians, mathematicians, and scientists. "This text is unique in bringing together so many resultshitherto found only in part in other texts and papers. . . . Thetext is fairly self-contained, inclusive of some basic mathematicalresults needed, and provides a rich diet of examples, applications,and exercises. The bibliographical material at the end of eachchapter is excellent, not only from a historical perspective, butbecause it is valuable for researchers in acquiring a goodperspective 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 havenow a complete volume (with more than 600 pages) devoted to thistopic. . . . Markov Decision Processes: Discrete Stochastic DynamicProgramming represents an up-to-date, unified, and rigoroustreatment of theoretical and computational aspects of discrete-timeMarkov decision processes." —Journal of the American Statistical Association
Category: Mathematics

Verification Model Checking And Abstract Interpretation

Author : Kenneth McMillan
ISBN : 9783642540134
Genre : Computers
File Size : 34.60 MB
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This book constitutes the refereed proceedings of the 15th International Conference on Verification, Model Checking and Abstract Interpretation, VMCAI 2014, held in San Diego, CA, USA, in January 2013. The 25 revised full papers presented were carefully reviewed and selected from 64 submissions. The papers cover a wide range of topics including program verification, model checking, abstract interpretation and abstract domains, program synthesis, static analysis, type systems, deductive methods, program certification, debugging techniques, program transformation, optimization, hybrid and cyber-physical systems.
Category: Computers

Optimization Control And Applications Of Stochastic Systems

Author : Daniel Hernández-Hernández
ISBN : 9780817683375
Genre : Science
File Size : 52.86 MB
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This volume provides a general overview of discrete- and continuous-time Markov control processes and stochastic games, along with a look at the range of applications of stochastic control and some of its recent theoretical developments. These topics include various aspects of dynamic programming, approximation algorithms, and infinite-dimensional linear programming. In all, the work comprises 18 carefully selected papers written by experts in their respective fields. Optimization, Control, and Applications of Stochastic Systems will be a valuable resource for all practitioners, researchers, and professionals in applied mathematics and operations research who work in the areas of stochastic control, mathematical finance, queueing theory, and inventory systems. It may also serve as a supplemental text for graduate courses in optimal control and dynamic games.
Category: Science

Continuous Average Control Of Piecewise Deterministic Markov Processes

Author : Oswaldo Luiz do Valle Costa
ISBN : 9781461469834
Genre : Mathematics
File Size : 68.89 MB
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The intent of this book is to present recent results in the control theory for the long run average continuous control problem of piecewise deterministic Markov processes (PDMPs). The book focuses mainly on the long run average cost criteria and extends to the PDMPs some well-known techniques related to discrete-time and continuous-time Markov decision processes, including the so-called ``average inequality approach'', ``vanishing discount technique'' and ``policy iteration algorithm''. We believe that what is unique about our approach is that, by using the special features of the PDMPs, we trace a parallel with the general theory for discrete-time Markov Decision Processes rather than the continuous-time case. The two main reasons for doing that is to use the powerful tools developed in the discrete-time framework and to avoid working with the infinitesimal generator associated to a PDMP, which in most cases has its domain of definition difficult to be characterized. Although the book is mainly intended to be a theoretically oriented text, it also contains some motivational examples. The book is targeted primarily for advanced students and practitioners of control theory. The book will be a valuable source for experts in the field of Markov decision processes. Moreover, the book should be suitable for certain advanced courses or seminars. As background, one needs an acquaintance with the theory of Markov decision processes and some knowledge of stochastic processes and modern analysis.
Category: Mathematics