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Estimation Of Markov Decision Processes In The Presence Of Model Uncertainty
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Book Synopsis Estimation of Markov Decision Processes in the Presence of Model Uncertainty by : Eldar A. Nigmatullin
Download or read book Estimation of Markov Decision Processes in the Presence of Model Uncertainty written by Eldar A. Nigmatullin and published by . This book was released on 2003 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Markov Decision Processes in Artificial Intelligence by : Olivier Sigaud
Download or read book Markov Decision Processes in Artificial Intelligence written by Olivier Sigaud and published by John Wiley & Sons. This book was released on 2013-03-04 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: Markov Decision Processes (MDPs) are a mathematical framework for modeling sequential decision problems under uncertainty as well as reinforcement learning problems. Written by experts in the field, this book provides a global view of current research using MDPs in artificial intelligence. It starts with an introductory presentation of the fundamental aspects of MDPs (planning in MDPs, reinforcement learning, partially observable MDPs, Markov games and the use of non-classical criteria). It then presents more advanced research trends in the field and gives some concrete examples using illustrative real life applications.
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 Robust Markov Decision Processes with Uncertain Transition Matrices by : Arnab Nilim
Download or read book Robust Markov Decision Processes with Uncertain Transition Matrices written by Arnab Nilim and published by . This book was released on 2004 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Robust Decision-making with Model Uncertainty in Aerospace Systems by : Luca Francesco Bertuccelli
Download or read book Robust Decision-making with Model Uncertainty in Aerospace Systems written by Luca Francesco Bertuccelli and published by . This book was released on 2008 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Actual performance of sequential decision-making problems can be extremely sensitive to errors in the models, and this research addressed the role of robustness in coping with this uncertainty. The first part of this thesis presents a computationally efficient sampling methodology, Dirichlet Sigma Points, for solving robust Markov Decision Processes with transition probability uncertainty. A Dirichlet prior is used to model the uncertainty in the transition probabilities. This approach uses the first two moments of the Dirichlet to generates samples of the uncertain probabilities and uses these samples to find the optimal robust policy. The Dirichlet Sigma Point method requires a much smaller number of samples than conventional Monte Carlo approaches, and is empirically demonstrated to be a very good approximation to the robust solution obtained with a very large number of samples. The second part of this thesis discusses the area of robust hybrid estimation. Model uncertainty in hybrid estimation can result in significant covariance mismatches and inefficient estimates. The specific problem of covariance underestimation is addressed, and a new robust estimator is developed that finds the largest covariance admissible within a prescribed uncertainty set. The robust estimator can be found by solving a small convex optimization problem in conjunction with Monte Carlo sampling, and reduces estimation errors in the presence of transition probability uncertainty. The Dirichlet Sigma Points are extended to this problem to reduce the computational requirements of the estimator. In the final part of the thesis, the Dirichlet Sigma Points are extended for real-time adaptation. Using insight from estimation theory, a modified version of the Dirichlet Sigma Points is presented that significantly improves the response time of classical estimators. The thesis is concluded with hardware implementation of these robust and adaptive algorithms on the RAVEN testbed, demonstrating their applicability to real-life UAV missions.
Book Synopsis Simulation-Based Algorithms for Markov Decision Processes by : Hyeong Soo Chang
Download or read book Simulation-Based Algorithms for Markov Decision Processes written by Hyeong Soo Chang and published by Springer Science & Business Media. This book was released on 2013-02-26 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Markov decision process (MDP) models are widely used for modeling sequential decision-making problems that arise in engineering, economics, computer science, and the social sciences. Many real-world problems modeled by MDPs have huge state and/or action spaces, giving an opening to the curse of dimensionality and so making practical solution of the resulting models intractable. In other cases, the system of interest is too complex to allow explicit specification of some of the MDP model parameters, but simulation samples are readily available (e.g., for random transitions and costs). For these settings, various sampling and population-based algorithms have been developed to overcome the difficulties of computing an optimal solution in terms of a policy and/or value function. Specific approaches include adaptive sampling, evolutionary policy iteration, evolutionary random policy search, and model reference adaptive search. This substantially enlarged new edition reflects the latest developments in novel algorithms and their underpinning theories, and presents an updated account of the topics that have emerged since the publication of the first edition. Includes: innovative material on MDPs, both in constrained settings and with uncertain transition properties; game-theoretic method for solving MDPs; theories for developing roll-out based algorithms; and details of approximation stochastic annealing, a population-based on-line simulation-based algorithm. The self-contained approach of this book will appeal not only to researchers in MDPs, stochastic modeling, and control, and simulation but will be a valuable source of tuition and reference for students of control and operations research.
Book Synopsis Partially Observable Markov Decision Process by : Gerard Blokdyk
Download or read book Partially Observable Markov Decision Process written by Gerard Blokdyk and published by Createspace Independent Publishing Platform. This book was released on 2018-05-29 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Which customers cant participate in our Partially observable Markov decision process domain because they lack skills, wealth, or convenient access to existing solutions? Can we add value to the current Partially observable Markov decision process decision-making process (largely qualitative) by incorporating uncertainty modeling (more quantitative)? Who are the people involved in developing and implementing Partially observable Markov decision process? How does Partially observable Markov decision process integrate with other business initiatives? Does the Partially observable Markov decision process performance meet the customer's requirements? This premium Partially observable Markov decision process self-assessment will make you the assured Partially observable Markov decision process domain master by revealing just what you need to know to be fluent and ready for any Partially observable Markov decision process challenge. How do I reduce the effort in the Partially observable Markov decision process work to be done to get problems solved? How can I ensure that plans of action include every Partially observable Markov decision process task and that every Partially observable Markov decision process outcome is in place? How will I save time investigating strategic and tactical options and ensuring Partially observable Markov decision process costs are low? How can I deliver tailored Partially observable Markov decision process advice instantly with structured going-forward plans? There's no better guide through these mind-expanding questions than acclaimed best-selling author Gerard Blokdyk. Blokdyk ensures all Partially observable Markov decision process essentials are covered, from every angle: the Partially observable Markov decision process self-assessment shows succinctly and clearly that what needs to be clarified to organize the required activities and processes so that Partially observable Markov decision process outcomes are achieved. Contains extensive criteria grounded in past and current successful projects and activities by experienced Partially observable Markov decision process practitioners. Their mastery, combined with the easy elegance of the self-assessment, provides its superior value to you in knowing how to ensure the outcome of any efforts in Partially observable Markov decision process are maximized with professional results. Your purchase includes access details to the Partially observable Markov decision process self-assessment dashboard download which gives you your dynamically prioritized projects-ready tool and shows you exactly what to do next. Your exclusive instant access details can be found in your book.
Book Synopsis Markov Decision Processes with Their Applications by : Qiying Hu
Download or read book Markov Decision Processes with Their Applications written by Qiying Hu and published by Springer Science & Business Media. This book was released on 2007-09-14 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Formal Techniques for the Verification and Optimal Control of Probabilistic Systems in the Presence of Modeling Uncertainties by : Alberto Puggelli
Download or read book Formal Techniques for the Verification and Optimal Control of Probabilistic Systems in the Presence of Modeling Uncertainties written by Alberto Puggelli and published by . This book was released on 2014 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a framework to design and verify the behavior of stochastic systems whose parameters are not known with certainty but are instead affected by modeling uncertainties, due for example to modeling errors, non-modeled dynamics or inaccuracies in the probability estimation. Our framework can be applied to the analysis of intrinsically randomized systems (e.g., random back off schemes in wireless protocols) and of abstractions of deterministic systems whose dynamics are interpreted stochastically to simplify their representation (e.g., the forecast of wind availability). In the first part of the dissertation, we introduce the model of Convex Markov Decision Processes (Convex-MDPs) as the modeling framework to represent the behavior of stochastic systems. Convex-MDPs generalize MDPs by expressing state-transition probabilities not only with fixed realization frequencies but also with non-linear convex sets of probability distribution functions. These convex sets represent the uncertainty in the modeling process. In the second part of the dissertation, we address the problem of formally verifying properties of the execution behavior of Convex-MDPs. In particular, we aim to verify that the system behaves correctly under all valid operating conditions and under all possible resolutions of the uncertainty in the state-transition probabilities. We use Probabilistic Computation Tree Logic (PCTL) as the formal logic to express system properties. Using results on strong duality for convex programs, we present a model-checking algorithm for PCTL properties of Convex-MDPs, and prove that it runs in time polynomial in the size of the model under analysis. The developed algorithm is the first known polynomial-time algorithm for the verification of PCTL properties of Convex-MDPs. This result allows us to lower the previously known algorithmic complexity upper bound for Interval-MDPs from co-NP to P, and it is valid also for the more expressive (convex) uncertainty models supported by the Convex-MDP formalism. We apply the proposed framework and model-checking algorithm to the problem of formally verifying quantitative properties of models of the behavior of human drivers. We first propose a novel stochastic model of the driver behavior based on Convex Markov chains. The model is capable of capturing the intrinsic uncertainty in estimating the intricacies of the human behavior starting from experimentally collected data. We then formally verify properties of the model expressed in PCTL. Results show that our approach can correctly predict quantitative information about the driver behavior depending on his/her attention state, e.g., whether the driver is attentive or distracted while driving, and on the environmental conditions, e.g., the presence of an obstacle on the road. Finally, in the third part of the dissertation, we analyze the problem of synthesizing optimal control strategies for Convex-MDPs, aiming to optimize a given system performance, while guaranteeing that the system behavior fulfills a specification expressed in PCTL under all resolutions of the uncertainty in the state-transition probabilities. In particular, we focus on Markov strategies, i.e., strategies that depend only on the instantaneous execution state and not on the full execution history. We first prove that adding uncertainty in the representation of the state-transition probabilities does not increase the theoretical complexity of the synthesis problem, which remains in the class NP-complete as the analogous problem applied to MDPs, i.e., when all transition probabilities are known with certainty. We then interpret the strategy-synthesis problem as a constrained optimization problem and propose the first sound and complete algorithm to solve it. We apply the developed strategy-synthesis algorithm to the problem of generating optimal energy pricing and purchasing strategies for a for-profit energy aggregator whose portfolio of energy supplies includes renewable sources, e.g., wind. Economic incentives have been proposed to manage user demand and compensate for the intrinsic uncertainty in the prediction of the supply generation. Stochastic control techniques are however needed to maximize the economic profit for the energy aggregator while quantitatively guaranteeing quality-of-service for the users. We use Convex-MDPs to model the decision-making scenario and train the models with measured data, to quantitatively capture the uncertainty in the prediction of renewable energy generation. An experimental comparison shows that the control strategies synthesized using the proposed technique significantly increase system performance with respect to previous approaches presented in the literature.
Book Synopsis Examples In Markov Decision Processes by : Alexey B Piunovskiy
Download or read book Examples In Markov Decision Processes written by Alexey B Piunovskiy and published by World Scientific. This book was released on 2012-09-21 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 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 Hidden Markov Models by : Robert J Elliott
Download or read book Hidden Markov Models written by Robert J Elliott and published by Springer Science & Business Media. This book was released on 2008-09-27 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: As more applications are found, interest in Hidden Markov Models continues to grow. Following comments and feedback from colleagues, students and other working with Hidden Markov Models the corrected 3rd printing of this volume contains clarifications, improvements and some new material, including results on smoothing for linear Gaussian dynamics. In Chapter 2 the derivation of the basic filters related to the Markov chain are each presented explicitly, rather than as special cases of one general filter. Furthermore, equations for smoothed estimates are given. The dynamics for the Kalman filter are derived as special cases of the authors’ general results and new expressions for a Kalman smoother are given. The Chapters on the control of Hidden Markov Chains are expanded and clarified. The revised Chapter 4 includes state estimation for discrete time Markov processes and Chapter 12 has a new section on robust control.
Book Synopsis Competitive Markov Decision Processes by : Jerzy Filar
Download or read book Competitive Markov Decision Processes written by Jerzy Filar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as a text covering the central concepts and techniques of Competitive Markov Decision Processes. It is an attempt to present a rig orous treatment that combines two significant research topics: Stochastic Games and Markov Decision Processes, which have been studied exten sively, and at times quite independently, by mathematicians, operations researchers, engineers, and economists. Since Markov decision processes can be viewed as a special noncompeti tive case of stochastic games, we introduce the new terminology Competi tive Markov Decision Processes that emphasizes the importance of the link between these two topics and of the properties of the underlying Markov processes. The book is designed to be used either in a classroom or for self-study by a mathematically mature reader. In the Introduction (Chapter 1) we outline a number of advanced undergraduate and graduate courses for which this book could usefully serve as a text. A characteristic feature of competitive Markov decision processes - and one that inspired our long-standing interest - is that they can serve as an "orchestra" containing the "instruments" of much of modern applied (and at times even pure) mathematics. They constitute a topic where the instruments of linear algebra, applied probability, mathematical program ming, analysis, and even algebraic geometry can be "played" sometimes solo and sometimes in harmony to produce either beautifully simple or equally beautiful, but baroque, melodies, that is, theorems.
Book Synopsis Decision Making Under Uncertainty by : Mykel J. Kochenderfer
Download or read book Decision Making Under Uncertainty written by Mykel J. Kochenderfer and published by MIT Press. This book was released on 2015-07-24 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to decision making under uncertainty from a computational perspective, covering both theory and applications ranging from speech recognition to airborne collision avoidance. Many important problems involve decision making under uncertainty—that is, choosing actions based on often imperfect observations, with unknown outcomes. Designers of automated decision support systems must take into account the various sources of uncertainty while balancing the multiple objectives of the system. This book provides an introduction to the challenges of decision making under uncertainty from a computational perspective. It presents both the theory behind decision making models and algorithms and a collection of example applications that range from speech recognition to aircraft collision avoidance. Focusing on two methods for designing decision agents, planning and reinforcement learning, the book covers probabilistic models, introducing Bayesian networks as a graphical model that captures probabilistic relationships between variables; utility theory as a framework for understanding optimal decision making under uncertainty; Markov decision processes as a method for modeling sequential problems; model uncertainty; state uncertainty; and cooperative decision making involving multiple interacting agents. A series of applications shows how the theoretical concepts can be applied to systems for attribute-based person search, speech applications, collision avoidance, and unmanned aircraft persistent surveillance. Decision Making Under Uncertainty unifies research from different communities using consistent notation, and is accessible to students and researchers across engineering disciplines who have some prior exposure to probability theory and calculus. It can be used as a text for advanced undergraduate and graduate students in fields including computer science, aerospace and electrical engineering, and management science. It will also be a valuable professional reference for researchers in a variety of disciplines.
Download or read book Journal of Economic Literature written by and published by . This book was released on 2003 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Dynamic Risk Management with Markov Decision Processes by : André Philipp Mundt
Download or read book Dynamic Risk Management with Markov Decision Processes written by André Philipp Mundt and published by . This book was released on 2008 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: