Download or read book A Design and Analysis of Computer Experiments based Approach to Approximate Infinite Horizon Dynamic Programming with Continuous State Spaces written by Asama Kulvanitchaiyanunt and published by . This book was released on 2014 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamic programming (DP) is an optimization approach that transforms a complex problem into a sequence of simpler sub-problems at different points in stage. The original DP approach used Bellman's equation to compute the "cost-to-go" function. This method is useful when considering a few states and decisions. However, when dealing with high-dimensional data set with continuous state space, the limit called 'curse of dimensionality' obstructs the solution as the size of the state space grows exponentially. Given recent advances in computational power, approximate dynamic programming (ADP) is introduced by not seeking to compute the future value function exactly and at each point of the state space; rather opting for an approximation of the future value function in the domain of the state space. Two main components of ADP method which have been challenged among existing ADP studies are discretization of the state space and estimation of the cost-to-go or future value function. The first part of this dissertation research seeks to develop a solution method to solve an infinite horizon dynamic programming called Design and Analysis of Computer Experiment (DACE)-based Approach to ADP. Multivariate Adaptive Regression Splines (MARS) which is a flexible, nonparametric statistical modeling tool is used to approximate future value functions in stochastic dynamic programming (SDP) problems with continuous state variables. The training data set is updated sequentially based on the conditions. This sequential grid discretization explores the state space and provides a statistically parsimonious ADP methodology which 'adaptively' captures the important variables from the state space. There are 3 different algorithms presented in this dissertation based on the conditions of sampling process of the training data set. Comparisons are presented on a forward simulation with 12 time periods. The second part of the dissertation research is to develop a batch mode Reinforcement Learning (RL) using MARS as an approximator to solve the same problem with the first part. The main difference between these two methods is the input variables to approximate future value function. In batch mode RL method, the state-action space is used, thus the estimated function (output) is a function of both state and action variables. By contrast, DACE-based ADP used only state variable and the estimated future function is based only on state variables. The study on state-action discretization is presented in this dissertation. Two different designs are used, including Monte Carlo sampling and Sobol' sequence design. Comparisons are presented on the same forward simulation. The third part is to develop a two-stage framework for Adaptive Design for Controllability of a System of Plug-in Hybrid Electric Vehicle Charging Stations Case Study. The second-stage dynamic control problem is formulated and initially solved by mean value problem using linear programming. After that a DACE approach is used to develop a metamodel of the second stage solution based on the possible solution from the first stage. Then the metamodel will be turned into the first stage and at this point the final solution will be made. DACE helps reduce time-consuming computer models by replacing the loop between first and second stage with a constraint generated from the gradient of the approximation function. Moreover, the metamodel can give more accessible description to the second stage.
Download or read book Using Approximate Dynamic Programming to Control an Electric Vehicle Charging Station System written by Ying Chen and published by . This book was released on 2017 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamic programming (DP) as a mathematical programming approach to optimize a system evolving over time has been applied to solve the multi-stage optimization problems in a lot of areas such as manufacturing systems and environmental engineering. Due to the “curses of dimensionality”, traditional DP method is only able to solve a low dimensional problem or problems under very limiting restrictions, In order to employ DP to solve high-dimensional practical complex systems, approximate dynamic programming (ADP) is proposed. Several versions of ADP has been introduced in the literature and for this study, the author takes advantage of design and analysis of computer experiments (DACE) approach to discretize the state space via design of experiments and build the value function with statistical tools, which is named as DACE based ADP approach. In this research, the author first takes advantage of support vector regression (SVR) to build the value function instead of the previous ones such as neural network and multivariate adaptive regression spines, and explore the performance of SVR in the value function approximation compared to the other techniques. After that, 45-degree line correspondence stopping criterion is specified with an algorithm. Then, we formulates the complex electric vehicle (EV) charging stations system located in Dallas-Fort Worth (DFW) metropolitan area in Texas as a Markov decision process (MDP) problem and DACE based infinite horizon ADP algorithm with SVR is used to solve this high-dimensional, continuous-state, infinite horizon problem. Specified 45-degree line correspondence criterion is used to stop the DP iterations and select the ADP policy. Greedy algorithm as a benchmark is proposed to conduct a comparison through paired t-test with the selected ADP policy. The results demonstrate that DACE based infinite horizon ADP algorithm is able to solve the high-dimensional, large-scale, complex DP problem over continuous spaces and quantified 45-degree line correspondence rule is able to stop the DP iterations reasonably and select a high-quality ADP policy.
Download or read book Approximate Dynamic Programming written by Warren B. Powell and published by John Wiley & Sons. This book was released on 2007-10-05 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete and accessible introduction to the real-world applications of approximate dynamic programming With the growing levels of sophistication in modern-day operations, it is vital for practitioners to understand how to approach, model, and solve complex industrial problems. Approximate Dynamic Programming is a result of the author's decades of experience working in large industrial settings to develop practical and high-quality solutions to problems that involve making decisions in the presence of uncertainty. This groundbreaking book uniquely integrates four distinct disciplines—Markov design processes, mathematical programming, simulation, and statistics—to demonstrate how to successfully model and solve a wide range of real-life problems using the techniques of approximate dynamic programming (ADP). The reader is introduced to the three curses of dimensionality that impact complex problems and is also shown how the post-decision state variable allows for the use of classical algorithmic strategies from operations research to treat complex stochastic optimization problems. Designed as an introduction and assuming no prior training in dynamic programming of any form, Approximate Dynamic Programming contains dozens of algorithms that are intended to serve as a starting point in the design of practical solutions for real problems. The book provides detailed coverage of implementation challenges including: modeling complex sequential decision processes under uncertainty, identifying robust policies, designing and estimating value function approximations, choosing effective stepsize rules, and resolving convergence issues. With a focus on modeling and algorithms in conjunction with the language of mainstream operations research, artificial intelligence, and control theory, Approximate Dynamic Programming: Models complex, high-dimensional problems in a natural and practical way, which draws on years of industrial projects Introduces and emphasizes the power of estimating a value function around the post-decision state, allowing solution algorithms to be broken down into three fundamental steps: classical simulation, classical optimization, and classical statistics Presents a thorough discussion of recursive estimation, including fundamental theory and a number of issues that arise in the development of practical algorithms Offers a variety of methods for approximating dynamic programs that have appeared in previous literature, but that have never been presented in the coherent format of a book Motivated by examples from modern-day operations research, Approximate Dynamic Programming is an accessible introduction to dynamic modeling and is also a valuable guide for the development of high-quality solutions to problems that exist in operations research and engineering. The clear and precise presentation of the material makes this an appropriate text for advanced undergraduate and beginning graduate courses, while also serving as a reference for researchers and practitioners. A companion Web site is available for readers, which includes additional exercises, solutions to exercises, and data sets to reinforce the book's main concepts.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1976 with total page 984 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1967 with total page 1428 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Reinforcement Learning and Dynamic Programming Using Function Approximators written by Lucian Busoniu and published by CRC Press. This book was released on 2017-07-28 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: From household appliances to applications in robotics, engineered systems involving complex dynamics can only be as effective as the algorithms that control them. While Dynamic Programming (DP) has provided researchers with a way to optimally solve decision and control problems involving complex dynamic systems, its practical value was limited by algorithms that lacked the capacity to scale up to realistic problems. However, in recent years, dramatic developments in Reinforcement Learning (RL), the model-free counterpart of DP, changed our understanding of what is possible. Those developments led to the creation of reliable methods that can be applied even when a mathematical model of the system is unavailable, allowing researchers to solve challenging control problems in engineering, as well as in a variety of other disciplines, including economics, medicine, and artificial intelligence. Reinforcement Learning and Dynamic Programming Using Function Approximators provides a comprehensive and unparalleled exploration of the field of RL and DP. With a focus on continuous-variable problems, this seminal text details essential developments that have substantially altered the field over the past decade. In its pages, pioneering experts provide a concise introduction to classical RL and DP, followed by an extensive presentation of the state-of-the-art and novel methods in RL and DP with approximation. Combining algorithm development with theoretical guarantees, they elaborate on their work with illustrative examples and insightful comparisons. Three individual chapters are dedicated to representative algorithms from each of the major classes of techniques: value iteration, policy iteration, and policy search. The features and performance of these algorithms are highlighted in extensive experimental studies on a range of control applications. The recent development of applications involving complex systems has led to a surge of interest in RL and DP methods and the subsequent need for a quality resource on the subject. For graduate students and others new to the field, this book offers a thorough introduction to both the basics and emerging methods. And for those researchers and practitioners working in the fields of optimal and adaptive control, machine learning, artificial intelligence, and operations research, this resource offers a combination of practical algorithms, theoretical analysis, and comprehensive examples that they will be able to adapt and apply to their own work. Access the authors' website at www.dcsc.tudelft.nl/rlbook/ for additional material, including computer code used in the studies and information concerning new developments.
Download or read book Optimizing a System of Electric Vehicle Charging Stations written by Ukesh Chawal and published by . This book was released on 2019 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: There has been a significant increase in the number of electric vehicles (EVs) mainly because of the need to have a greener living. Thus, ease of access to charging facilities is a prerequisite for large scale deployment for EV. The first component of this dissertation research seeks to formulate a deterministic mixed-integer linear programming (MILP) model to optimize the system of EV charging stations, the locations of the stations and the number of slots to be opened to maximize the profit based on the user-specified cost of opening a station. Despite giving the optimal solution, the drawback of MILP formulation is its extremely high computational time (as much as 5 days). The other limit of this deterministic model is that it does not take uncertainty in to consideration. The second component of this dissertation is to overcome the first drawback of the MILP model by implementing a two-stage framework developed by (Chawal et al. 2018), which integrates the first-stage system design problem and second-stage control problem of an EV charging stations using a design and analysis of computer experiments (DACE) based system design optimization approach. The first stage specifies the design of the system that maximizes expected profit. Profit incorporates costs for building stations and revenue evaluated by solving a system control problem in the second stage. The results obtained from the DACE based system design optimization approach, when compared to the MILP, provide near optimal solutions. Moreover, the computation time with the DACE approach is significantly lower, making it a more suitable option for practical use. The third component of this dissertation is to overcome the second drawback of the MILP model by introducing stochasticity in our model. A two-stage framework is developed to address the design of a system of electric vehicle (EV) charging stations. The first stage specifies the design of the system that maximizes expected profit. Profit incorporates costs for building stations and revenue evaluated by solving a system control problem in the second stage. The control problem is formulated as an infinite horizon, continuous-state stochastic dynamic programming problem. To reduce computational demands, a numerical solution is obtained using approximate dynamic programming (ADP) to approximate the optimal value function. To obtain a system design solution using our two-stage framework, we propose an approach based on DACE. DACE is employed in two ways. First, for the control problem, a DACE-based ADP method for continuous-state spaces is used. Second, we introduce a new DACE approach specifically for our two-stage EV charging stations system design problem. This second version of DACE is the focus of this paper. The "design" part of the DACE approach uses experimental design to organize a set of feasible first-stage system designs. For each of these system designs, the second-stage control problem is executed, and the corresponding expected revenue is obtained. The "analysis" part of the DACE approach uses the expected revenue data to build a metamodel that approximates the expected revenue as a function of the first-stage system design. Finally, this expected revenue approximation is employed in the profit objective of the first stage to enable a more computationally-efficient method to optimize the system design. To our knowledge, this is the only two-stage stochastic problem which uses infinite horizon dynamic programming approach to optimize the second stage dynamic control problem and the first stage system design problem. Moreover, when the designs obtained from our DACE approach and MILP design are solved using DACE-based ADP method (simulation), an improvement of approximately 8% is observed in the simulated profit obtained from ADP design compared to that of MILP design indicating that when uncertainty is considered, DACE ADP design provides the better solution.
Download or read book International Aerospace Abstracts written by and published by . This book was released on 1998 with total page 980 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Selected Rand Abstracts written by Rand Corporation and published by . This book was released on 1963 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes Reports (R-series), Rand Memorandums (RM-series), papers (P-series), and Books.
Download or read book A Concise Introduction to Decentralized POMDPs written by Frans A. Oliehoek and published by Springer. This book was released on 2016-06-03 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces multiagent planning under uncertainty as formalized by decentralized partially observable Markov decision processes (Dec-POMDPs). The intended audience is researchers and graduate students working in the fields of artificial intelligence related to sequential decision making: reinforcement learning, decision-theoretic planning for single agents, classical multiagent planning, decentralized control, and operations research.
Download or read book Neural Approximations for Optimal Control and Decision written by Riccardo Zoppoli and published by Springer Nature. This book was released on 2019-12-17 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neural Approximations for Optimal Control and Decision provides a comprehensive methodology for the approximate solution of functional optimization problems using neural networks and other nonlinear approximators where the use of traditional optimal control tools is prohibited by complicating factors like non-Gaussian noise, strong nonlinearities, large dimension of state and control vectors, etc. Features of the text include: • a general functional optimization framework; • thorough illustration of recent theoretical insights into the approximate solutions of complex functional optimization problems; • comparison of classical and neural-network based methods of approximate solution; • bounds to the errors of approximate solutions; • solution algorithms for optimal control and decision in deterministic or stochastic environments with perfect or imperfect state measurements over a finite or infinite time horizon and with one decision maker or several; • applications of current interest: routing in communications networks, traffic control, water resource management, etc.; and • numerous, numerically detailed examples. The authors’ diverse backgrounds in systems and control theory, approximation theory, machine learning, and operations research lend the book a range of expertise and subject matter appealing to academics and graduate students in any of those disciplines together with computer science and other areas of engineering.
Download or read book Adaptive Dynamic Programming Single and Multiple Controllers written by Ruizhuo Song and published by Springer. This book was released on 2018-12-28 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a class of novel optimal control methods and games schemes based on adaptive dynamic programming techniques. For systems with one control input, the ADP-based optimal control is designed for different objectives, while for systems with multi-players, the optimal control inputs are proposed based on games. In order to verify the effectiveness of the proposed methods, the book analyzes the properties of the adaptive dynamic programming methods, including convergence of the iterative value functions and the stability of the system under the iterative control laws. Further, to substantiate the mathematical analysis, it presents various application examples, which provide reference to real-world practices.
Download or read book Planning Algorithms written by Steven M. LaValle and published by Cambridge University Press. This book was released on 2006-05-29 with total page 844 pages. Available in PDF, EPUB and Kindle. Book excerpt: Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. Written for computer scientists and engineers with interests in artificial intelligence, robotics, or control theory, this is the only book on this topic that tightly integrates a vast body of literature from several fields into a coherent source for teaching and reference in a wide variety of applications. Difficult mathematical material is explained through hundreds of examples and illustrations.
Download or read book Algorithms for Reinforcement Learning written by Csaba Grossi and published by Springer Nature. This book was released on 2022-05-31 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reinforcement learning is a learning paradigm concerned with learning to control a system so as to maximize a numerical performance measure that expresses a long-term objective. What distinguishes reinforcement learning from supervised learning is that only partial feedback is given to the learner about the learner's predictions. Further, the predictions may have long term effects through influencing the future state of the controlled system. Thus, time plays a special role. The goal in reinforcement learning is to develop efficient learning algorithms, as well as to understand the algorithms' merits and limitations. Reinforcement learning is of great interest because of the large number of practical applications that it can be used to address, ranging from problems in artificial intelligence to operations research or control engineering. In this book, we focus on those algorithms of reinforcement learning that build on the powerful theory of dynamic programming. We give a fairly comprehensive catalog of learning problems, describe the core ideas, note a large number of state of the art algorithms, followed by the discussion of their theoretical properties and limitations. Table of Contents: Markov Decision Processes / Value Prediction Problems / Control / For Further Exploration
Download or read book Reinforcement Learning second edition written by Richard S. Sutton and published by MIT Press. This book was released on 2018-11-13 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: The significantly expanded and updated new edition of a widely used text on reinforcement learning, one of the most active research areas in artificial intelligence. Reinforcement learning, one of the most active research areas in artificial intelligence, is a computational approach to learning whereby an agent tries to maximize the total amount of reward it receives while interacting with a complex, uncertain environment. In Reinforcement Learning, Richard Sutton and Andrew Barto provide a clear and simple account of the field's key ideas and algorithms. This second edition has been significantly expanded and updated, presenting new topics and updating coverage of other topics. Like the first edition, this second edition focuses on core online learning algorithms, with the more mathematical material set off in shaded boxes. Part I covers as much of reinforcement learning as possible without going beyond the tabular case for which exact solutions can be found. Many algorithms presented in this part are new to the second edition, including UCB, Expected Sarsa, and Double Learning. Part II extends these ideas to function approximation, with new sections on such topics as artificial neural networks and the Fourier basis, and offers expanded treatment of off-policy learning and policy-gradient methods. Part III has new chapters on reinforcement learning's relationships to psychology and neuroscience, as well as an updated case-studies chapter including AlphaGo and AlphaGo Zero, Atari game playing, and IBM Watson's wagering strategy. The final chapter discusses the future societal impacts of reinforcement learning.
Download or read book American Doctoral Dissertations written by and published by . This book was released on 1984 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamic Economics written by Jerome Adda and published by MIT Press. This book was released on 2023-05-09 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated approach to the empirical application of dynamic optimization programming models, for students and researchers. This book is an effective, concise text for students and researchers that combines the tools of dynamic programming with numerical techniques and simulation-based econometric methods. Doing so, it bridges the traditional gap between theoretical and empirical research and offers an integrated framework for studying applied problems in macroeconomics and microeconomics. In part I the authors first review the formal theory of dynamic optimization; they then present the numerical tools and econometric techniques necessary to evaluate the theoretical models. In language accessible to a reader with a limited background in econometrics, they explain most of the methods used in applied dynamic research today, from the estimation of probability in a coin flip to a complicated nonlinear stochastic structural model. These econometric techniques provide the final link between the dynamic programming problem and data. Part II is devoted to the application of dynamic programming to specific areas of applied economics, including the study of business cycles, consumption, and investment behavior. In each instance the authors present the specific optimization problem as a dynamic programming problem, characterize the optimal policy functions, estimate the parameters, and use models for policy evaluation. The original contribution of Dynamic Economics: Quantitative Methods and Applications lies in the integrated approach to the empirical application of dynamic optimization programming models. This integration shows that empirical applications actually complement the underlying theory of optimization, while dynamic programming problems provide needed structure for estimation and policy evaluation.
