The Master Equation and the Convergence Problem in Mean Field Games PDF Download
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Author: Pierre Cardaliaguet
Publisher: Princeton University Press
ISBN: 0691190712
Category : Mathematics
Languages : en
Pages : 224
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Book Description
This book describes the latest advances in the theory of mean field games, which are optimal control problems with a continuum of players, each of them interacting with the whole statistical distribution of a population. While it originated in economics, this theory now has applications in areas as diverse as mathematical finance, crowd phenomena, epidemiology, and cybersecurity. Because mean field games concern the interactions of infinitely many players in an optimal control framework, one expects them to appear as the limit for Nash equilibria of differential games with finitely many players as the number of players tends to infinity. This book rigorously establishes this convergence, which has been an open problem until now. The limit of the system associated with differential games with finitely many players is described by the so-called master equation, a nonlocal transport equation in the space of measures. After defining a suitable notion of differentiability in the space of measures, the authors provide a complete self-contained analysis of the master equation. Their analysis includes the case of common noise problems in which all the players are affected by a common Brownian motion. They then go on to explain how to use the master equation to prove the mean field limit. This groundbreaking book presents two important new results in mean field games that contribute to a unified theoretical framework for this exciting and fast-developing area of mathematics.
Author: Pierre Cardaliaguet
Publisher: Princeton University Press
ISBN: 0691190712
Category : Mathematics
Languages : en
Pages : 224
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Book Description
This book describes the latest advances in the theory of mean field games, which are optimal control problems with a continuum of players, each of them interacting with the whole statistical distribution of a population. While it originated in economics, this theory now has applications in areas as diverse as mathematical finance, crowd phenomena, epidemiology, and cybersecurity. Because mean field games concern the interactions of infinitely many players in an optimal control framework, one expects them to appear as the limit for Nash equilibria of differential games with finitely many players as the number of players tends to infinity. This book rigorously establishes this convergence, which has been an open problem until now. The limit of the system associated with differential games with finitely many players is described by the so-called master equation, a nonlocal transport equation in the space of measures. After defining a suitable notion of differentiability in the space of measures, the authors provide a complete self-contained analysis of the master equation. Their analysis includes the case of common noise problems in which all the players are affected by a common Brownian motion. They then go on to explain how to use the master equation to prove the mean field limit. This groundbreaking book presents two important new results in mean field games that contribute to a unified theoretical framework for this exciting and fast-developing area of mathematics.
Author: Pedro Domingos
Publisher: Basic Books
ISBN: 0465061923
Category : Computers
Languages : en
Pages : 354
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Book Description
Recommended by Bill Gates A thought-provoking and wide-ranging exploration of machine learning and the race to build computer intelligences as flexible as our own In the world's top research labs and universities, the race is on to invent the ultimate learning algorithm: one capable of discovering any knowledge from data, and doing anything we want, before we even ask. In The Master Algorithm, Pedro Domingos lifts the veil to give us a peek inside the learning machines that power Google, Amazon, and your smartphone. He assembles a blueprint for the future universal learner--the Master Algorithm--and discusses what it will mean for business, science, and society. If data-ism is today's philosophy, this book is its bible.
Author: Jay Rush
Publisher:
ISBN:
Category :
Languages : en
Pages : 108
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Book Description
Solve All Your Current Challenges Plus That of Businesses and Other Individuals Do you have problems or challenges that are still unresolved?Do you want to possess a skill that will make you in demand by businesses and other individuals?Are money challenges a good place you want to have solutions for?Well, you are no more than a click away from one of the best investments you will ever make in your life.In this book, you will learn about the 3 major benefits of problem solving including monetary gains. Problem solvers are the highest paid in the world. You can sit on that high table too.You will get to know how you can become a problem solver in less than 48 hours. The problem-solving process will be second nature to you.Additionally, you will discover the 4 keys of master problem solvers and how to add them to your war chest of solving problems efficiently. You will operate like a master problem solver once you understand these 4 keys. They are sacred.Furthermore, you will learn how to solve all your current problems and more. There is also a complimentary key within the book that will cause your life to move 5 years ahead of your contemporaries. (It is a proven fact)Whether it is personal, business or national problems you would like to solve, the training you require to be a master problem solver are in the pages of this book.Make the smart move and accomplish your desire to solve problems while being rewarded at the same time.Scroll up to the top and click the BUY BUTTON and end the problems of many that will come to recognize your skill and importance.
Author: Shengyuan Liu
Publisher: Frontiers Media SA
ISBN: 283255444X
Category : Technology & Engineering
Languages : en
Pages : 321
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Book Description
The energy landscape is shifting toward renewable energy sources to mitigate climate change and reduce dependence on fossil fuels. The integration of renewable energy sources into the power grid presents various challenges, including uncertainty and variability of renewable energy sources, grid stability, and management of energy storage. Power system operation and optimization play a crucial role in managing the energy supply-demand balance, reducing operational costs, and improving the reliability of the power system. This call for papers aims to bring together the latest research and practical applications related to power system operation and optimization in the context of high penetration of renewable energy sources. We welcome contributions from researchers and practitioners from a broad range of disciplines to shed light on the challenges and opportunities associated with renewable energy integration in power systems. The objective of this Research Topic is to explore the latest advances in power system operation and optimization with a focus on the high penetration of renewable energy sources. We invite potential authors to submit articles for publication on the Research Topic of Frontiers in Energy Research on Power System Operation and Optimization Considering the High Penetration of Renewable Energy.
Author: Toby Walsh
Publisher: Springer
ISBN: 3540455787
Category : Computers
Languages : en
Pages : 802
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Book Description
This book constitutes the refereed proceedings of the 7th International Conference on Principles and Practice of Constraint Programming, CP 2001, held in Paphos, Cyprus, in November/December 2001. The 37 revised full papers, 9 innovative applications presentations, and 14 short papers presented were carefully reviewed and selected from a total of 135 submissions. All current issues in constraint processing are addressed, ranging from theoretical and foundational issues to advanced and innovative applications in a variety of fields.
Author: Teodor Gabriel Crainic
Publisher: Springer Nature
ISBN: 3031576039
Category :
Languages : en
Pages : 506
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Book Description
Author: Kurt Mehlhorn
Publisher: Springer
ISBN: 3540877444
Category : Computers
Languages : en
Pages : 860
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Book Description
This book constitutes the refereed proceedings of the 16th Annual European Symposium on Algorithms, ESA 2008, held in Karlsruhe, Germany, in September 2008 in the context of the combined conference ALGO 2008. The 67 revised full papers presented together with 2 invited lectures were carefully reviewed and selected: 51 papers out of 147 submissions for the design and analysis track and 16 out of 53 submissions in the engineering and applications track. The papers address all current subjects in algorithmics reaching from design and analysis issues of algorithms over to real-world applications and engineering of algorithms in various fields. Special focus is given to mathematical programming and operations research, including combinatorial optimization, integer programming, polyhedral combinatorics and network optimization.
Author: Victor Parada
Publisher: CRC Press
ISBN: 104030706X
Category : Computers
Languages : en
Pages : 215
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Book Description
In the rapidly evolving domain of computational problem-solving, this book delves into the cutting-edge Automatic Generation of Algorithms (AGA) paradigm, a groundbreaking approach poised to redefine algorithm design for optimization problems. Spanning combinatorial optimization, machine learning, genetic programming, and beyond, it investigates AGA's transformative capabilities across diverse application areas. The book initiates by introducing fundamental combinatorial optimization concepts and NPhardness significance, laying the foundation for understanding AGA's necessity and potential. It then scrutinizes the pivotal Master Problem concept in AGA and the art of modeling for algorithm generation. The exploration progresses with integrating genetic programming and synergizing AGA with evolutionary computing. Subsequent chapters delve into the AGA-machine learning intersection, highlighting their shared optimization foundation while contrasting divergent objectives. The automatic generation of metaheuristics is examined, aiming to develop versatile algorithmic frameworks adaptable to various optimization problems. Furthermore, the book explores applying reinforcement learning techniques to automatic algorithm generation. Throughout, it invites readers to reimagine algorithmic design boundaries, offering insights into AGA's conceptual underpinnings, practical applications, and future directions, serving as an invitation for researchers, practitioners, and enthusiasts in computer science, operations research, artificial intelligence, and beyond to embark on a journey toward computational excellence where algorithms are born, evolved, and adapted to meet ever-changing real-world problem landscapes.
Author: Antonio J. Conejo
Publisher: Springer Science & Business Media
ISBN: 3540276866
Category : Technology & Engineering
Languages : en
Pages : 542
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Book Description
Optimization plainly dominates the design, planning, operation, and c- trol of engineering systems. This is a book on optimization that considers particular cases of optimization problems, those with a decomposable str- ture that can be advantageously exploited. Those decomposable optimization problems are ubiquitous in engineering and science applications. The book considers problems with both complicating constraints and complicating va- ables, and analyzes linear and nonlinear problems, with and without in- ger variables. The decomposition techniques analyzed include Dantzig-Wolfe, Benders, Lagrangian relaxation, Augmented Lagrangian decomposition, and others. Heuristic techniques are also considered. Additionally, a comprehensive sensitivity analysis for characterizing the solution of optimization problems is carried out. This material is particularly novel and of high practical interest. This book is built based on many clarifying, illustrative, and compu- tional examples, which facilitate the learning procedure. For the sake of cl- ity, theoretical concepts and computational algorithms are assembled based on these examples. The results are simplicity, clarity, and easy-learning. We feel that this book is needed by the engineering community that has to tackle complex optimization problems, particularly by practitioners and researchersinEngineering,OperationsResearch,andAppliedEconomics.The descriptions of most decomposition techniques are available only in complex and specialized mathematical journals, di?cult to understand by engineers. A book describing a wide range of decomposition techniques, emphasizing problem-solving, and appropriately blending theory and application, was not previously available.
Author: Mordecai Avriel
Publisher: CRC Press
ISBN: 9780824796204
Category : Mathematics
Languages : en
Pages : 662
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Book Description
Setting out to bridge the gap between the theory of mathematical programming and the varied, real-world practices of industrial engineers, this work introduces developments in linear, integer, multiobjective, stochastic, network and dynamic programing. It details many relevant industrial-engineering applications.;College or university bookstores may order five or more copies at a special student price, available upon request from Marcel Dekker, Inc.
