Download or read book Bayesian and High Dimensional Global Optimization written by Anatoly Zhigljavsky and published by Springer Nature. This book was released on 2021-03-02 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible to a variety of readers, this book is of interest to specialists, graduate students and researchers in mathematics, optimization, computer science, operations research, management science, engineering and other applied areas interested in solving optimization problems. Basic principles, potential and boundaries of applicability of stochastic global optimization techniques are examined in this book. A variety of issues that face specialists in global optimization are explored, such as multidimensional spaces which are frequently ignored by researchers. The importance of precise interpretation of the mathematical results in assessments of optimization methods is demonstrated through examples of convergence in probability of random search. Methodological issues concerning construction and applicability of stochastic global optimization methods are discussed, including the one-step optimal average improvement method based on a statistical model of the objective function. A significant portion of this book is devoted to an analysis of high-dimensional global optimization problems and the so-called ‘curse of dimensionality’. An examination of the three different classes of high-dimensional optimization problems, the geometry of high-dimensional balls and cubes, very slow convergence of global random search algorithms in large-dimensional problems , and poor uniformity of the uniformly distributed sequences of points are included in this book.
Download or read book Bayesian and High Dimensional Global Optimization Bi objective decisions and partition based methods in Bayesian global optimization written by Anatoly Zhigljavsky and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible to a variety of readers, this book is of interest to specialists, graduate students and researchers in mathematics, optimization, computer science, operations research, management science, engineering and other applied areas interested in solving optimization problems. Basic principles, potential and boundaries of applicability of stochastic global optimization techniques are examined in this book. A variety of issues that face specialists in global optimization are explored, such as multidimensional spaces which are frequently ignored by researchers. The importance of precise interpretation of the mathematical results in assessments of optimization methods is demonstrated through examples of convergence in probability of random search. Methodological issues concerning construction and applicability of stochastic global optimization methods are discussed, including the one-step optimal average improvement method based on a statistical model of the objective function. A significant portion of this book is devoted to an analysis of high-dimensional global optimization problems and the so-called 'curse of dimensionality'. An examination of the three different classes of high-dimensional optimization problems, the geometry of high-dimensional balls and cubes, very slow convergence of global random search algorithms in large-dimensional problems , and poor uniformity of the uniformly distributed sequences of points are included in this book. .
Download or read book Bayesian Approach to Global Optimization written by Jonas Mockus and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: ·Et moi ... si j'avait su comment en revcnir. One service mathematics has rendered the je o'y semis point alle.' human race. It has put common sense back Jules Verne where it beloogs. on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense', able to do something with it. Eric T. BclI O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ... '; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Download or read book Bayesian Heuristic Approach to Discrete and Global Optimization written by Jonas Mockus and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian decision theory is known to provide an effective framework for the practical solution of discrete and nonconvex optimization problems. This book is the first to demonstrate that this framework is also well suited for the exploitation of heuristic methods in the solution of such problems, especially those of large scale for which exact optimization approaches can be prohibitively costly. The book covers all aspects ranging from the formal presentation of the Bayesian Approach, to its extension to the Bayesian Heuristic Strategy, and its utilization within the informal, interactive Dynamic Visualization strategy. The developed framework is applied in forecasting, in neural network optimization, and in a large number of discrete and continuous optimization problems. Specific application areas which are discussed include scheduling and visualization problems in chemical engineering, manufacturing process control, and epidemiology. Computational results and comparisons with a broad range of test examples are presented. The software required for implementation of the Bayesian Heuristic Approach is included. Although some knowledge of mathematical statistics is necessary in order to fathom the theoretical aspects of the development, no specialized mathematical knowledge is required to understand the application of the approach or to utilize the software which is provided. Audience: The book is of interest to both researchers in operations research, systems engineering, and optimization methods, as well as applications specialists concerned with the solution of large scale discrete and/or nonconvex optimization problems in a broad range of engineering and technological fields. It may be used as supplementary material for graduate level courses.
Download or read book The Bayesian Approach to Global Optimization written by Jonas Mockus and published by . This book was released on 1984 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bayesian Optimization and Data Science written by Francesco Archetti and published by Springer Nature. This book was released on 2019-09-25 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings together the main results in the field of Bayesian Optimization (BO), focusing on the last ten years and showing how, on the basic framework, new methods have been specialized to solve emerging problems from machine learning, artificial intelligence, and system optimization. It also analyzes the software resources available for BO and a few selected application areas. Some areas for which new results are shown include constrained optimization, safe optimization, and applied mathematics, specifically BO's use in solving difficult nonlinear mixed integer problems. The book will help bring readers to a full understanding of the basic Bayesian Optimization framework and gain an appreciation of its potential for emerging application areas. It will be of particular interest to the data science, computer science, optimization, and engineering communities.
Download or read book Stochastic Global Optimization written by Anatoly Zhigljavsky and published by Springer Science & Business Media. This book was released on 2007-11-20 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the main methodological and theoretical developments in stochastic global optimization. It is designed to inspire readers to explore various stochastic methods of global optimization by clearly explaining the main methodological principles and features of the methods. Among the book’s features is a comprehensive study of probabilistic and statistical models underlying the stochastic optimization algorithms.
Download or read book Bayesian Heuristic Approach to Discrete and Global Optimization written by Jonas Mockus and published by Springer. This book was released on 1996-12-31 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian decision theory is known to provide an effective framework for the practical solution of discrete and nonconvex optimization problems. This book is the first to demonstrate that this framework is also well suited for the exploitation of heuristic methods in the solution of such problems, especially those of large scale for which exact optimization approaches can be prohibitively costly. The book covers all aspects ranging from the formal presentation of the Bayesian Approach, to its extension to the Bayesian Heuristic Strategy, and its utilization within the informal, interactive Dynamic Visualization strategy. The developed framework is applied in forecasting, in neural network optimization, and in a large number of discrete and continuous optimization problems. Specific application areas which are discussed include scheduling and visualization problems in chemical engineering, manufacturing process control, and epidemiology. Computational results and comparisons with a broad range of test examples are presented. The software required for implementation of the Bayesian Heuristic Approach is included. Although some knowledge of mathematical statistics is necessary in order to fathom the theoretical aspects of the development, no specialized mathematical knowledge is required to understand the application of the approach or to utilize the software which is provided. Audience: The book is of interest to both researchers in operations research, systems engineering, and optimization methods, as well as applications specialists concerned with the solution of large scale discrete and/or nonconvex optimization problems in a broad range of engineering and technological fields. It may be used as supplementary material for graduate level courses.
Download or read book Bayesian Optimization written by Peng Liu and published by Apress. This book was released on 2023-04-10 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the essential theory and implementation of popular Bayesian optimization techniques in an intuitive and well-illustrated manner. The techniques covered in this book will enable you to better tune the hyperparemeters of your machine learning models and learn sample-efficient approaches to global optimization. The book begins by introducing different Bayesian Optimization (BO) techniques, covering both commonly used tools and advanced topics. It follows a “develop from scratch” method using Python, and gradually builds up to more advanced libraries such as BoTorch, an open-source project introduced by Facebook recently. Along the way, you’ll see practical implementations of this important discipline along with thorough coverage and straightforward explanations of essential theories. This book intends to bridge the gap between researchers and practitioners, providing both with a comprehensive, easy-to-digest, and useful reference guide. After completing this book, you will have a firm grasp of Bayesian optimization techniques, which you’ll be able to put into practice in your own machine learning models. What You Will Learn Apply Bayesian Optimization to build better machine learning models Understand and research existing and new Bayesian Optimization techniques Leverage high-performance libraries such as BoTorch, which offer you the ability to dig into and edit the inner working Dig into the inner workings of common optimization algorithms used to guide the search process in Bayesian optimization Who This Book Is ForBeginner to intermediate level professionals in machine learning, analytics or other roles relevant in data science.
Download or read book Bayesian Optimization written by Roman Garnett and published by Cambridge University Press. This book was released on 2023-01-31 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian optimization is a methodology for optimizing expensive objective functions that has proven success in the sciences, engineering, and beyond. This timely text provides a self-contained and comprehensive introduction to the subject, starting from scratch and carefully developing all the key ideas along the way. This bottom-up approach illuminates unifying themes in the design of Bayesian optimization algorithms and builds a solid theoretical foundation for approaching novel situations. The core of the book is divided into three main parts, covering theoretical and practical aspects of Gaussian process modeling, the Bayesian approach to sequential decision making, and the realization and computation of practical and effective optimization policies. Following this foundational material, the book provides an overview of theoretical convergence results, a survey of notable extensions, a comprehensive history of Bayesian optimization, and an extensive annotated bibliography of applications.
Download or read book Scaling Bayesian Optimization for Engineering Design written by Remi Roger Alain Paul Lam and published by . This book was released on 2018 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective functions and constraints that arise in engineering design problems are often non-convex, multi-modal and do not have closed-form expressions. Evaluation of these functions can be expensive, requiring a time-consuming computation (e.g., solving a set of partial differential equations) or a costly experiment (e.g., conducting wind-tunnel measurements). Accordingly, whether the task is formal optimization or just design space exploration, there is often a finite budget specifying the maximum number of evaluations of the objectives and constraints allowed. Bayesian optimization (BO) has become a popular global optimization technique for solving problems governed by such expensive functions. BO iteratively updates a statistical model and uses it to quantify the expected benefits of evaluating a given design under consideration. The next design to evaluate can be selected in order to maximize such benefits. Most existing BO algorithms are greedy strategies, making decisions to maximize the immediate benefits, without planning over several steps. This is typically a suboptimal approach. In the first part of this thesis, we develop a novel BO algorithm with planning capabilities. This algorithm selects the next design to evaluate in order to maximize the long-term expected benefit obtained at the end of the optimization. This lookahead approach requires tools to quantify the effects a decision has over several steps in the future. To do so, we use Gaussian processes as generative models and combine them with dynamic programming to formulate the optimal planning strategy. We first illustrate the proposed algorithm on unconstrained optimization problems. In the second part, we demonstrate how the proposed lookahead BO algorithm can be extended to handle non-linear expensive inequality constraints, a ubiquitous situation in engineering design. We illustrate the proposed lookahead constrained BO algorithm on a reacting flow optimization problem. In the last part of this thesis, we develop techniques to scale BO to high dimension by exploiting a special structure arising when the objective function varies only in a low-dimensional subspace. Such a subspace can be detected using the (randomized) method of Active Subspaces. We propose a multifidelity active subspace algorithm that reduces the computational cost by leveraging a cheap-to-evaluate approximation of the objective function. We analyze the number of evaluations sufficient to control the error incurred, both in expectation and with high probability. We illustrate the proposed algorithm on an ONERA M6 wing shape-optimization problem.
Download or read book A Set of Examples of Global and Discrete Optimization written by Jonas Mockus and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows how the Bayesian Approach (BA) improves well known heuristics by randomizing and optimizing their parameters. That is the Bayesian Heuristic Approach (BHA). The ten in-depth examples are designed to teach Operations Research using Internet. Each example is a simple representation of some impor tant family of real-life problems. The accompanying software can be run by remote Internet users. The supporting web-sites include software for Java, C++, and other lan guages. A theoretical setting is described in which one can discuss a Bayesian adaptive choice of heuristics for discrete and global optimization prob lems. The techniques are evaluated in the spirit of the average rather than the worst case analysis. In this context, "heuristics" are understood to be an expert opinion defining how to solve a family of problems of dis crete or global optimization. The term "Bayesian Heuristic Approach" means that one defines a set of heuristics and fixes some prior distribu tion on the results obtained. By applying BHA one is looking for the heuristic that reduces the average deviation from the global optimum. The theoretical discussions serve as an introduction to examples that are the main part of the book. All the examples are interconnected. Dif ferent examples illustrate different points of the general subject. How ever, one can consider each example separately, too.
Download or read book Bayesian Optimization in Action written by Quan Nguyen and published by Simon and Schuster. This book was released on 2023-11-14 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian Optimization in Action teaches you how to build Bayesian Optimisation systems from the ground up. This book transforms state-of-the-art research into usable techniques you can easily put into practice. With a range of illustrations, and concrete examples, this book proves that Bayesian Optimisation doesn't have to be difficult!
Download or read book Bayesian Optimization with Parallel Function Evaluations and Multiple Information Sources written by Jialei Wang and published by . This book was released on 2017 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian optimization, a framework for global optimization of expensive-to-evaluate functions, has recently gained popularity in machine learning and global optimization because it can find good feasible points with few function evaluations. In this dissertation, we present novel Bayesian optimization algorithms for problems with parallel function evaluations and multiple information sources, for use in machine learning, biochemistry, and aerospace engineering applications. First, we present a novel algorithm that extends expected improvement, a widely-used Bayesian optimization algorithm that evaluates one point at a time, to settings with parallel function evaluations. This algorithm is based on a new efficient solution method for finding the Bayes-optimal set of points to evaluate next in the context of parallel Bayesian optimization. The author implemented this algorithm in an open source software package co-developed with engineers at Yelp, which was used by Yelp and Netflix for automatic tuning of hyperparameters in machine learning algorithms, and for choosing parameters in online content delivery systems based on evaluations in A/B tests on live traffic. Second, we present a novel parallel Bayesian optimization algorithm with a worst-case approximation guarantee applied to peptide optimization in biochemistry, where we face a large collection of peptides with unknown fitness prior to experimentation, and our goal is to identify peptides with a high score using a small number of experiments. High scoring peptides can be used for biolabeling, targeted drug delivery, and self-assembly of metamaterials. This problem has two novelties: first, unlike traditional Bayesian optimization, where the objective function has a continuous domain and real-valued output well-modeled by a Gaussian Process, this problem has a discrete domain, and involves binary output not well-modeled by a Gaussian process; second, it uses hundreds of parallel function evaluations, which is a level of parallelism too large to be approached with other previously-proposed parallel Bayesian optimization methods. Third, we present a novel Bayesian optimization algorithm for problems in which there are multiple methods or "information sources" for evaluating the objective function, each with its own bias, noise and cost of evaluation. For example, in aerospace engineering, to evaluate an aircraft wing design, different computational models may simulate performance. Our algorithm explores the correlation and model discrepancy of each information source, and optimally chooses the information source to evaluate next and the point at which to evaluate it. We describe how this algorithm can be used in general multi information source optimization problems, and also how a related algorithm can be used in "warm start" problems, where we have results from previous optimizations of closely related objective functions, and we wish to leverage these results to more quickly optimize a new objective function.
Download or read book High dimensional Bayesian Optimization with Intrinsically Low dimensional Response Surfaces written by Riccardo Moriconi and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Global Optimization written by Aimo Törn and published by . This book was released on 1989 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bayesian Optimization with Application to Computer Experiments written by Tony Pourmohamad and published by Springer Nature. This book was released on 2021-10-04 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces readers to Bayesian optimization, highlighting advances in the field and showcasing its successful applications to computer experiments. R code is available as online supplementary material for most included examples, so that readers can better comprehend and reproduce methods. Compact and accessible, the volume is broken down into four chapters. Chapter 1 introduces the reader to the topic of computer experiments; it includes a variety of examples across many industries. Chapter 2 focuses on the task of surrogate model building and contains a mix of several different surrogate models that are used in the computer modeling and machine learning communities. Chapter 3 introduces the core concepts of Bayesian optimization and discusses unconstrained optimization. Chapter 4 moves on to constrained optimization, and showcases some of the most novel methods found in the field. This will be a useful companion to researchers and practitioners working with computer experiments and computer modeling. Additionally, readers with a background in machine learning but minimal background in computer experiments will find this book an interesting case study of the applicability of Bayesian optimization outside the realm of machine learning.
