Download or read book Large scale Optimization Methods for Data science Applications written by Haihao Lu (Ph.D.) and published by . This book was released on 2019 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we present several contributions of large scale optimization methods with the applications in data science and machine learning. In the first part, we present new computational methods and associated computational guarantees for solving convex optimization problems using first-order methods. We consider general convex optimization problem, where we presume knowledge of a strict lower bound (like what happened in empirical risk minimization in machine learning). We introduce a new functional measure called the growth constant for the convex objective function, that measures how quickly the level sets grow relative to the function value, and that plays a fundamental role in the complexity analysis. Based on such measure, we present new computational guarantees for both smooth and non-smooth convex optimization, that can improve existing computational guarantees in several ways, most notably when the initial iterate is far from the optimal solution set. The usual approach to developing and analyzing first-order methods for convex optimization always assumes that either the gradient of the objective function is uniformly continuous (in the smooth setting) or the objective function itself is uniformly continuous. However, in many settings, especially in machine learning applications, the convex function is neither of them. For example, the Poisson Linear Inverse Model, the D-optimal design problem, the Support Vector Machine problem, etc. In the second part, we develop a notion of relative smoothness, relative continuity and relative strong convexity that is determined relative to a user-specified "reference function" (that should be computationally tractable for algorithms), and we show that many differentiable convex functions are relatively smooth or relatively continuous with respect to a correspondingly fairly-simple reference function. We extend the mirror descent algorithm to our new setting, with associated computational guarantees. Gradient Boosting Machine (GBM) introduced by Friedman is an extremely powerful supervised learning algorithm that is widely used in practice -- it routinely features as a leading algorithm in machine learning competitions such as Kaggle and the KDDCup. In the third part, we propose the Randomized Gradient Boosting Machine (RGBM) and the Accelerated Gradient Boosting Machine (AGBM). RGBM leads to significant computational gains compared to GBM, by using a randomization scheme to reduce the search in the space of weak-learners. AGBM incorporate Nesterov's acceleration techniques into the design of GBM, and this is the first GBM type of algorithm with theoretically-justified accelerated convergence rate. We demonstrate the effectiveness of RGBM and AGBM over GBM in obtaining a model with good training and/or testing data fidelity..

Download or read book Large scale Optimization Methods written by Nuri Denizcan Vanli and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large-scale optimization problems appear quite frequently in data science and machine learning applications. In this thesis, we show the efficiency of coordinate descent (CD) and mirror descent (MD) methods in solving large-scale optimization problems.

Download or read book Large Scale and Distributed Optimization written by Pontus Giselsson and published by Springer. This book was released on 2018-11-11 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents tools and methods for large-scale and distributed optimization. Since many methods in "Big Data" fields rely on solving large-scale optimization problems, often in distributed fashion, this topic has over the last decade emerged to become very important. As well as specific coverage of this active research field, the book serves as a powerful source of information for practitioners as well as theoreticians. Large-Scale and Distributed Optimization is a unique combination of contributions from leading experts in the field, who were speakers at the LCCC Focus Period on Large-Scale and Distributed Optimization, held in Lund, 14th–16th June 2017. A source of information and innovative ideas for current and future research, this book will appeal to researchers, academics, and students who are interested in large-scale optimization.

Download or read book Optimization for Data Analysis written by Stephen J. Wright and published by Cambridge University Press. This book was released on 2022-04-21 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise text that presents and analyzes the fundamental techniques and methods in optimization that are useful in data science.

Download or read book Optimization for Machine Learning written by Suvrit Sra and published by MIT Press. This book was released on 2012 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date account of the interplay between optimization and machine learning, accessible to students and researchers in both communities. The interplay between optimization and machine learning is one of the most important developments in modern computational science. Optimization formulations and methods are proving to be vital in designing algorithms to extract essential knowledge from huge volumes of data. Machine learning, however, is not simply a consumer of optimization technology but a rapidly evolving field that is itself generating new optimization ideas. This book captures the state of the art of the interaction between optimization and machine learning in a way that is accessible to researchers in both fields. Optimization approaches have enjoyed prominence in machine learning because of their wide applicability and attractive theoretical properties. The increasing complexity, size, and variety of today's machine learning models call for the reassessment of existing assumptions. This book starts the process of reassessment. It describes the resurgence in novel contexts of established frameworks such as first-order methods, stochastic approximations, convex relaxations, interior-point methods, and proximal methods. It also devotes attention to newer themes such as regularized optimization, robust optimization, gradient and subgradient methods, splitting techniques, and second-order methods. Many of these techniques draw inspiration from other fields, including operations research, theoretical computer science, and subfields of optimization. The book will enrich the ongoing cross-fertilization between the machine learning community and these other fields, and within the broader optimization community.

Download or read book Large Scale Convex Optimization written by Ernest K. Ryu and published by Cambridge University Press. This book was released on 2022-12-01 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting from where a first course in convex optimization leaves off, this text presents a unified analysis of first-order optimization methods – including parallel-distributed algorithms – through the abstraction of monotone operators. With the increased computational power and availability of big data over the past decade, applied disciplines have demanded that larger and larger optimization problems be solved. This text covers the first-order convex optimization methods that are uniquely effective at solving these large-scale optimization problems. Readers will have the opportunity to construct and analyze many well-known classical and modern algorithms using monotone operators, and walk away with a solid understanding of the diverse optimization algorithms. Graduate students and researchers in mathematical optimization, operations research, electrical engineering, statistics, and computer science will appreciate this concise introduction to the theory of convex optimization algorithms.

Download or read book Big Data Optimization Recent Developments and Challenges written by Ali Emrouznejad and published by Springer. This book was released on 2016-05-26 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main objective of this book is to provide the necessary background to work with big data by introducing some novel optimization algorithms and codes capable of working in the big data setting as well as introducing some applications in big data optimization for both academics and practitioners interested, and to benefit society, industry, academia, and government. Presenting applications in a variety of industries, this book will be useful for the researchers aiming to analyses large scale data. Several optimization algorithms for big data including convergent parallel algorithms, limited memory bundle algorithm, diagonal bundle method, convergent parallel algorithms, network analytics, and many more have been explored in this book.

Download or read book Optimization Methods for Large Scale Problems and Applications to Machine Learning written by Luca Bravi and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Large scale Optimization written by Vladimir Tsurkov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Decomposition methods aim to reduce large-scale problems to simpler problems. This monograph presents selected aspects of the dimension-reduction problem. Exact and approximate aggregations of multidimensional systems are developed and from a known model of input-output balance, aggregation methods are categorized. The issues of loss of accuracy, recovery of original variables (disaggregation), and compatibility conditions are analyzed in detail. The method of iterative aggregation in large-scale problems is studied. For fixed weights, successively simpler aggregated problems are solved and the convergence of their solution to that of the original problem is analyzed. An introduction to block integer programming is considered. Duality theory, which is widely used in continuous block programming, does not work for the integer problem. A survey of alternative methods is presented and special attention is given to combined methods of decomposition. Block problems in which the coupling variables do not enter the binding constraints are studied. These models are worthwhile because they permit a decomposition with respect to primal and dual variables by two-level algorithms instead of three-level algorithms. Audience: This book is addressed to specialists in operations research, optimization, and optimal control.

Download or read book Approximation and Optimization written by Ioannis C. Demetriou and published by Springer. This book was released on 2019-05-10 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the development of approximation-related algorithms and their relevant applications. Individual contributions are written by leading experts and reflect emerging directions and connections in data approximation and optimization. Chapters discuss state of the art topics with highly relevant applications throughout science, engineering, technology and social sciences. Academics, researchers, data science practitioners, business analysts, social sciences investigators and graduate students will find the number of illustrations, applications, and examples provided useful. This volume is based on the conference Approximation and Optimization: Algorithms, Complexity, and Applications, which was held in the National and Kapodistrian University of Athens, Greece, June 29–30, 2017. The mix of survey and research content includes topics in approximations to discrete noisy data; binary sequences; design of networks and energy systems; fuzzy control; large scale optimization; noisy data; data-dependent approximation; networked control systems; machine learning ; optimal design; no free lunch theorem; non-linearly constrained optimization; spectroscopy.

Download or read book Online Optimization of Large Scale Systems written by Martin Grötschel and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 789 pages. Available in PDF, EPUB and Kindle. Book excerpt: In its thousands of years of history, mathematics has made an extraordinary ca reer. It started from rules for bookkeeping and computation of areas to become the language of science. Its potential for decision support was fully recognized in the twentieth century only, vitally aided by the evolution of computing and communi cation technology. Mathematical optimization, in particular, has developed into a powerful machinery to help planners. Whether costs are to be reduced, profits to be maximized, or scarce resources to be used wisely, optimization methods are available to guide decision making. Opti mization is particularly strong if precise models of real phenomena and data of high quality are at hand - often yielding reliable automated control and decision proce dures. But what, if the models are soft and not all data are around? Can mathematics help as well? This book addresses such issues, e. g. , problems of the following type: - An elevator cannot know all transportation requests in advance. In which order should it serve the passengers? - Wing profiles of aircrafts influence the fuel consumption. Is it possible to con tinuously adapt the shape of a wing during the flight under rapidly changing conditions? - Robots are designed to accomplish specific tasks as efficiently as possible. But what if a robot navigates in an unknown environment? - Energy demand changes quickly and is not easily predictable over time. Some types of power plants can only react slowly.

Download or read book Evolutionary Large Scale Multi Objective Optimization and Applications written by Xingyi Zhang and published by John Wiley & Sons. This book was released on 2024-09-11 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tackle the most challenging problems in science and engineering with these cutting-edge algorithms Multi-objective optimization problems (MOPs) are those in which more than one objective needs to be optimized simultaneously. As a ubiquitous component of research and engineering projects, these problems are notoriously challenging. In recent years, evolutionary algorithms (EAs) have shown significant promise in their ability to solve MOPs, but challenges remain at the level of large-scale multi-objective optimization problems (LSMOPs), where the number of variables increases and the optimized solution is correspondingly harder to reach. Evolutionary Large-Scale Multi-Objective Optimization and Applications constitutes a systematic overview of EAs and their capacity to tackle LSMOPs. It offers an introduction to both the problem class and the algorithms before delving into some of the cutting-edge algorithms which have been specifically adapted to solving LSMOPs. Deeply engaged with specific applications and alert to the latest developments in the field, it’s a must-read for students and researchers facing these famously complex but crucial optimization problems. The book’s readers will also find: Analysis of multi-optimization problems in fields such as machine learning, network science, vehicle routing, and more Discussion of benchmark problems and performance indicators for LSMOPs Presentation of a new taxonomy of algorithms in the field Evolutionary Large-Scale Multi-Objective Optimization and Applications is ideal for advanced students, researchers, and scientists and engineers facing complex optimization problems.

Download or read book Essays in Large Scale Optimization Algorithm and Its Application in Revenue Management written by Mingxi Zhu (Researcher in optimization algorithms) and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation focuses on the large-scale optimization algorithm and its application in revenue management. It comprises three chapters. Chapter 1, Managing Randomization in the Multi-Block Alternating Direction Method of Multipliers for Quadratic Optimization, provides theoretical foundations for managing randomization in the multi-block alternating direction method of multipliers (ADMM) method for quadratic optimization. Chapter 2, How a Small Amount of Data Sharing Benefits Distributed Optimization and Learning, presents both the theoretical and practical evidences on sharing a small amount of data could hugely benefit distributed optimization and learning. Chapter 3, Dynamic Exploration and Exploitation: The Case of Online Lending, studies exploration/ exploitation trade-offs, and the value of dynamic extracting information in the context of online lending. The first chapter is a joint work with Kresimir Mihic and Yinyu Ye. The Alternating Direction Method of Multipliers (ADMM) has gained a lot of attention for solving large-scale and objective-separable constrained optimization. However, the two-block variable structure of the ADMM still limits the practical computational efficiency of the method, because one big matrix factorization is needed at least once even for linear and convex quadratic programming. This drawback may be overcome by enforcing a multi-block structure of the decision variables in the original optimization problem. Unfortunately, the multi-block ADMM, with more than two blocks, is not guaranteed to be convergent. On the other hand, two positive developments have been made: first, if in each cyclic loop one randomly permutes the updating order of the multiple blocks, then the method converges in expectation for solving any system of linear equations with any number of blocks. Secondly, such a randomly permuted ADMM also works for equality-constrained convex quadratic programming even when the objective function is not separable. The goal of this paper is twofold. First, we add more randomness into the ADMM by developing a randomly assembled cyclic ADMM (RAC-ADMM) where the decision variables in each block are randomly assembled. We discuss the theoretical properties of RAC-ADMM and show when random assembling helps and when it hurts, and develop a criterion to guarantee that it converges almost surely. Secondly, using the theoretical guidance on RAC-ADMM, we conduct multiple numerical tests on solving both randomly generated and large-scale benchmark quadratic optimization problems, which include continuous, and binary graph-partition and quadratic assignment, and selected machine learning problems. Our numerical tests show that the RAC-ADMM, with a variable-grouping strategy, could significantly improve the computation efficiency on solving most quadratic optimization problems. The second chapter is a joint work with Yinyu Ye. Distributed optimization algorithms have been widely used in machine learning and statistical estimation, especially under the context where multiple decentralized data centers exist and the decision maker is required to perform collaborative learning across those centers. While distributed optimization algorithms have the merits in parallel processing and protecting local data security, they often suffer from slow convergence compared with centralized optimization algorithms. This paper focuses on how small amount of data sharing could benefit distributed optimization and learning for more advanced optimization algorithms. Specifically, we consider how data sharing could benefit distributed multi-block alternating direction method of multipliers (ADMM) and preconditioned conjugate gradient method (PCG) with application in machine learning tasks of linear and logistic regression. These algorithms are commonly known as algorithms between the first and the second order methods, and we show that data share could hugely boost the convergence speed for this class of the algorithms. Theoretically, we prove that a small amount of data share leads to improvements from near-worst to near-optimal convergence rate when applying ADMM and PCG methods to machine learning tasks. A side theory product is the tight upper bound of linear convergence rate for distributed ADMM applied in linear regression. We further propose a meta randomized data-sharing scheme and provide its tailored applications in multi-block ADMM and PCG methods in order to enjoy both the benefit from data-sharing and from the efficiency of distributed computing. From the numerical evidences, we are convinced that our algorithms provide good quality of estimators in both the least square and the logistic regressions within much fewer iterations by only sharing 5% of pre-fixed data, while purely distributed optimization algorithms may take hundreds more times of iterations to converge. We hope that the discovery resulted from this paper would encourage even small amount of data sharing among different regions to combat difficult global learning problems. The third chapter is a joint work with Haim Mendelson. This paper studies exploration and exploitation tradeoffs in the context of online lending. Unlike traditional contexts where the cost of exploration is an opportunity cost of lost revenue or some other implicit cost, in the case of unsecured online lending, the lender effectively gives away money in order to learn about the borrower's ability to repay. In our model, the lender maximizes the expected net present value of the cash flow she receives by dynamically adjusting the loan amounts and the interest (discount) rate as she learns about the borrower's unknown income. The lender has to carefully balance the trade-offs between earning more interest when she lends more and the risk of default, and we provided the optimal dynamic policy for the lender. The optimal policy support the classic "lean experimentation" in certain regime, while challenge such concept in other regime. When the demand elasticity is zero (the discount rate is set exogenously), or the elasticity a decreasing function of the discount rate, the optimal policy is characterized by a large number of small experiments with increasing repayment amounts. When the demand elasticity is constant or when it is an increasing function of the discount rate, we obtain a two-step optimal policy: the lender performs a single experiment and then, if the borrower repays the loan, offers the same loan amount and discount rate in each subsequent period without any further experimentation. This result sheds light in how to take into account the market churn measured by elasticity, in the dynamic experiment design under uncertain environment. We further provide the implications under the optimal policies, including the impact of the income variability, the value of information and the consumer segmentation. Lastly, we extend the methodology to analyze the Buy-Now-Pay-Later business model and provide the policy suggestions.

Download or read book Large Scale Convex Optimization written by Ernest K. Ryu and published by Cambridge University Press. This book was released on 2022-11-30 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified analysis of first-order optimization methods, including parallel-distributed algorithms, using monotone operators.

Download or read book Proceedings of COMPSTAT 2010 written by Yves Lechevallier and published by Springer Science & Business Media. This book was released on 2010-11-08 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the 19th international symposium on computational statistics, held in Paris august 22-27, 2010.Together with 3 keynote talks, there were 14 invited sessions and more than 100 peer-reviewed contributed communications.

Download or read book Resource Management for Big Data Platforms written by Florin Pop and published by Springer. This book was released on 2016-10-27 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: Serving as a flagship driver towards advance research in the area of Big Data platforms and applications, this book provides a platform for the dissemination of advanced topics of theory, research efforts and analysis, and implementation oriented on methods, techniques and performance evaluation. In 23 chapters, several important formulations of the architecture design, optimization techniques, advanced analytics methods, biological, medical and social media applications are presented. These chapters discuss the research of members from the ICT COST Action IC1406 High-Performance Modelling and Simulation for Big Data Applications (cHiPSet). This volume is ideal as a reference for students, researchers and industry practitioners working in or interested in joining interdisciplinary works in the areas of intelligent decision systems using emergent distributed computing paradigms. It will also allow newcomers to grasp the key concerns and their potential solutions.

Download or read book Optimization and Its Applications in Control and Data Sciences written by Boris Goldengorin and published by Springer. This book was released on 2016-09-29 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on recent research in modern optimization and its implications in control and data analysis. This book is a collection of papers from the conference “Optimization and Its Applications in Control and Data Science” dedicated to Professor Boris T. Polyak, which was held in Moscow, Russia on May 13-15, 2015. This book reflects developments in theory and applications rooted by Professor Polyak’s fundamental contributions to constrained and unconstrained optimization, differentiable and nonsmooth functions, control theory and approximation. Each paper focuses on techniques for solving complex optimization problems in different application areas and recent developments in optimization theory and methods. Open problems in optimization, game theory and control theory are included in this collection which will interest engineers and researchers working with efficient algorithms and software for solving optimization problems in market and data analysis. Theoreticians in operations research, applied mathematics, algorithm design, artificial intelligence, machine learning, and software engineering will find this book useful and graduate students will find the state-of-the-art research valuable.