Download or read book Optimization Algorithms for Distributed Machine Learning written by Gauri Joshi and published by Springer Nature. This book was released on 2022-11-25 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses state-of-the-art stochastic optimization algorithms for distributed machine learning and analyzes their convergence speed. The book first introduces stochastic gradient descent (SGD) and its distributed version, synchronous SGD, where the task of computing gradients is divided across several worker nodes. The author discusses several algorithms that improve the scalability and communication efficiency of synchronous SGD, such as asynchronous SGD, local-update SGD, quantized and sparsified SGD, and decentralized SGD. For each of these algorithms, the book analyzes its error versus iterations convergence, and the runtime spent per iteration. The author shows that each of these strategies to reduce communication or synchronization delays encounters a fundamental trade-off between error and runtime.

Download or read book Distributed Machine Learning and Gradient Optimization written by Jiawei Jiang and published by Springer Nature. This book was released on 2022-02-23 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the state of the art in distributed machine learning algorithms that are based on gradient optimization methods. In the big data era, large-scale datasets pose enormous challenges for the existing machine learning systems. As such, implementing machine learning algorithms in a distributed environment has become a key technology, and recent research has shown gradient-based iterative optimization to be an effective solution. Focusing on methods that can speed up large-scale gradient optimization through both algorithm optimizations and careful system implementations, the book introduces three essential techniques in designing a gradient optimization algorithm to train a distributed machine learning model: parallel strategy, data compression and synchronization protocol. Written in a tutorial style, it covers a range of topics, from fundamental knowledge to a number of carefully designed algorithms and systems of distributed machine learning. It will appeal to a broad audience in the field of machine learning, artificial intelligence, big data and database management.

Download or read book First order and Stochastic Optimization Methods for Machine Learning written by Guanghui Lan and published by Springer Nature. This book was released on 2020-05-15 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers not only foundational materials but also the most recent progresses made during the past few years on the area of machine learning algorithms. In spite of the intensive research and development in this area, there does not exist a systematic treatment to introduce the fundamental concepts and recent progresses on machine learning algorithms, especially on those based on stochastic optimization methods, randomized algorithms, nonconvex optimization, distributed and online learning, and projection free methods. This book will benefit the broad audience in the area of machine learning, artificial intelligence and mathematical programming community by presenting these recent developments in a tutorial style, starting from the basic building blocks to the most carefully designed and complicated algorithms for machine learning.

Download or read book Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers written by Stephen Boyd and published by Now Publishers Inc. This book was released on 2011 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: Surveys the theory and history of the alternating direction method of multipliers, and discusses its applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others.

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 412 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 Machine Learning and Optimization Models for Optimization in Cloud written by Punit Gupta and published by CRC Press. This book was released on 2022-02-17 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Machine Learning and Models for Optimization in Cloud’s main aim is to meet the user requirement with high quality of service, least time for computation and high reliability. With increase in services migrating over cloud providers, the load over the cloud increases resulting in fault and various security failure in the system results in decreasing reliability. To fulfill this requirement cloud system uses intelligent metaheuristic and prediction algorithm to provide resources to the user in an efficient manner to manage the performance of the system and plan for upcoming requests. Intelligent algorithm helps the system to predict and find a suitable resource for a cloud environment in real time with least computational complexity taking into mind the system performance in under loaded and over loaded condition. This book discusses the future improvements and possible intelligent optimization models using artificial intelligence, deep learning techniques and other hybrid models to improve the performance of cloud. Various methods to enhance the directivity of cloud services have been presented which would enable cloud to provide better services, performance and quality of service to user. It talks about the next generation intelligent optimization and fault model to improve security and reliability of cloud. Key Features · Comprehensive introduction to cloud architecture and its service models. · Vulnerability and issues in cloud SAAS, PAAS and IAAS · Fundamental issues related to optimizing the performance in Cloud Computing using meta-heuristic, AI and ML models · Detailed study of optimization techniques, and fault management techniques in multi layered cloud. · Methods to improve reliability and fault in cloud using nature inspired algorithms and artificial neural network. · Advanced study of algorithms using artificial intelligence for optimization in cloud · Method for power efficient virtual machine placement using neural network in cloud · Method for task scheduling using metaheuristic algorithms. · A study of machine learning and deep learning inspired resource allocation algorithm for cloud in fault aware environment. This book aims to create a research interest & motivation for graduates degree or post-graduates. It aims to present a study on optimization algorithms in cloud for researchers to provide them with a glimpse of future of cloud computing in the era of artificial intelligence.

Download or read book Distributed Machine Learning with Communication Constraints written by Yuchen Zhang and published by . This book was released on 2016 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Distributed machine learning bridges the traditional fields of distributed systems and machine learning, nurturing a rich family of research problems. Classical machine learning algorithms process the data by a single-thread procedure, but as the scale of the dataset and the complexity of the models grow rapidly, it becomes prohibitively slow to process on a single machine. The usage of distributed computing involves several fundamental trade-offs. On one hand, the computation time is reduced by allocating the data to multiple computing nodes. But since the algorithm is parallelized, there are compromises in terms of accuracy and communication cost. Such trade-offs puts our interests in the intersection of multiple areas, including statistical theory, communication complexity theory, information theory and optimization theory. In this thesis, we explore theoretical foundations of distributed machine learning under communication constraints. We study the trade-offs between communication and computation, as well as the trade-off between communication and learning accuracy. In particular settings, we are able to design algorithms that don't compromise on either side. We also establish fundamental limits that apply to all distributed algorithms. In more detail, this thesis makes the following contributions: * We propose communication-efficient algorithms for statistical optimization. These algorithms achieve the best possible statistical accuracy and suffer the least possible computation overhead. * We extend the same algorithmic idea to non-parametric regression, proposing an algorithm which also guarantees the optimal statistical rate and superlinearly reduces the computation time. * In the general setting of regularized empirical risk minimization, we propose a distributed optimization algorithm whose communication cost is independent of the data size, and is only weakly dependent on the number of machines. * We establish lower bounds on the communication complexity of statistical estimation and linear algebraic operations. These lower bounds characterize the fundamental limits of any distributed algorithm. * We design and implement a general framework for parallelizing sequential algorithms. The framework consists of a programming interface and an execution engine. The programming interface allows machine learning experts to implement the algorithm without concerning any detail about the distributed system. The execution engine automatically parallelizes the algorithm in a communication-efficient manner.

Download or read book Distributed Machine Learning and Computing written by M. Hadi Amini and published by Springer Nature. This book was released on with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Distributed Optimization in Networked Systems written by Qingguo Lü and published by Springer Nature. This book was released on 2023-02-08 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on improving the performance (convergence rate, communication efficiency, computational efficiency, etc.) of algorithms in the context of distributed optimization in networked systems and their successful application to real-world applications (smart grids and online learning). Readers may be particularly interested in the sections on consensus protocols, optimization skills, accelerated mechanisms, event-triggered strategies, variance-reduction communication techniques, etc., in connection with distributed optimization in various networked systems. This book offers a valuable reference guide for researchers in distributed optimization and for senior undergraduate and graduate students alike.

Download or read book Optimal Stochastic and Distributed Algorithms for Machine Learning written by Hua Ouyang and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic and data-distributed optimization algorithms have received lots of attention from the machine learning community due to the tremendous demand from the large-scale learning and the big-data related optimization. A lot of stochastic and deterministic learning algorithms are proposed recently under various application scenarios. Nevertheless, many of these algorithms are based on heuristics and their optimality in terms of the generalization error is not sufficiently justified. In this talk, I will explain the concept of an optimal learning algorithm, and show that given a time budget and proper hypothesis space, only those achieving the lower bounds of the estimation error and the optimization error are optimal. Guided by this concept, we investigated the stochastic minimization of nonsmooth convex loss functions, a central problem in machine learning. We proposed a novel algorithm named Accelerated Nonsmooth Stochastic Gradient Descent, which exploits the structure of common nonsmooth loss functions to achieve optimal convergence rates for a class of problems including SVMs. It is the first stochastic algorithm that can achieve the optimal O(1/t) rate for minimizing nonsmooth loss functions. The fast rates are confirmed by empirical comparisons with state-of-the-art algorithms including the averaged SGD. The Alternating Direction Method of Multipliers (ADMM) is another flexible method to explore function structures. In the second part we proposed stochastic ADMM that can be applied to a general class of convex and nonsmooth functions, beyond the smooth and separable least squares loss used in lasso. We also demonstrate the rates of convergence for our algorithm under various structural assumptions of the stochastic function: O(1/sqrt{t}) for convex functions and O(log t/t) for strongly convex functions. A novel application named Graph-Guided SVM is proposed to demonstrate the usefulness of our algorithm. We also extend the scalability of stochastic algorithms to nonlinear kernel machines, where the problem is formulated as a constrained dual quadratic optimization. The simplex constraint can be handled by the classic Frank-Wolfe method. The proposed stochastic Frank-Wolfe methods achieve comparable or even better accuracies than state-of-the-art batch and online kernel SVM solvers, and are significantly faster. The last part investigates the problem of data-distributed learning. We formulate it as a consensus-constrained optimization problem and solve it with ADMM. It turns out that the underlying communication topology is a key factor in achieving a balance between a fast learning rate and computation resource consumption. We analyze the linear convergence behavior of consensus ADMM so as to characterize the interplay between the communication topology and the penalty parameters used in ADMM. We observe that given optimal parameters, the complete bipartite and the master-slave graphs exhibit the fastest convergence, followed by bi-regular graphs.

Download or read book Design of Distributed and Robust Optimization Algorithms A Systems Theoretic Approach written by Simon Michalowsky and published by Logos Verlag Berlin GmbH. This book was released on 2020-04-17 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization algorithms are the backbone of many modern technologies. In this thesis, we address the analysis and design of optimization algorithms from a systems theoretic viewpoint. By properly recasting the algorithm design as a controller synthesis problem, we derive methods that enable a systematic design of tailored optimization algorithms. We consider two specific classes of optimization algorithms: (i) distributed, and (ii) robust optimization algorithms. Concerning (i), we utilize ideas from geometric control in an innovative fashion to derive a novel methodology that enables the design of distributed optimization algorithms under minimal assumptions on the graph topology and the structure of the optimization problem. Concerning (ii), we employ robust control techniques to establish a framework for the analysis of existing algorithms as well as the design of novel robust optimization algorithms with specified guarantees.

Download or read book Distributed Optimization Advances in Theories Methods and Applications written by Huaqing Li and published by Springer Nature. This book was released on 2020-08-04 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a valuable reference guide for researchers in distributed optimization and for senior undergraduate and graduate students alike. Focusing on the natures and functions of agents, communication networks and algorithms in the context of distributed optimization for networked control systems, this book introduces readers to the background of distributed optimization; recent developments in distributed algorithms for various types of underlying communication networks; the implementation of computation-efficient and communication-efficient strategies in the execution of distributed algorithms; and the frameworks of convergence analysis and performance evaluation. On this basis, the book then thoroughly studies 1) distributed constrained optimization and the random sleep scheme, from an agent perspective; 2) asynchronous broadcast-based algorithms, event-triggered communication, quantized communication, unbalanced directed networks, and time-varying networks, from a communication network perspective; and 3) accelerated algorithms and stochastic gradient algorithms, from an algorithm perspective. Finally, the applications of distributed optimization in large-scale statistical learning, wireless sensor networks, and for optimal energy management in smart grids are discussed.

Download or read book Distributed Optimization and Learning written by Zhongguo Li and published by Elsevier. This book was released on 2024-08-06 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Distributed Optimization and Learning: A Control-Theoretic Perspective illustrates the underlying principles of distributed optimization and learning. The book presents a systematic and self-contained description of distributed optimization and learning algorithms from a control-theoretic perspective. It focuses on exploring control-theoretic approaches and how those approaches can be utilized to solve distributed optimization and learning problems over network-connected, multi-agent systems. As there are strong links between optimization and learning, this book provides a unified platform for understanding distributed optimization and learning algorithms for different purposes. Provides a series of the latest results, including but not limited to, distributed cooperative and competitive optimization, machine learning, and optimal resource allocation Presents the most recent advances in theory and applications of distributed optimization and machine learning, including insightful connections to traditional control techniques Offers numerical and simulation results in each chapter in order to reflect engineering practice and demonstrate the main focus of developed analysis and synthesis approaches

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 Accelerated Optimization for Machine Learning written by Zhouchen Lin and published by Springer Nature. This book was released on 2020-05-29 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on optimization includes forewords by Michael I. Jordan, Zongben Xu and Zhi-Quan Luo. Machine learning relies heavily on optimization to solve problems with its learning models, and first-order optimization algorithms are the mainstream approaches. The acceleration of first-order optimization algorithms is crucial for the efficiency of machine learning. Written by leading experts in the field, this book provides a comprehensive introduction to, and state-of-the-art review of accelerated first-order optimization algorithms for machine learning. It discusses a variety of methods, including deterministic and stochastic algorithms, where the algorithms can be synchronous or asynchronous, for unconstrained and constrained problems, which can be convex or non-convex. Offering a rich blend of ideas, theories and proofs, the book is up-to-date and self-contained. It is an excellent reference resource for users who are seeking faster optimization algorithms, as well as for graduate students and researchers wanting to grasp the frontiers of optimization in machine learning in a short time.

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 Optimization and Machine Learning written by Rachid Chelouah and published by John Wiley & Sons. This book was released on 2022-02-15 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Machine learning and optimization techniques are revolutionizing our world. Other types of information technology have not progressed as rapidly in recent years, in terms of real impact. The aim of this book is to present some of the innovative techniques in the field of optimization and machine learning, and to demonstrate how to apply them in the fields of engineering. Optimization and Machine Learning presents modern advances in the selection, configuration and engineering of algorithms that rely on machine learning and optimization. The first part of the book is dedicated to applications where optimization plays a major role, and the second part describes and implements several applications that are mainly based on machine learning techniques. The methods addressed in these chapters are compared against their competitors, and their effectiveness in their chosen field of application is illustrated.