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 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 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 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 Rollout Policy Iteration and Distributed Reinforcement Learning written by Dimitri Bertsekas and published by Athena Scientific. This book was released on 2021-08-20 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to develop in greater depth some of the methods from the author's Reinforcement Learning and Optimal Control recently published textbook (Athena Scientific, 2019). In particular, we present new research, relating to systems involving multiple agents, partitioned architectures, and distributed asynchronous computation. We pay special attention to the contexts of dynamic programming/policy iteration and control theory/model predictive control. We also discuss in some detail the application of the methodology to challenging discrete/combinatorial optimization problems, such as routing, scheduling, assignment, and mixed integer programming, including the use of neural network approximations within these contexts. The book focuses on the fundamental idea of policy iteration, i.e., start from some policy, and successively generate one or more improved policies. If just one improved policy is generated, this is called rollout, which, based on broad and consistent computational experience, appears to be one of the most versatile and reliable of all reinforcement learning methods. In this book, rollout algorithms are developed for both discrete deterministic and stochastic DP problems, and the development of distributed implementations in both multiagent and multiprocessor settings, aiming to take advantage of parallelism. Approximate policy iteration is more ambitious than rollout, but it is a strictly off-line method, and it is generally far more computationally intensive. This motivates the use of parallel and distributed computation. One of the purposes of the monograph is to discuss distributed (possibly asynchronous) methods that relate to rollout and policy iteration, both in the context of an exact and an approximate implementation involving neural networks or other approximation architectures. Much of the new research is inspired by the remarkable AlphaZero chess program, where policy iteration, value and policy networks, approximate lookahead minimization, and parallel computation all play an important role.

Download or read book Distributed Optimization Game and Learning Algorithms written by Huiwei Wang and published by Springer Nature. This book was released on 2021-01-04 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the fundamental theory of distributed optimization, game and learning. It includes those working directly in optimization,-and also many other issues like time-varying topology, communication delay, equality or inequality constraints,-and random projections. This book is meant for the researcher and engineer who uses distributed optimization, game and learning theory in fields like dynamic economic dispatch, demand response management and PHEV routing of smart grids.

Download or read book Stochastic Algorithms Foundations and Applications written by Kathleen Steinhöfel and published by Springer. This book was released on 2003-07-31 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: SAGA 2001, the ?rst Symposium on Stochastic Algorithms, Foundations and Applications, took place on December 13–14, 2001 in Berlin, Germany. The present volume comprises contributed papers and four invited talks that were included in the ?nal program of the symposium. Stochastic algorithms constitute a general approach to ?nding approximate solutions to a wide variety of problems. Although there is no formal proof that stochastic algorithms perform better than deterministic ones, there is evidence by empirical observations that stochastic algorithms produce for a broad range of applications near-optimal solutions in a reasonable run-time. The symposium aims to provide a forum for presentation of original research in the design and analysis, experimental evaluation, and real-world application of stochastic algorithms. It focuses, in particular, on new algorithmic ideas invo- ing stochastic decisions and exploiting probabilistic properties of the underlying problem domain. The program of the symposium re?ects the e?ort to promote cooperation among practitioners and theoreticians and among algorithmic and complexity researchers of the ?eld. In this context, we would like to express our special gratitude to DaimlerChrysler AG for supporting SAGA 2001. The contributed papers included in the proceedings present results in the following areas: Network and distributed algorithms; local search methods for combinatorial optimization with application to constraint satisfaction problems, manufacturing systems, motor control unit calibration, and packing ?exible - jects; and computational learning theory.

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 Meta Heuristic Algorithms for Advanced Distributed Systems written by Rohit Anand and published by John Wiley & Sons. This book was released on 2024-03-12 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: META-HEURISTIC ALGORITHMS FOR ADVANCED DISTRIBUTED SYSTEMS Discover a collection of meta-heuristic algorithms for distributed systems in different application domains Meta-heuristic techniques are increasingly gaining favor as tools for optimizing distributed systems—generally, to enhance the utility and precision of database searches. Carefully applied, they can increase system effectiveness, streamline operations, and reduce cost. Since many of these techniques are derived from nature, they offer considerable scope for research and development, with the result that this field is growing rapidly. Meta-Heuristic Algorithms for Advanced Distributed Systems offers an overview of these techniques and their applications in various distributed systems. With strategies based on both global and local searching, it covers a wide range of key topics related to meta-heuristic algorithms. Those interested in the latest developments in distributed systems will find this book indispensable. Meta-Heuristic Algorithms for Advanced Distributed Systems readers will also find: Analysis of security issues, distributed system design, stochastic optimization techniques, and more Detailed discussion of meta-heuristic techniques such as the genetic algorithm, particle swam optimization, and many others Applications of optimized distribution systems in healthcare and other key??industries Meta-Heuristic Algorithms for Advanced Distributed Systems is ideal for academics and researchers studying distributed systems, their design, and their applications.

Download or read book Optimal Decentralized Distributed Algorithms for Stochastic Convex Optimization written by Eduard Gorbunov and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider stochastic convex optimization problems with affine constraints and develop several methods using either primal or dual approach to solve it. In the primal case we use special penalization technique to make the initial problem more convenient for using optimization methods. We propose algorithms to solve it based on Similar Triangles Method [25, 59] with Inexact Proximal Step for the convex smooth and strongly convex smooth objective functions and methods based on Gradient Sliding algorithm [47] to solve the same problems in the non-smooth case. We prove the convergence guarantees in smooth convex case with deterministic first-order oracle. We propose and analyze three novel methods to handle stochastic convex optimization problems with affine constraints: SPDSTM, R-RRMA-AC-SA2 and SSTM_sc. All methods use stochastic dual oracle. SPDSTM is the stochastic primal-dual modification of STM and it is applied for the dual problem when the primal functional is strongly convex and Lipschitz continuous on some ball. We extend the result from [15] for this method to the case when only biased stochastic oracle is available. R-RRMA-AC-SA2 is an accelerated stochastic method based on the restarts of RRMA-AC-SA2 from [21] and SSTM_sc is just stochastic STM for strongly convex problems. Both methods are applied to the dual problem when the primal functional is strongly convex, smooth and Lipschitz continuous on some ball and use stochastic dual first-order oracle. We develop convergence analysis for these methods for the unbiased and biased oracles respectively. Finally, we apply all aforementioned results and approaches to solve decentralized distributed optimization problem and discuss optimality of the obtained results in terms of communication rounds and number of oracle calls per node.

Download or read book Scalable Optimization via Probabilistic Modeling written by Martin Pelikan and published by Springer. This book was released on 2007-01-12 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: I’m not usually a fan of edited volumes. Too often they are an incoherent hodgepodge of remnants, renegades, or rejects foisted upon an unsuspecting reading public under a misleading or fraudulent title. The volume Scalable Optimization via Probabilistic Modeling: From Algorithms to Applications is a worthy addition to your library because it succeeds on exactly those dimensions where so many edited volumes fail. For example, take the title, Scalable Optimization via Probabilistic M- eling: From Algorithms to Applications. You need not worry that you’re going to pick up this book and ?nd stray articles about anything else. This book focuseslikealaserbeamononeofthehottesttopicsinevolutionary compu- tion over the last decade or so: estimation of distribution algorithms (EDAs). EDAs borrow evolutionary computation’s population orientation and sel- tionism and throw out the genetics to give us a hybrid of substantial power, elegance, and extensibility. The article sequencing in most edited volumes is hard to understand, but from the get go the editors of this volume have assembled a set of articles sequenced in a logical fashion. The book moves from design to e?ciency enhancement and then concludes with relevant applications. The emphasis on e?ciency enhancement is particularly important, because the data-mining perspectiveimplicitinEDAsopensuptheworldofoptimizationtonewme- ods of data-guided adaptation that can further speed solutions through the construction and utilization of e?ective surrogates, hybrids, and parallel and temporal decompositions.

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 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 Reinforcement Learning and Optimal Control written by Dimitri Bertsekas and published by Athena Scientific. This book was released on 2019-07-01 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers large and challenging multistage decision problems, which can be solved in principle by dynamic programming (DP), but their exact solution is computationally intractable. We discuss solution methods that rely on approximations to produce suboptimal policies with adequate performance. These methods are collectively known by several essentially equivalent names: reinforcement learning, approximate dynamic programming, neuro-dynamic programming. They have been at the forefront of research for the last 25 years, and they underlie, among others, the recent impressive successes of self-learning in the context of games such as chess and Go. Our subject has benefited greatly from the interplay of ideas from optimal control and from artificial intelligence, as it relates to reinforcement learning and simulation-based neural network methods. One of the aims of the book is to explore the common boundary between these two fields and to form a bridge that is accessible by workers with background in either field. Another aim is to organize coherently the broad mosaic of methods that have proved successful in practice while having a solid theoretical and/or logical foundation. This may help researchers and practitioners to find their way through the maze of competing ideas that constitute the current state of the art. This book relates to several of our other books: Neuro-Dynamic Programming (Athena Scientific, 1996), Dynamic Programming and Optimal Control (4th edition, Athena Scientific, 2017), Abstract Dynamic Programming (2nd edition, Athena Scientific, 2018), and Nonlinear Programming (Athena Scientific, 2016). However, the mathematical style of this book is somewhat different. While we provide a rigorous, albeit short, mathematical account of the theory of finite and infinite horizon dynamic programming, and some fundamental approximation methods, we rely more on intuitive explanations and less on proof-based insights. Moreover, our mathematical requirements are quite modest: calculus, a minimal use of matrix-vector algebra, and elementary probability (mathematically complicated arguments involving laws of large numbers and stochastic convergence are bypassed in favor of intuitive explanations). The book illustrates the methodology with many examples and illustrations, and uses a gradual expository approach, which proceeds along four directions: (a) From exact DP to approximate DP: We first discuss exact DP algorithms, explain why they may be difficult to implement, and then use them as the basis for approximations. (b) From finite horizon to infinite horizon problems: We first discuss finite horizon exact and approximate DP methodologies, which are intuitive and mathematically simple, and then progress to infinite horizon problems. (c) From deterministic to stochastic models: We often discuss separately deterministic and stochastic problems, since deterministic problems are simpler and offer special advantages for some of our methods. (d) From model-based to model-free implementations: We first discuss model-based implementations, and then we identify schemes that can be appropriately modified to work with a simulator. The book is related and supplemented by the companion research monograph Rollout, Policy Iteration, and Distributed Reinforcement Learning (Athena Scientific, 2020), which focuses more closely on several topics related to rollout, approximate policy iteration, multiagent problems, discrete and Bayesian optimization, and distributed computation, which are either discussed in less detail or not covered at all in the present book. The author's website contains class notes, and a series of videolectures and slides from a 2021 course at ASU, which address a selection of topics from both books.

Download or read book Stochastic Optimization written by Stanislav Uryasev and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic programming is the study of procedures for decision making under the presence of uncertainties and risks. Stochastic programming approaches have been successfully used in a number of areas such as energy and production planning, telecommunications, and transportation. Recently, the practical experience gained in stochastic programming has been expanded to a much larger spectrum of applications including financial modeling, risk management, and probabilistic risk analysis. Major topics in this volume include: (1) advances in theory and implementation of stochastic programming algorithms; (2) sensitivity analysis of stochastic systems; (3) stochastic programming applications and other related topics. Audience: Researchers and academies working in optimization, computer modeling, operations research and financial engineering. The book is appropriate as supplementary reading in courses on optimization and financial engineering.

Download or read book Alternating Direction Method of Multipliers for Machine Learning written by Zhouchen Lin and published by Springer Nature. This book was released on 2022-06-15 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Machine learning heavily relies on optimization algorithms to solve its learning models. Constrained problems constitute a major type of optimization problem, and the alternating direction method of multipliers (ADMM) is a commonly used algorithm to solve constrained problems, especially linearly constrained ones. Written by experts in machine learning and optimization, this is the first book providing a state-of-the-art review on ADMM under various scenarios, including deterministic and convex optimization, nonconvex optimization, stochastic optimization, and distributed optimization. Offering a rich blend of ideas, theories and proofs, the book is up-to-date and self-contained. It is an excellent reference book for users who are seeking a relatively universal algorithm for constrained problems. Graduate students or researchers can read it to grasp the frontiers of ADMM in machine learning in a short period of time.