Non Convex Optimization For Machine Learning

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Non-convex Optimization for Machine Learning

Prateek Jain,Purushottam Kar
Non convex Optimization for Machine Learning Book PDF

Author : Prateek Jain,Purushottam Kar
Publisher : Foundations and Trends in Machine Learning
Page : 218 pages
File Size : 45,9 Mb
Release : 2017-12-04
Category : Machine learning
ISBN : 1680833685

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Non-convex Optimization for Machine Learning by Prateek Jain,Purushottam Kar Pdf

Non-convex Optimization for Machine Learning takes an in-depth look at the basics of non-convex optimization with applications to machine learning. It introduces the rich literature in this area, as well as equips the reader with the tools and techniques needed to apply and analyze simple but powerful procedures for non-convex problems. Non-convex Optimization for Machine Learning is as self-contained as possible while not losing focus of the main topic of non-convex optimization techniques. The monograph initiates the discussion with entire chapters devoted to presenting a tutorial-like treatment of basic concepts in convex analysis and optimization, as well as their non-convex counterparts. The monograph concludes with a look at four interesting applications in the areas of machine learning and signal processing, and exploring how the non-convex optimization techniques introduced earlier can be used to solve these problems. The monograph also contains, for each of the topics discussed, exercises and figures designed to engage the reader, as well as extensive bibliographic notes pointing towards classical works and recent advances. Non-convex Optimization for Machine Learning can be used for a semester-length course on the basics of non-convex optimization with applications to machine learning. On the other hand, it is also possible to cherry pick individual portions, such the chapter on sparse recovery, or the EM algorithm, for inclusion in a broader course. Several courses such as those in machine learning, optimization, and signal processing may benefit from the inclusion of such topics.

Optimization for Machine Learning

Suvrit Sra,Sebastian Nowozin,Stephen J. Wright
Optimization for Machine Learning Book PDF

Author : Suvrit Sra,Sebastian Nowozin,Stephen J. Wright
Publisher : MIT Press
Page : 509 pages
File Size : 53,9 Mb
Release : 2012
Category : Computers
ISBN : 9780262016469

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Optimization for Machine Learning by Suvrit Sra,Sebastian Nowozin,Stephen J. Wright Pdf

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.

Convex Optimization

Stephen P. Boyd,Lieven Vandenberghe
Convex Optimization Book PDF

Author : Stephen P. Boyd,Lieven Vandenberghe
Publisher : Cambridge University Press
Page : 744 pages
File Size : 53,7 Mb
Release : 2004-03-08
Category : Business & Economics
ISBN : 0521833787

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Convex Optimization by Stephen P. Boyd,Lieven Vandenberghe Pdf

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.

Convex Optimization for Machine Learning

Changho Suh
Convex Optimization for Machine Learning Book PDF

Author : Changho Suh
Publisher : Unknown
Page : 0 pages
File Size : 48,7 Mb
Release : 2022-09-27
Category : Electronic
ISBN : 1638280525

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Convex Optimization for Machine Learning by Changho Suh Pdf

This book covers an introduction to convex optimization, one of the powerful and tractable optimization problems that can be efficiently solved on a computer. The goal of the book is to help develop a sense of what convex optimization is, and how it can be used in a widening array of practical contexts with a particular emphasis on machine learning. The first part of the book covers core concepts of convex sets, convex functions, and related basic definitions that serve understanding convex optimization and its corresponding models. The second part deals with one very useful theory, called duality, which enables us to: (1) gain algorithmic insights; and (2) obtain an approximate solution to non-convex optimization problems which are often difficult to solve. The last part focuses on modern applications in machine learning and deep learning. A defining feature of this book is that it succinctly relates the "story" of how convex optimization plays a role, via historical examples and trending machine learning applications. Another key feature is that it includes programming implementation of a variety of machine learning algorithms inspired by optimization fundamentals, together with a brief tutorial of the used programming tools. The implementation is based on Python, CVXPY, and TensorFlow. This book does not follow a traditional textbook-style organization, but is streamlined via a series of lecture notes that are intimately related, centered around coherent themes and concepts. It serves as a textbook mainly for a senior-level undergraduate course, yet is also suitable for a first-year graduate course. Readers benefit from having a good background in linear algebra, some exposure to probability, and basic familiarity with Python.

Accelerated Optimization for Machine Learning

Zhouchen Lin,Huan Li,Cong Fang
Accelerated Optimization for Machine Learning Book PDF

Author : Zhouchen Lin,Huan Li,Cong Fang
Publisher : Springer Nature
Page : 286 pages
File Size : 47,7 Mb
Release : 2020-05-29
Category : Computers
ISBN : 9789811529108

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Accelerated Optimization for Machine Learning by Zhouchen Lin,Huan Li,Cong Fang Pdf

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.

Convex Optimization

Sébastien Bubeck
Convex Optimization Book PDF

Author : Sébastien Bubeck
Publisher : Foundations and Trends (R) in Machine Learning
Page : 142 pages
File Size : 45,5 Mb
Release : 2015-11-12
Category : Convex domains
ISBN : 1601988605

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Convex Optimization by Sébastien Bubeck Pdf

This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms. It begins with the fundamental theory of black-box optimization and proceeds to guide the reader through recent advances in structural optimization and stochastic optimization. The presentation of black-box optimization, strongly influenced by the seminal book by Nesterov, includes the analysis of cutting plane methods, as well as (accelerated) gradient descent schemes. Special attention is also given to non-Euclidean settings (relevant algorithms include Frank-Wolfe, mirror descent, and dual averaging), and discussing their relevance in machine learning. The text provides a gentle introduction to structural optimization with FISTA (to optimize a sum of a smooth and a simple non-smooth term), saddle-point mirror prox (Nemirovski's alternative to Nesterov's smoothing), and a concise description of interior point methods. In stochastic optimization it discusses stochastic gradient descent, mini-batches, random coordinate descent, and sublinear algorithms. It also briefly touches upon convex relaxation of combinatorial problems and the use of randomness to round solutions, as well as random walks based methods.

First-order and Stochastic Optimization Methods for Machine Learning

Guanghui Lan
First order and Stochastic Optimization Methods for Machine Learning Book PDF

Author : Guanghui Lan
Publisher : Springer Nature
Page : 591 pages
File Size : 43,7 Mb
Release : 2020-05-15
Category : Mathematics
ISBN : 9783030395681

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First-order and Stochastic Optimization Methods for Machine Learning by Guanghui Lan Pdf

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.

Modern Nonconvex Nondifferentiable Optimization

Ying Cui,Jong-Shi Pang
Modern Nonconvex Nondifferentiable Optimization Book PDF

Author : Ying Cui,Jong-Shi Pang
Publisher : SIAM
Page : 792 pages
File Size : 45,8 Mb
Release : 2021-12-02
Category : Mathematics
ISBN : 9781611976748

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Modern Nonconvex Nondifferentiable Optimization by Ying Cui,Jong-Shi Pang Pdf

Starting with the fundamentals of classical smooth optimization and building on established convex programming techniques, this research monograph presents a foundation and methodology for modern nonconvex nondifferentiable optimization. It provides readers with theory, methods, and applications of nonconvex and nondifferentiable optimization in statistical estimation, operations research, machine learning, and decision making. A comprehensive and rigorous treatment of this emergent mathematical topic is urgently needed in today’s complex world of big data and machine learning. This book takes a thorough approach to the subject and includes examples and exercises to enrich the main themes, making it suitable for classroom instruction. Modern Nonconvex Nondifferentiable Optimization is intended for applied and computational mathematicians, optimizers, operations researchers, statisticians, computer scientists, engineers, economists, and machine learners. It could be used in advanced courses on optimization/operations research and nonconvex and nonsmooth optimization.

Algorithms for Convex Optimization

Nisheeth K. Vishnoi
Algorithms for Convex Optimization Book PDF

Author : Nisheeth K. Vishnoi
Publisher : Cambridge University Press
Page : 314 pages
File Size : 52,9 Mb
Release : 2021-10-07
Category : Computers
ISBN : 9781108633994

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Algorithms for Convex Optimization by Nisheeth K. Vishnoi Pdf

In the last few years, Algorithms for Convex Optimization have revolutionized algorithm design, both for discrete and continuous optimization problems. For problems like maximum flow, maximum matching, and submodular function minimization, the fastest algorithms involve essential methods such as gradient descent, mirror descent, interior point methods, and ellipsoid methods. The goal of this self-contained book is to enable researchers and professionals in computer science, data science, and machine learning to gain an in-depth understanding of these algorithms. The text emphasizes how to derive key algorithms for convex optimization from first principles and how to establish precise running time bounds. This modern text explains the success of these algorithms in problems of discrete optimization, as well as how these methods have significantly pushed the state of the art of convex optimization itself.

Introduction to Online Convex Optimization, second edition

Elad Hazan
Introduction to Online Convex Optimization second edition Book PDF

Author : Elad Hazan
Publisher : MIT Press
Page : 249 pages
File Size : 49,7 Mb
Release : 2022-09-06
Category : Computers
ISBN : 9780262046985

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Introduction to Online Convex Optimization, second edition by Elad Hazan Pdf

New edition of a graduate-level textbook on that focuses on online convex optimization, a machine learning framework that views optimization as a process. In many practical applications, the environment is so complex that it is not feasible to lay out a comprehensive theoretical model and use classical algorithmic theory and/or mathematical optimization. Introduction to Online Convex Optimization presents a robust machine learning approach that contains elements of mathematical optimization, game theory, and learning theory: an optimization method that learns from experience as more aspects of the problem are observed. This view of optimization as a process has led to some spectacular successes in modeling and systems that have become part of our daily lives. Based on the “Theoretical Machine Learning” course taught by the author at Princeton University, the second edition of this widely used graduate level text features: Thoroughly updated material throughout New chapters on boosting, adaptive regret, and approachability and expanded exposition on optimization Examples of applications, including prediction from expert advice, portfolio selection, matrix completion and recommendation systems, SVM training, offered throughout Exercises that guide students in completing parts of proofs

Evaluation Complexity of Algorithms for Nonconvex Optimization

Coralia Cartis,Nicholas I. M. Gould,Philippe L. Toint
Evaluation Complexity of Algorithms for Nonconvex Optimization Book PDF

Author : Coralia Cartis,Nicholas I. M. Gould,Philippe L. Toint
Publisher : SIAM
Page : 549 pages
File Size : 43,6 Mb
Release : 2022-07-06
Category : Mathematics
ISBN : 9781611976991

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Evaluation Complexity of Algorithms for Nonconvex Optimization by Coralia Cartis,Nicholas I. M. Gould,Philippe L. Toint Pdf

A popular way to assess the “effort” needed to solve a problem is to count how many evaluations of the problem functions (and their derivatives) are required. In many cases, this is often the dominating computational cost. Given an optimization problem satisfying reasonable assumptions—and given access to problem-function values and derivatives of various degrees—how many evaluations might be required to approximately solve the problem? Evaluation Complexity of Algorithms for Nonconvex Optimization: Theory, Computation, and Perspectives addresses this question for nonconvex optimization problems, those that may have local minimizers and appear most often in practice. This is the first book on complexity to cover topics such as composite and constrained optimization, derivative-free optimization, subproblem solution, and optimal (lower and sharpness) bounds for nonconvex problems. It is also the first to address the disadvantages of traditional optimality measures and propose useful surrogates leading to algorithms that compute approximate high-order critical points, and to compare traditional and new methods, highlighting the advantages of the latter from a complexity point of view. This is the go-to book for those interested in solving nonconvex optimization problems. It is suitable for advanced undergraduate and graduate students in courses on advanced numerical analysis, data science, numerical optimization, and approximation theory.

Convex Optimization Algorithms

Dimitri Bertsekas
Convex Optimization Algorithms Book PDF

Author : Dimitri Bertsekas
Publisher : Athena Scientific
Page : 576 pages
File Size : 47,6 Mb
Release : 2015-02-01
Category : Mathematics
ISBN : 9781886529281

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Convex Optimization Algorithms by Dimitri Bertsekas Pdf

This book provides a comprehensive and accessible presentation of algorithms for solving convex optimization problems. It relies on rigorous mathematical analysis, but also aims at an intuitive exposition that makes use of visualization where possible. This is facilitated by the extensive use of analytical and algorithmic concepts of duality, which by nature lend themselves to geometrical interpretation. The book places particular emphasis on modern developments, and their widespread applications in fields such as large-scale resource allocation problems, signal processing, and machine learning. The book is aimed at students, researchers, and practitioners, roughly at the first year graduate level. It is similar in style to the author's 2009"Convex Optimization Theory" book, but can be read independently. The latter book focuses on convexity theory and optimization duality, while the present book focuses on algorithmic issues. The two books share notation, and together cover the entire finite-dimensional convex optimization methodology. To facilitate readability, the statements of definitions and results of the "theory book" are reproduced without proofs in Appendix B.

Beyond the Worst-Case Analysis of Algorithms

Tim Roughgarden
Beyond the Worst Case Analysis of Algorithms Book PDF

Author : Tim Roughgarden
Publisher : Cambridge University Press
Page : 705 pages
File Size : 41,8 Mb
Release : 2021-01-14
Category : Computers
ISBN : 9781108494311

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Beyond the Worst-Case Analysis of Algorithms by Tim Roughgarden Pdf

Introduces exciting new methods for assessing algorithms for problems ranging from clustering to linear programming to neural networks.

Convex Analysis and Nonlinear Optimization

Jonathan Borwein,Adrian S. Lewis
Convex Analysis and Nonlinear Optimization Book PDF

Author : Jonathan Borwein,Adrian S. Lewis
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 45,7 Mb
Release : 2010-05-05
Category : Mathematics
ISBN : 9780387312569

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Convex Analysis and Nonlinear Optimization by Jonathan Borwein,Adrian S. Lewis Pdf

Optimization is a rich and thriving mathematical discipline, and the underlying theory of current computational optimization techniques grows ever more sophisticated. This book aims to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. Each section concludes with an often extensive set of optional exercises. This new edition adds material on semismooth optimization, as well as several new proofs.

Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers

Stephen Boyd,Neal Parikh,Eric Chu
Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers Book PDF

Author : Stephen Boyd,Neal Parikh,Eric Chu
Publisher : Now Publishers Inc
Page : 138 pages
File Size : 46,5 Mb
Release : 2011
Category : Computers
ISBN : 9781601984609

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Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers by Stephen Boyd,Neal Parikh,Eric Chu Pdf

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.