Accelerated Optimization For Machine Learning

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.

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.

Optimization happens everywhere. Machine learning is one example of such and gradient descent is probably the most famous algorithm for performing optimization. Optimization means to find the best value of some function or model. That can be the maximum or the minimum according to some metric. Using clear explanations, standard Python libraries, and step-by-step tutorial lessons, you will learn how to find the optimum point to numerical functions confidently using modern optimization algorithms.

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.

This book discusses one of the major applications of artificial intelligence: the use of machine learning to extract useful information from multimodal data. It discusses the optimization methods that help minimize the error in developing patterns and classifications, which further helps improve prediction and decision-making. The book also presents formulations of real-world machine learning problems, and discusses AI solution methodologies as standalone or hybrid approaches. Lastly, it proposes novel metaheuristic methods to solve complex machine learning problems. Featuring valuable insights, the book helps readers explore new avenues leading toward multidisciplinary research discussions.

Hello humans & welcome to the world of machines! Specifically, machine learning & algorithms. We are about to embark on an exciting adventure through the vast and varied landscape of algorithms that power the cutting-edge field of artificial intelligence. Machine learning is changing the world as we know it. From predicting stock market trends and diagnosing diseases to powering the virtual assistants in our smartphones and enabling self-driving cars, and picking up the slack on your online dating conversations. What makes this book unique is its structure and depth. With 100 chapters, each dedicated to a different machine learning concept, this book is designed to be your ultimate guide to the world of machine learning algorithms. Whether you are a student, a data science professional, or someone curious about machine learning, this book aims to provide a comprehensive overview that is both accessible and in-depth. The algorithms covered in this book span various categories including: Classification & Regression: Learn about algorithms like Decision Trees, Random Forests, Support Vector Machines, and Logistic Regression which are used to classify data or predict numerical values. Clustering: Discover algorithms like k-Means, Hierarchical Clustering, and DBSCAN that group data points together based on similarities. Neural Networks & Deep Learning: Dive into algorithms and architectures like Perceptrons, Convolutional Neural Networks (CNN), and Long Short-Term Memory Networks (LSTM). Optimization: Understand algorithms like Gradient Descent, Genetic Algorithms, and Particle Swarm Optimization which find the best possible solutions in different scenarios. Ensemble Methods: Explore algorithms like AdaBoost, Gradient Boosting, and Random Forests which combine the predictions of multiple models for improved accuracy. Dimensionality Reduction: Learn about algorithms like Principal Component Analysis (PCA) and t-Distributed Stochastic Neighbor Embedding (t-SNE) which reduce the number of features in a dataset while retaining important information. Reinforcement Learning: Get to know algorithms like Q-learning, Deep Q-Network (DQN), and Monte Carlo Tree Search which are used in systems that learn from their environment. Each chapter is designed as a standalone introduction to its respective algorithm. This means you can start from any chapter that catches your interest or proceed sequentially. Along with the theory, practical examples, applications, and insights into how these algorithms work under the hood are provided. This book is not just an academic endeavor but a bridge that connects theory with practical real-world applications. It's an invitation to explore, learn, and harness the power of algorithms to solve complex problems and make informed decisions. Fasten your seat belts as we dive into the mesmerizing world of machine learning algorithms. Whether you are looking to expand your knowledge, seeking inspiration, or in pursuit of technical mastery, this book should sit on your coffee table and make you look intelligent in front of all invited (and uninvited) guests.

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.

During his long and distinguished career, J. Rowland Higgins (1935-2020) made a substantial impact on many mathematical fields through his work on sampling theory, his deep knowledge of its history, and his service to the community. This volume is a tribute to his work and legacy, featuring chapters written by distinguished mathematicians that explore cutting-edge research in sampling, approximation, signal analysis, and other related areas. An introductory chapter provides a biography of Higgins that explores his rich and unique life, along with a bibliography of his papers; a brief history of the SampTA meetings – of which he was a Founding Member – is also included. The remaining articles are grouped into four sections – classical sampling, theoretical extensions, frame theory, and applications of sampling theory – and explore Higgins’ contributions to these areas, as well as some of the latest developments.