Suvrit Sra

Sebastian Nowozin

Stephen J. Wright

Francis Bach

Rodolphe Jenatton

Julien Mairal

Guillaume Obozinski

Martin Andersen

Joachim Dahl

Zhang Liu

Lieven Vandenberghe

Dimitri Bertsekas

Anatoli Juditsky

Arkadi Nemirovski

Vojtech Franc

Soeren Sonnenburg

Thomáš Werner

David Sontag

Amir Globerson

Tommi Jaakkola

Ryota Tomioka

Taiji Suzuki

Masashi Sugiyama

Elad Hazan

Mark Schmidt

Dongmin Kim

Jacek Gondzio

Léon Bottou

Olivier Bousquet

Constantine Caramanis

Shie Mannor

Huan Xu

Nicolas Le Roux

Yoshua Bengio

Andrew Fitzgibbon

Jean-Yves Audibert

Sébsatien Bubeck

Rémi Munos

Katya Scheinberg

Shiqian Ma

Vijay Krishnamurthy

Selin Damla Ahipasaoglu

Alexandre d'Aspremont

Michael I. Jordan

Thomas G. Dietterich PhD

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.

内容詳細

Optimization for Machine Learning (Neural Information Processing series)

Stephen Boyd

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.

内容紹介

'Boyd and Vandenberghe have written a beautiful book that I strongly recommend to everyone interested in optimization and computational mathematics: Convex Optimization is a very readable introduction to this modern field of research.' Mathematics of Operations Research '… a beautiful book that I strongly recommend to everyone interested in optimization and computational mathematics … a very readable and inspiring introduction to this modern field of research. I recommend it as one of the best optimization textbooks that have appeared in the last years.' Mathematical Methods of Operations Research 'I highly recommend it either if you teach nonlinear optimization at the graduate level for a supplementary reading list and for your library, or if you solve optimization problems and wish to know more about solution methods and applications.' International Statistical institute '… the whole book is characterized by clarity. … a very good pedagogical book … excellent to grasp the important concepts of convex analysis [and] to develop an art in modelling optimization problems intelligently.' Matapli 'The book by Boyd and Vandenberghe reviewed here is one of … the best I have ever seen … it is a gentle, but rigorous, introduction to the basic concepts and methods of the field … this book is meant to be a 'first book' for the student or practitioner of optimization. However, I think that even the experienced researcher in the field has something to gain from reading this book: I have very much enjoyed the easy to follow presentation of many meaningful examples and suggestive interpretations meant to help the student's understanding penetrate beyond the surface of the formal description of the concepts and techniques. For teachers of convex optimization this book can be a gold mine of exercises. MathSciNet

レビュー

Stephen Boyd received his PhD from the University of California, Berkeley. Since 1985 he has been a member of the Electrical Engineering Department at Stanford University, where he is now Professor and Director of the Information Systems Laboratory. He has won numerous awards for teaching and research, and is a Fellow of the IEEE. He was one of the co-founders of Barcelona Design, and is the co-author of two previous books Linear Controller Design: Limits of Performance and Linear Matrix Inequalities in System and Control Theory.

著者について

Convex Optimization

著者：Lieven Vandenbergheの検索結果

Optimization for Machine Learning (Neural Information Processing series)

Convex Optimization