Introduction to Online Convex Optimization" provides a timely synthesis of mathematical optimization and machine learning. The book emphasizes the concept of regret minimization, demonstrating its power for generalization through rigorous theoretical analysis and practical examples. A wide array of topics is covered, including game theory, projection-free methods, matrix completion, boosting, and multi-armed bandits. The text offers an insightful exposition of adaptive gradient methods, which have become widely impactful in large-scale deep learning optimization, tracing their roots to regret minimization in online convex optimization. This book is a valuable resource for researchers and students interested in the intersection of convex optimization and machine learning.
Arkadi Nemirovski
Second edition is now published by MIT Press, has new chapters, expanded exposition on optimization, and expanded teaching materials.
The first version was published as a survey in the Foundation and Trends series. The most complete version, including errata by various contributors, is the arxiv version.
Available for purchase on Amazon in hardcopy, kindle, and soon softcopy editions.
This graduate text arose from lectures given at the Technion, 2010-2014. It developed further in Princeton University, and served as the basis for a graduate-level course in machine learning and optimization. It is and always will be available free of charge as a contribution to the scientific community.
This manuscript concerns the view of optimization as a process. In many practical applications the environment is so complex that it is infeasible to lay a comprehensive theoretical model and use classical algorithmic theory and mathematical optimization. It is necessary as well as beneficial to take a robust approach: apply an optimization method that learns as one goes along, learning from experience as more aspects of the problem are observed. This view of optimization as a process has become prominent in varied fields and led to some spectacular success in modeling and systems that are now part of our daily lives.
Contains original illustrations and artwork by Udi Aharoni