This book serves as an introduction to the expanding theory of online convex optimization. It was written as an advanced text to serve as a basis for a graduate course, and/or as a reference to the researcher diving into this fascinating world at the intersection of optimization and machine learning.Such a course was given at the Technion in the years 2010–2014 with slight variations from year to year, and later at Princeton University in the years 2015-2016. The core material in these courses is fully covered in this book, along with exercises that allow the students to complete parts of proofs, or that were found illuminating and thoughtprovoking. Most of the material is given with examples of applications, which are interlaced throughout different topics. These include prediction from expert advice, portfolio selection, matrix completion and recommendation systems, SVM training and more.Our hope is that this compendium of material and exercises will be useful to you; the educator and the researcher.Book’s structureThis book is intended to serve as a reference for a self-contained course for the educated graduate student in computer science/electrical engineering/operations research/statistics and related fields. As such, its organization follows the structure of the course “decision analysis” taught at the Technion.Each chapter should take one or two weeks of classes, depending on the depth and breadth of the intended course. The first chapter is designed to be a “teaser” for the field, and thus less rigorous than the rest of the book.Roughly speaking, the book can be thought of as two units. The first, from chapter 2 through 5, contains the basic definitions, framework and core algorithms for online convex optimization. The rest of the book deals with more advanced algorithms, more difficult settings and relationships to well-known machine learning paradigms.

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