The book "Introduction to Online Convex Optimization" by Elad Hazan is an advanced textbook designed for graduate courses and researchers in the field of optimization and machine learning. It covers the theory and applications of online convex optimization (OCO), a framework that models decision-making processes where outcomes are unknown at the time of decision and can be adversarially chosen. The book is structured into several chapters, each focusing on different aspects of OCO, including basic concepts, algorithms, and advanced topics. Key topics include: - **Introduction to OCO**: Definitions, framework, and examples such as prediction from expert advice, online spam filtering, shortest paths, portfolio selection, and matrix completion. - **Basic Concepts in Convex Optimization**: Definitions, optimality conditions, gradient descent, and constrained optimization. - **First-Order Algorithms for OCO**: Online gradient descent, regret bounds, and applications like stochastic gradient descent. - **Second-Order Methods**: Exp-concave functions, the Online Newton Step, and universal portfolio selection. - **Regularization**: Techniques like randomized regularization and adaptive gradient descent. - **Bandit Convex Optimization**: Multi-armed bandit problems and regret minimization. - **Projection-Free Algorithms**: Conditional gradient methods and their applications. - **Games, Duality, and Regret**: Linear programming, zero-sum games, and regret minimization in games. - **Learning Theory and Generalization**: Statistical learning theory, agnostic learning, and compression schemes. - **Learning in Changing Environments**: Adaptive regret algorithms and efficient methods. - **Boosting and Regret**: Boosting methods and their analysis. - **Blackwell Approachability and OCO**: Vector-valued games and approachability. The book also includes exercises and bibliographic remarks to enhance understanding and provide additional context. The second edition includes expanded coverage of optimization, corrections, and solutions to selected exercises. The author acknowledges the contributions of students, colleagues, and friends who have helped with research and corrections.The book "Introduction to Online Convex Optimization" by Elad Hazan is an advanced textbook designed for graduate courses and researchers in the field of optimization and machine learning. It covers the theory and applications of online convex optimization (OCO), a framework that models decision-making processes where outcomes are unknown at the time of decision and can be adversarially chosen. The book is structured into several chapters, each focusing on different aspects of OCO, including basic concepts, algorithms, and advanced topics. Key topics include: - **Introduction to OCO**: Definitions, framework, and examples such as prediction from expert advice, online spam filtering, shortest paths, portfolio selection, and matrix completion. - **Basic Concepts in Convex Optimization**: Definitions, optimality conditions, gradient descent, and constrained optimization. - **First-Order Algorithms for OCO**: Online gradient descent, regret bounds, and applications like stochastic gradient descent. - **Second-Order Methods**: Exp-concave functions, the Online Newton Step, and universal portfolio selection. - **Regularization**: Techniques like randomized regularization and adaptive gradient descent. - **Bandit Convex Optimization**: Multi-armed bandit problems and regret minimization. - **Projection-Free Algorithms**: Conditional gradient methods and their applications. - **Games, Duality, and Regret**: Linear programming, zero-sum games, and regret minimization in games. - **Learning Theory and Generalization**: Statistical learning theory, agnostic learning, and compression schemes. - **Learning in Changing Environments**: Adaptive regret algorithms and efficient methods. - **Boosting and Regret**: Boosting methods and their analysis. - **Blackwell Approachability and OCO**: Vector-valued games and approachability. The book also includes exercises and bibliographic remarks to enhance understanding and provide additional context. The second edition includes expanded coverage of optimization, corrections, and solutions to selected exercises. The author acknowledges the contributions of students, colleagues, and friends who have helped with research and corrections.