Optimization for Learning and Control

Comprehensive resource providing a masters' level introduction to optimization theory and algorithms for learning and control

Optimization for Learning and Control describes how optimization is used in these domains, giving a thorough introduction to both unsupervised learning, supervised learning, and reinforcement learning, with an emphasis on optimization methods for large-scale learning and control problems.

Several applications areas are also discussed, including signal processing, system identification, optimal control, and machine learning.

Today, most of the material on the optimization aspects of deep learning that is accessible for students at a Masters' level is focused on surface-level computer programming; deeper knowledge about the optimization methods and the trade-offs that are behind these methods is not provided. The objective of this book is to make this scattered knowledge, currently mainly available in publications in academic journals, accessible for Masters' students in a coherent way. The focus is on basic algorithmic principles and trade-offs

Optimization for Learning and Control covers sample topics such as:

• Optimization theory and optimization methods, covering classes of optimization problems like least squares problems, quadratic problems, conic optimization problems and rank optimization.
• First-order methods, second-order methods, variable metric methods, and methods for nonlinear least squares problems
• Stochastic optimization methods, augmented Lagrangian methods, interior-point methods, and conic optimization methods
• Dynamic programming for solving optimal control problems and its generalization to reinforcement learning.
• How optimization theory is used to develop theory and tools of statistics and learning, e.g., the maximum likelihood method, expectation maximization, k-means clustering, and support vector machines.
• How calculus of variations is used in optimal control and for deriving the family of exponential distributions.

Optimization for Learning and Control is an ideal resource on the subject for scientists and engineers learning about which optimization methods are useful for learning and control problems; the text will also appeal to industry professionals using machine learning for different practical applications.

《優化學習與控制》是一本全面的資源，提供了碩士級別的優化理論和算法介紹，適用於學習和控制領域。本書描述了優化在這些領域中的應用，全面介紹了無監督學習、監督學習和強化學習，並重點介紹了大規模學習和控制問題的優化方法。同時還討論了幾個應用領域，包括信號處理、系統識別、最優控制和機器學習。

如今，對於碩士級別的學生來說，關於深度學習優化方面的大部分資料都集中在表面層次的計算機編程上，並未提供更深入的優化方法和背後的權衡。本書的目標是以一種有條理的方式，使這些分散的知識，目前主要僅在學術期刊的出版物中提供，對碩士生可得到。重點是基本的算法原則和權衡。

《優化學習與控制》涵蓋了以下主題：
- 優化理論和優化方法，包括最小二乘問題、二次問題、錐優化問題和秩優化問題等優化問題類別。
- 一階方法、二階方法、變量度量方法和非線性最小二乘問題的方法。
- 隨機優化方法、增廣拉格朗日方法、內點方法和錐優化方法。
- 動態規劃用於解決最優控制問題及其在強化學習中的推廣。
- 優化理論如何用於發展統計學和學習的理論和工具，例如最大似然方法、期望最大化、k均值聚類和支持向量機。
- 變分計算在最優控制和導出指數分佈族的應用。

《優化學習與控制》是科學家和工程師學習哪些優化方法對學習和控制問題有用的理想資源；同時也適合從事不同實際應用的行業專業人士使用機器學習。

Anders Hansson, PhD, is a Professor in the Department of Electrical Engineering at Linköping University, Sweden. His research interests include the fields of optimal control, stochastic control, linear systems, signal processing, applications of control, and telecommunications.

Martin Andersen, PhD, is an Associate Professor in the Department of Applied Mathematics and Computer Science at the Technical University of Denmark. His research interests include optimization, numerical methods, signal and image processing, and systems and control.

Anders Hansson博士是瑞典林雪平大學電機工程系的教授。他的研究興趣包括最佳控制、隨機控制、線性系統、信號處理、控制應用和電信等領域。

Martin Andersen博士是丹麥技術大學應用數學和計算機科學系的副教授。他的研究興趣包括優化、數值方法、信號和圖像處理以及系統和控制等領域。