Machine Learning, Dynamic Optimization, and Control

From Adjoints and Bellman Equations to Reinforcement Learning, Diffusion Models, and Neural Dynamics
Erscheinungsjahr 2027
ISBN: 978-3-032-41770-1
Verlag: Birkhäuser

Buch, Englisch, 330 Seiten, Format (B × H): 155 mm x 235 mm

Reihe: PNLDE Subseries in Control

Machine learning and control theory address two closely related mathematical problems: Machine learning begins with data and seeks rules that can predict, classify, estimate, or decide. Control theory begins with a dynamical system and seeks an input or feedback law that steers the system, stabilizes it, or optimizes its performance. Both fields study decision making under uncertainty, and both rely on approximation, optimization, and the careful use of information. In modern settings, the separation between machine learning and control becomes artificial: A controller can learn a model while acting, and a generative model can be written as a controlled stochastic process.

This text develops a unified mathematical framework for control theory and machine learning by exploring the ideas and structures shared by these rapidly converging fields. Rather than simply providing a survey of current machine-learning algorithms or control-theoretic techniques, it focuses on the concepts that recur in both areas: approximation, estimation, optimization, feedback, stability, uncertainty, and dynamic programming. These are developed progressively through the book in a sequence that moves from static supervised learning to function-space approximation; from probability to stochastic approximation; from optimal control to reinforcement and Bayesian learning; and finally, from deep networks to the identification of dynamical systems.

The text is intended for both graduate students and researchers. By integrating topics that are traditionally taught separately, it will provide graduate students with a rigorous framework for understanding learning systems. For control theorists, it will offer a pathway into modern machine learning and AI, and for machine-learning researchers, it will increase understanding of the underlying structure of learning problems.

Zielgruppe

Graduate

Autoren/Hrsg.

Bensoussan, Alain

Tran, Minh-Binh

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Maschinelles Lernen
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme

Inhaltsverzeichnis

Preface.- Reader's Guide and Reference Apparatus.- Introduction.- Supervised Learning.- Nonparametric Methods and Reproducing Kernels.- Probability and Stochastic Processes.- Stochastic Approximation and Learning Algorithms.- Overview of Control Theory.- Generative Modeling and Controllability.- Dynamic Programming Foundations of Reinforcement Learning.- Bayesian Learning in Inventory Control.- Deep Learning as Optimal Control.- Learning Dynamical Systems under Full and Partial Observation.

Über Autor(innen)

Alain Bensoussan received a PhD in mathematics from the University of Paris in 1969. He is currently an Ashbel Smith Professor and the Director of the International Center for Decision and Risk Analysis at the University of Texas at Dallas. He is also the Chair Professor of risk and decision analysis with the City University of Hong Kong and a Professor Emeritus with the University Paris Dauphine. He has authored/coauthored 13 books and more than 450 papers and proceedings. Prof. Bensoussan was the President of the National Institute for Research in Computer Science and Control (INRIA) from 1984 to 1996, the President of the French Space Agency (CNES) from 1996 to 2003, and the Chairman of the European Space Agency (ESA) Council from 1999 to 2002. He developed a comprehensive approach to risk analysis to apprehend technical and socioeconomic risks simultaneously, and has an extensive research background in stochastic control, risk analysis, and decision making.

Minh-Binh Tran received a PhD in mathematics from Sorbonne Paris Nord University, in 2011. He is currently a tenured Associate Professor in the department of mathematics, Texas A&M University. Before joining Texas A&M University, he held positions at University of Wisconsin Madison, University of Texas at Austin, Southern Methodist University, and Massachusetts Institute of Technology. He has authored or coauthored 2 books and more than 70 papers. He has a diverse interest in different cross-disciplinary research in mathematics and its various applications, with extensive research background in partial differential equations, control theory, and machine learning.