Optimization and Learning via Stochastic Gradient Search (eBook)

Felisa Vázquez-Abad, Bernd Heidergott (Autoren)

eBook Download: PDF

2025
433 Seiten
Princeton University Press (Verlag)
978-0-691-24587-4 (ISBN)

Infos

An introduction to gradient-based stochastic optimization that integrates theory and implementationThis book explains gradient-based stochastic optimization, exploiting the methodologies of stochastic approximation and gradient estimation. Although the approach is theoretical, the book emphasizes developing algorithms that implement the methods. The underlying philosophy of this book is that when solving real problems, mathematical theory, the art of modeling, and numerical algorithms complement each other, with no one outlook dominating the others.The book first covers the theory of stochastic approximation including advanced models and state-of-the-art analysis methodology, treating applications that do not require the use of gradient estimation. It then presents gradient estimation, developing a modern approach that incorporates cutting-edge numerical algorithms. Finally, the book culminates in a rich set of case studies that integrate the concepts previously discussed into fully worked models. The use of stochastic approximation in statistics and machine learning is discussed, and in-depth theoretical treatments for selected gradient estimation approaches are included.Numerous examples show how the methods are applied concretely, and end-of-chapter exercises enable readers to consolidate their knowledge. Many chapters end with a section on ';Practical Considerations' that addresses typical tradeoffs encountered in implementation. The book provides the first unified treatment of the topic, written for a wide audience that includes researchers and graduate students in applied mathematics, engineering, computer science, physics, and economics.

Produkt-Details

• Erscheint lt. Verlag: 28.10.2025
• Reihe/Serie: Princeton Series in Applied Mathematics
• Zusatzinfo: 53 b/w illus. 1 table.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Schlagworte: adaptive methods • Algorithm design • algorithmic development • Applied mathematics • approximation algorithms • asymptotic analysis • bias-variance tradeoff • Computational Complexity • computational mathematics • Computational Optimization • Constrained optimization • convergence analysis • convergence theory • Convex Optimization • cost functions • finite differences • First-Order Methods • Global Optimization • Gradient-Based Optimization • Gradient descent • gradient estimation • gradient methods • infinitesimal perturbation analysis • Inventory • iteration complexity • Learning rate • local minima • loss functions • machine learning • Markov Processes. • Mathematical Theory • measure-valued differentiation • Model Fitting • momentum methods • Monte Carlo simulation • non-convex optimization • non-smooth optimization • Numerical Algorithms • Numerical Methods • objective functions • Optimization • optimization algorithms • optimization landscapes • Optimization Methods • Optimization Problems • optimization theory • Ordinary differential equations • Parameter Estimation • Practical implementation • Quasi-Newton Methods • Queuing • Reinforcement Learning • sample complexity • score function method • second-order methods • Simulation Optimization. • smoothed perturbation analysis • smooth optimization • Statistical Learning • statistical optimization • step size • stochastic approximation • Stochastic Gradient descent • stochastic methods • stochastic optimization • Stochastic Processes • theoretical analysis • Unconstrained optimization • variance reduction • weak derivatives
• ISBN-10: 0-691-24587-8 / 0691245878
• ISBN-13: 978-0-691-24587-4 / 9780691245874