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Stochastic Recursive Algorithms For Optimization

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Stochastic Recursive Algorithms For Optimization

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Author : S. Bhatnagar
language : en
Publisher: Springer
Release Date : 2012-08-12

Stochastic Recursive Algorithms For Optimization written by S. Bhatnagar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-12 with Technology & Engineering categories.

Stochastic Recursive Algorithms for Optimization presents algorithms for constrained and unconstrained optimization and for reinforcement learning. Efficient perturbation approaches form a thread unifying all the algorithms considered. Simultaneous perturbation stochastic approximation and smooth fractional estimators for gradient- and Hessian-based methods are presented. These algorithms: • are easily implemented; • do not require an explicit system model; and • work with real or simulated data. Chapters on their application in service systems, vehicular traffic control and communications networks illustrate this point. The book is self-contained with necessary mathematical results placed in an appendix. The text provides easy-to-use, off-the-shelf algorithms that are given detailed mathematical treatment so the material presented will be of significant interest to practitioners, academic researchers and graduate students alike. The breadth of applications makes the book appropriate for reader from similarly diverse backgrounds: workers in relevant areas of computer science, control engineering, management science, applied mathematics, industrial engineering and operations research will find the content of value.

Stochastic Recursive Algorithms For Optimization

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Author : S. Bhatnagar
language : en
Publisher: Springer
Release Date : 2012-08-11

Stochastic Recursive Algorithms For Optimization

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Author : S. Bhatnagar
language : en
Publisher: Springer
Release Date : 2012-08-12

Stochastic Approximation And Recursive Algorithms And Applications

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Author : Harold Kushner
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-04

Stochastic Approximation And Recursive Algorithms And Applications written by Harold Kushner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-04 with Mathematics categories.

The basic stochastic approximation algorithms introduced by Robbins and MonroandbyKieferandWolfowitzintheearly1950shavebeenthesubject of an enormous literature, both theoretical and applied. This is due to the large number of applications and the interesting theoretical issues in the analysis of “dynamically de?ned” stochastic processes. The basic paradigm is a stochastic di?erence equation such as ? = ? + Y , where ? takes n+1 n n n n its values in some Euclidean space, Y is a random variable, and the “step n size” > 0 is small and might go to zero as n??. In its simplest form, n ? is a parameter of a system, and the random vector Y is a function of n “noise-corrupted” observations taken on the system when the parameter is set to ? . One recursively adjusts the parameter so that some goal is met n asymptotically. Thisbookisconcernedwiththequalitativeandasymptotic properties of such recursive algorithms in the diverse forms in which they arise in applications. There are analogous continuous time algorithms, but the conditions and proofs are generally very close to those for the discrete time case. The original work was motivated by the problem of ?nding a root of a continuous function g ̄(?), where the function is not known but the - perimenter is able to take “noisy” measurements at any desired value of ?. Recursive methods for root ?nding are common in classical numerical analysis, and it is reasonable to expect that appropriate stochastic analogs would also perform well.

Algorithms For Optimization

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Author : Mykel J. Kochenderfer
language : en
Publisher: MIT Press
Release Date : 2019-03-12

Algorithms For Optimization written by Mykel J. Kochenderfer and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-12 with Computers categories.

A comprehensive introduction to optimization with a focus on practical algorithms for the design of engineering systems. This book offers a comprehensive introduction to optimization with a focus on practical algorithms. The book approaches optimization from an engineering perspective, where the objective is to design a system that optimizes a set of metrics subject to constraints. Readers will learn about computational approaches for a range of challenges, including searching high-dimensional spaces, handling problems where there are multiple competing objectives, and accommodating uncertainty in the metrics. Figures, examples, and exercises convey the intuition behind the mathematical approaches. The text provides concrete implementations in the Julia programming language. Topics covered include derivatives and their generalization to multiple dimensions; local descent and first- and second-order methods that inform local descent; stochastic methods, which introduce randomness into the optimization process; linear constrained optimization, when both the objective function and the constraints are linear; surrogate models, probabilistic surrogate models, and using probabilistic surrogate models to guide optimization; optimization under uncertainty; uncertainty propagation; expression optimization; and multidisciplinary design optimization. Appendixes offer an introduction to the Julia language, test functions for evaluating algorithm performance, and mathematical concepts used in the derivation and analysis of the optimization methods discussed in the text. The book can be used by advanced undergraduates and graduate students in mathematics, statistics, computer science, any engineering field, (including electrical engineering and aerospace engineering), and operations research, and as a reference for professionals.

Stochastic Approximation Methods For Constrained And Unconstrained Systems

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Author : H.J. Kushner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Stochastic Approximation Methods For Constrained And Unconstrained Systems written by H.J. Kushner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The book deals with a powerful and convenient approach to a great variety of types of problems of the recursive monte-carlo or stochastic approximation type. Such recu- sive algorithms occur frequently in stochastic and adaptive control and optimization theory and in statistical esti- tion theory. Typically, a sequence {X } of estimates of a n parameter is obtained by means of some recursive statistical th st procedure. The n estimate is some function of the n_l estimate and of some new observational data, and the aim is to study the convergence, rate of convergence, and the pa- metric dependence and other qualitative properties of the - gorithms. In this sense, the theory is a statistical version of recursive numerical analysis. The approach taken involves the use of relatively simple compactness methods. Most standard results for Kiefer-Wolfowitz and Robbins-Monro like methods are extended considerably. Constrained and unconstrained problems are treated, as is the rate of convergence problem. While the basic method is rather simple, it can be elaborated to allow a broad and deep coverage of stochastic approximation like problems. The approach, relating algorithm behavior to qualitative properties of deterministic or stochastic differ ential equations, has advantages in algorithm conceptualiza tion and design. It is often possible to obtain an intuitive understanding of algorithm behavior or qualitative dependence upon parameters, etc., without getting involved in a great deal of deta~l.

Reinforcement Learning And Stochastic Optimization

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Author : Warren B. Powell
language : en
Publisher: John Wiley & Sons
Release Date : 2022-03-15

Reinforcement Learning And Stochastic Optimization written by Warren B. Powell and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-15 with Mathematics categories.

REINFORCEMENT LEARNING AND STOCHASTIC OPTIMIZATION Clearing the jungle of stochastic optimization Sequential decision problems, which consist of “decision, information, decision, information,” are ubiquitous, spanning virtually every human activity ranging from business applications, health (personal and public health, and medical decision making), energy, the sciences, all fields of engineering, finance, and e-commerce. The diversity of applications attracted the attention of at least 15 distinct fields of research, using eight distinct notational systems which produced a vast array of analytical tools. A byproduct is that powerful tools developed in one community may be unknown to other communities. Reinforcement Learning and Stochastic Optimization offers a single canonical framework that can model any sequential decision problem using five core components: state variables, decision variables, exogenous information variables, transition function, and objective function. This book highlights twelve types of uncertainty that might enter any model and pulls together the diverse set of methods for making decisions, known as policies, into four fundamental classes that span every method suggested in the academic literature or used in practice. Reinforcement Learning and Stochastic Optimization is the first book to provide a balanced treatment of the different methods for modeling and solving sequential decision problems, following the style used by most books on machine learning, optimization, and simulation. The presentation is designed for readers with a course in probability and statistics, and an interest in modeling and applications. Linear programming is occasionally used for specific problem classes. The book is designed for readers who are new to the field, as well as those with some background in optimization under uncertainty. Throughout this book, readers will find references to over 100 different applications, spanning pure learning problems, dynamic resource allocation problems, general state-dependent problems, and hybrid learning/resource allocation problems such as those that arose in the COVID pandemic. There are 370 exercises, organized into seven groups, ranging from review questions, modeling, computation, problem solving, theory, programming exercises and a "diary problem" that a reader chooses at the beginning of the book, and which is used as a basis for questions throughout the rest of the book.

Introduction To Derivative Free Optimization

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Author : Andrew R. Conn
language : en
Publisher: SIAM
Release Date : 2009-04-16

Introduction To Derivative Free Optimization written by Andrew R. Conn and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-16 with Mathematics categories.

The first contemporary comprehensive treatment of optimization without derivatives. This text explains how sampling and model techniques are used in derivative-free methods and how they are designed to solve optimization problems. It is designed to be readily accessible to both researchers and those with a modest background in computational mathematics.

Optimization For Machine Learning

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Author : Suvrit Sra
language : en
Publisher: MIT Press
Release Date : 2012

Optimization For Machine Learning written by Suvrit Sra and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Computers categories.

An up-to-date account of the interplay between optimization and machine learning, accessible to students and researchers in both communities. The interplay between optimization and machine learning is one of the most important developments in modern computational science. Optimization formulations and methods are proving to be vital in designing algorithms to extract essential knowledge from huge volumes of data. Machine learning, however, is not simply a consumer of optimization technology but a rapidly evolving field that is itself generating new optimization ideas. This book captures the state of the art of the interaction between optimization and machine learning in a way that is accessible to researchers in both fields. Optimization approaches have enjoyed prominence in machine learning because of their wide applicability and attractive theoretical properties. The increasing complexity, size, and variety of today's machine learning models call for the reassessment of existing assumptions. This book starts the process of reassessment. It describes the resurgence in novel contexts of established frameworks such as first-order methods, stochastic approximations, convex relaxations, interior-point methods, and proximal methods. It also devotes attention to newer themes such as regularized optimization, robust optimization, gradient and subgradient methods, splitting techniques, and second-order methods. Many of these techniques draw inspiration from other fields, including operations research, theoretical computer science, and subfields of optimization. The book will enrich the ongoing cross-fertilization between the machine learning community and these other fields, and within the broader optimization community.

Fundamentals Of Queueing Networks

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Author : Hong Chen
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-06-15

Fundamentals Of Queueing Networks written by Hong Chen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-15 with Business & Economics categories.

"The selection of materials is well balanced in breadth and depth, making the book an ideal graduate-level text for students in engineering, business, applied mathematics, and probability and statistics.

Stochastic Recursive Algorithms For Optimization

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