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Author : Yuri Ermoliev
Publisher :
ISBN 13 :
Total Pages : 13 pages
Book Rating : 4.:/5 (256 download)
Download or read book A Stochastic Algorithm for Minimax Problems written by Yuri Ermoliev and published by . This book was released on 1982 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ding-Zhu Du
Publisher : Springer Science & Business Media
ISBN 13 : 1461335574
Total Pages : 300 pages
Book Rating : 4.4/5 (613 download)
Download or read book Minimax and Applications written by Ding-Zhu Du and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Techniques and principles of minimax theory play a key role in many areas of research, including game theory, optimization, and computational complexity. In general, a minimax problem can be formulated as min max f(x, y) (1) ",EX !lEY where f(x, y) is a function defined on the product of X and Y spaces. There are two basic issues regarding minimax problems: The first issue concerns the establishment of sufficient and necessary conditions for equality minmaxf(x,y) = maxminf(x,y). (2) "'EX !lEY !lEY "'EX The classical minimax theorem of von Neumann is a result of this type. Duality theory in linear and convex quadratic programming interprets minimax theory in a different way. The second issue concerns the establishment of sufficient and necessary conditions for values of the variables x and y that achieve the global minimax function value f(x*, y*) = minmaxf(x, y). (3) "'EX !lEY There are two developments in minimax theory that we would like to mention.
Author : Breton, Michèle
Publisher : Montréal : Groupe d'études et de recherche en analyse des décisions
ISBN 13 :
Total Pages : 46 pages
Book Rating : 4.:/5 (268 download)
Download or read book Algorithms for the Solution of Stochastic Dynamic Minimax Problems written by Breton, Michèle and published by Montréal : Groupe d'études et de recherche en analyse des décisions. This book was released on 1992 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Guanghui Lan
Publisher : Springer Nature
ISBN 13 : 3030395685
Total Pages : 591 pages
Book Rating : 4.0/5 (33 download)
Download or read book First-order and Stochastic Optimization Methods for Machine Learning written by Guanghui Lan and published by Springer Nature. This book was released on 2020-05-15 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers not only foundational materials but also the most recent progresses made during the past few years on the area of machine learning algorithms. In spite of the intensive research and development in this area, there does not exist a systematic treatment to introduce the fundamental concepts and recent progresses on machine learning algorithms, especially on those based on stochastic optimization methods, randomized algorithms, nonconvex optimization, distributed and online learning, and projection free methods. This book will benefit the broad audience in the area of machine learning, artificial intelligence and mathematical programming community by presenting these recent developments in a tutorial style, starting from the basic building blocks to the most carefully designed and complicated algorithms for machine learning.
Author : Breton, Michèle
Publisher : Montréal : Groupe d'études et de recherche en analyse des décisions
ISBN 13 :
Total Pages : 46 pages
Book Rating : 4.:/5 (262 download)
Download or read book A Scenario Aggregation Algorithm for the Solution of Stochastic Dynamic Minimax Problems written by Breton, Michèle and published by Montréal : Groupe d'études et de recherche en analyse des décisions. This book was released on 1992 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A. Sukharev
Publisher : Springer Science & Business Media
ISBN 13 : 940112759X
Total Pages : 273 pages
Book Rating : 4.4/5 (11 download)
Download or read book Minimax Models in the Theory of Numerical Methods written by A. Sukharev and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the Russian edition published in 1989, this book was called "Minimax Algorithms in Problems of Numerical Analysis". The new title is better related to the subject of the book and its style. The basis for every decision or inference concerning the ways to solve a given problem is the computa tion model. Thus, the computation model is the epicenter of any structure studied in the book. Algorithms are not constructed here, they are rather derived from computation models. Quality of an algorithm depends entirely on consistency of the model with the real-life problem. So, constructing a model is an art, deriving an algorithm is a science. We study only minimax or, in other words, worst-case computation models. However, one of the characteristic features of the book is a new approach to the notion of the worst-case conditions in dynamic processes. This approach leads to the concept of sequentially optimal algorithms, which play the central role in the book. In conclusion, I would like to express my gratitude to Prof. Dr. Heinz J. Skala and Dr. Sergei A. Orlovsky for encouraging translation of this book. I also greatly appreciate the highly professional job of Dr. Olga R. Chuyan who translated the book.
Author : Robert Dyson
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (142 download)
Download or read book A Global Algorithm for Minimax Solutions to a Stochastic Programming Problem written by Robert Dyson and published by . This book was released on 1975 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Christodoulos A. Floudas
Publisher : Springer Science & Business Media
ISBN 13 : 0387747583
Total Pages : 4646 pages
Book Rating : 4.3/5 (877 download)
Download or read book Encyclopedia of Optimization written by Christodoulos A. Floudas and published by Springer Science & Business Media. This book was released on 2008-09-04 with total page 4646 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".
Author : Nima Hamidi
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (125 download)
Download or read book Minimax Regret Bounds for Stochastic Linear Bandit Algorithms written by Nima Hamidi and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The multi-armed bandit problem is a popular framework to model online experiments and the ideas in this domain are intended to help making better decisions as more data becomes available to a learner. Stochastic linear bandits are an important subclass of this general problem that have many applications in areas such as dynamic asset pricing and healthcare. In this dissertation, we study this problem and provide an analysis that produces many existing results as well as some new bounds. Our analysis also naturally leads to a new algorithm, called Sieved-Greedy (SG), that reduces the exploration while maintaining strong theoretical guarantees. Furthermore, we show that all of these bounds can be improved significantly under additional gap assumptions. In particular, we show that the regret of Optimism in Face of Uncertainty Linear bandit (OFUL) and Thompson Sampling (TS), two popular algorithms in this domain, scale poly-logarithmically under these assumptions (rather than as $\sqrt T$ ). Next, we focus on TS and prove that, although it achieves near optimal Bayesian regret bounds, it may perform poorly under mild distributional mismatches. Finally, we introduce a data-driven version of TS and prove that, under mild conditions, it achieves minimax optimal regret even in the worst case. An important property of both of our proposed algorithms (SG and improved TS) is that they use the observed data to adjust the rate of exploration.
![Download A Global Alogorithm [i.e. Algorithm] for Minimax Solutions to a Stochastic Programming Problem PDF Online Free](https://books.google.com/books/content/images/frontcover/QEnZGwAACAAJ?fife=w200-h370)
Author : Robert Dyson
Publisher :
ISBN 13 :
Total Pages : 16 pages
Book Rating : 4.:/5 (314 download)
Download or read book A Global Alogorithm [i.e. Algorithm] for Minimax Solutions to a Stochastic Programming Problem written by Robert Dyson and published by . This book was released on 1975 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Berç Rustem
Publisher : Princeton University Press
ISBN 13 : 1400825113
Total Pages : 405 pages
Book Rating : 4.4/5 (8 download)
Download or read book Algorithms for Worst-Case Design and Applications to Risk Management written by Berç Rustem and published by Princeton University Press. This book was released on 2009-02-09 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recognizing that robust decision making is vital in risk management, this book provides concepts and algorithms for computing the best decision in view of the worst-case scenario. The main tool used is minimax, which ensures robust policies with guaranteed optimal performance that will improve further if the worst case is not realized. The applications considered are drawn from finance, but the design and algorithms presented are equally applicable to problems of economic policy, engineering design, and other areas of decision making. Critically, worst-case design addresses not only Armageddon-type uncertainty. Indeed, the determination of the worst case becomes nontrivial when faced with numerous--possibly infinite--and reasonably likely rival scenarios. Optimality does not depend on any single scenario but on all the scenarios under consideration. Worst-case optimal decisions provide guaranteed optimal performance for systems operating within the specified scenario range indicating the uncertainty. The noninferiority of minimax solutions--which also offer the possibility of multiple maxima--ensures this optimality. Worst-case design is not intended to necessarily replace expected value optimization when the underlying uncertainty is stochastic. However, wise decision making requires the justification of policies based on expected value optimization in view of the worst-case scenario. Conversely, the cost of the assured performance provided by robust worst-case decision making needs to be evaluated relative to optimal expected values. Written for postgraduate students and researchers engaged in optimization, engineering design, economics, and finance, this book will also be invaluable to practitioners in risk management.
Author : Leland A. Gardner
Publisher :
ISBN 13 :
Total Pages : 39 pages
Book Rating : 4.:/5 (149 download)
Download or read book Stochastic Approximation and "minimax" Problems written by Leland A. Gardner and published by . This book was released on 1960 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Luyang Chen
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (11 download)
Download or read book Studies in Stochastic Optimization and Applications written by Luyang Chen and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: All machine learning problems reduce to some kind of stochastic optimization problem, which can be solved with variants of algorithms in stochastic approximation literature. In this thesis, we study the classical stochastic optimization algorithms and their extensions to two financial applications. In the first part of this thesis, we revisit the classical stochastic approximation algorithm introduced by Robbins and Monro in 1951, now referred to as the Robbins-Monro procedure. We establish its consistency and utilize the Martingale Central Limit Theorem to prove comprehensive asymptotic normality results for the algorithm. In the second part of this thesis, we introduce a trading algorithm to solve the optimal execution problem in the context of trading in dark pools. The stochastic optimization problem to minimize cost is solved together with an estimation problem to learn the underlying unknown distribution of trading volume limits. Our algorithm solves the two problems which are related, and updates the allocation strategy and the estimations of volume limits alternatively. In the third part of this thesis, we estimate a general non-linear asset pricing model with deep neural network applied to all U.S. equity data combined with a substantial set of macroeconomic and firm-specific information. We include the no-arbitrage condition in the objective and consider a GMM type problem with infinite moment conditions. We combine different neural network structures in a novel way and modify the stochastic optimization algorithms to solve a minimax optimization problem. Our model allows us to understand the key factors that drive asset prices, identify mis-pricing of stocks and generate the mean-variance efficient portfolio.
Author : Georg Ch. Pflug
Publisher : Springer
ISBN 13 : 3319088432
Total Pages : 309 pages
Book Rating : 4.3/5 (19 download)
Download or read book Multistage Stochastic Optimization written by Georg Ch. Pflug and published by Springer. This book was released on 2014-11-12 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multistage stochastic optimization problems appear in many ways in finance, insurance, energy production and trading, logistics and transportation, among other areas. They describe decision situations under uncertainty and with a longer planning horizon. This book contains a comprehensive treatment of today’s state of the art in multistage stochastic optimization. It covers the mathematical backgrounds of approximation theory as well as numerous practical algorithms and examples for the generation and handling of scenario trees. A special emphasis is put on estimation and bounding of the modeling error using novel distance concepts, on time consistency and the role of model ambiguity in the decision process. An extensive treatment of examples from electricity production, asset liability management and inventory control concludes the book.
Author : Johan Löfberg
Publisher : Linköping University Electronic Press
ISBN 13 : 9173736228
Total Pages : 212 pages
Book Rating : 4.1/5 (737 download)
Download or read book Minimax Approaches to Robust Model Predictive Control written by Johan Löfberg and published by Linköping University Electronic Press. This book was released on 2003-04-11 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Controlling a system with control and state constraints is one of the most important problems in control theory, but also one of the most challenging. Another important but just as demanding topic is robustness against uncertainties in a controlled system. One of the most successful approaches, both in theory and practice, to control constrained systems is model predictive control (MPC). The basic idea in MPC is to repeatedly solve optimization problems on-line to find an optimal input to the controlled system. In recent years, much effort has been spent to incorporate the robustness problem into this framework. The main part of the thesis revolves around minimax formulations of MPC for uncertain constrained linear discrete-time systems. A minimax strategy in MPC means that worst-case performance with respect to uncertainties is optimized. Unfortunately, many minimax MPC formulations yield intractable optimization problems with exponential complexity. Minimax algorithms for a number of uncertainty models are derived in the thesis. These include systems with bounded external additive disturbances, systems with uncertain gain, and systems described with linear fractional transformations. The central theme in the different algorithms is semidefinite relaxations. This means that the minimax problems are written as uncertain semidefinite programs, and then conservatively approximated using robust optimization theory. The result is an optimization problem with polynomial complexity. The use of semidefinite relaxations enables a framework that allows extensions of the basic algorithms, such as joint minimax control and estimation, and approx- imation of closed-loop minimax MPC using a convex programming framework. Additional topics include development of an efficient optimization algorithm to solve the resulting semidefinite programs and connections between deterministic minimax MPC and stochastic risk-sensitive control. The remaining part of the thesis is devoted to stability issues in MPC for continuous-time nonlinear unconstrained systems. While stability of MPC for un-constrained linear systems essentially is solved with the linear quadratic controller, no such simple solution exists in the nonlinear case. It is shown how tools from modern nonlinear control theory can be used to synthesize finite horizon MPC controllers with guaranteed stability, and more importantly, how some of the tech- nical assumptions in the literature can be dispensed with by using a slightly more complex controller.
Author : V. Jeyakumar
Publisher : Springer Science & Business Media
ISBN 13 : 9780387267692
Total Pages : 476 pages
Book Rating : 4.2/5 (676 download)
Download or read book Continuous Optimization written by V. Jeyakumar and published by Springer Science & Business Media. This book was released on 2005-08-10 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The search for the best possible performance is inherent in human nature. Individuals, enterprises and governments all seek optimal—that is, the best—possible solutions of problems that they meet. Evidently, continuous optimization plays an increasingly significant role in everyday management and technical decisions in science, engineering and commerce. The collection of 16 refereed papers in this book covers a diverse number of topics and provides a good picture of recent research in continuous optimization. The first part of the book presents substantive survey articles in a number of important topic areas of continuous optimization. Most of the papers in the second part present results on the theoretical aspects as well as numerical methods of continuous optimization. The papers in the third part are mainly concerned with applications of continuous optimization. Hence, the book will be an additional valuable source of information to faculty, students, and researchers who use continuous optimization to model and solve problems. Audience This book is intended for researchers in mathematical programming, optimization and operations research; engineers in various fields; and graduate students in applied mathematics, engineering and operations research.
Author : Tor Lattimore
Publisher : Cambridge University Press
ISBN 13 : 1108486827
Total Pages : 537 pages
Book Rating : 4.1/5 (84 download)
Download or read book Bandit Algorithms written by Tor Lattimore and published by Cambridge University Press. This book was released on 2020-07-16 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive and rigorous introduction for graduate students and researchers, with applications in sequential decision-making problems.
