Perturbations Optimization And Statistics
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Author | : Tamir Hazan |
Publisher | : MIT Press |
Total Pages | : 413 |
Release | : 2023-12-05 |
Genre | : Computers |
ISBN | : 0262549948 |
A description of perturbation-based methods developed in machine learning to augment novel optimization methods with strong statistical guarantees. In nearly all machine learning, decisions must be made given current knowledge. Surprisingly, making what is believed to be the best decision is not always the best strategy, even when learning in a supervised learning setting. An emerging body of work on learning under different rules applies perturbations to decision and learning procedures. These methods provide simple and highly efficient learning rules with improved theoretical guarantees. This book describes perturbation-based methods developed in machine learning to augment novel optimization methods with strong statistical guarantees, offering readers a state-of-the-art overview. Chapters address recent modeling ideas that have arisen within the perturbations framework, including Perturb & MAP, herding, and the use of neural networks to map generic noise to distribution over highly structured data. They describe new learning procedures for perturbation models, including an improved EM algorithm and a learning algorithm that aims to match moments of model samples to moments of data. They discuss understanding the relation of perturbation models to their traditional counterparts, with one chapter showing that the perturbations viewpoint can lead to new algorithms in the traditional setting. And they consider perturbation-based regularization in neural networks, offering a more complete understanding of dropout and studying perturbations in the context of deep neural networks.
Author | : J.Frederic Bonnans |
Publisher | : Springer Science & Business Media |
Total Pages | : 618 |
Release | : 2013-11-22 |
Genre | : Mathematics |
ISBN | : 1461213940 |
A presentation of general results for discussing local optimality and computation of the expansion of value function and approximate solution of optimization problems, followed by their application to various fields, from physics to economics. The book is thus an opportunity for popularizing these techniques among researchers involved in other sciences, including users of optimization in a wide sense, in mechanics, physics, statistics, finance and economics. Of use to research professionals, including graduate students at an advanced level.
Author | : Anthony V. Fiacco |
Publisher | : |
Total Pages | : 398 |
Release | : 1990 |
Genre | : |
ISBN | : 9783905135886 |
Author | : Doug E. Ward |
Publisher | : |
Total Pages | : 460 |
Release | : 2001 |
Genre | : |
ISBN | : |
Author | : Matthew James Staib |
Publisher | : |
Total Pages | : 241 |
Release | : 2020 |
Genre | : |
ISBN | : |
Many problems in the machine learning pipeline boil down to maximizing the expectation of a function over a distribution. This is the classic problem of stochastic optimization. There are two key challenges in solving such stochastic optimization problems: 1) the function is often non-convex, making optimization difficult; 2) the distribution is not known exactly, but may be perturbed adversarially or is otherwise obscured. Each issue is individually so challenging to warrant a substantial accompanying body of work addressing it, but addressing them simultaneously remains difficult. This thesis addresses problems at the intersection of non-convexity and data perturbations. We study the intersection of the two issues along two dual lines of inquiry: first, we build perturbation-aware algorithms with guarantees for non-convex problems; second, we seek to understand how data perturbations can be leveraged to enhance non-convex optimization algorithms. Along the way, we will study new types of data perturbations and seek to understand their connection to generalization.
Author | : Doug E. Ward |
Publisher | : |
Total Pages | : 472 |
Release | : 2001 |
Genre | : Mathematical optimization |
ISBN | : |
Author | : Anthony V. Fiacco |
Publisher | : CRC Press |
Total Pages | : 460 |
Release | : 2020-09-24 |
Genre | : Mathematics |
ISBN | : 1000153665 |
Presents research contributions and tutorial expositions on current methodologies for sensitivity, stability and approximation analyses of mathematical programming and related problem structures involving parameters. The text features up-to-date findings on important topics, covering such areas as the effect of perturbations on the performance of algorithms, approximation techniques for optimal control problems, and global error bounds for convex inequalities.
Author | : Anthony V. Fiacco |
Publisher | : CRC Press |
Total Pages | : 456 |
Release | : 2020-09-23 |
Genre | : Mathematics |
ISBN | : 1000117111 |
Presents research contributions and tutorial expositions on current methodologies for sensitivity, stability and approximation analyses of mathematical programming and related problem structures involving parameters. The text features up-to-date findings on important topics, covering such areas as the effect of perturbations on the performance of algorithms, approximation techniques for optimal control problems, and global error bounds for convex inequalities.
Author | : Fiacco |
Publisher | : CRC Press |
Total Pages | : 174 |
Release | : 2020-09-24 |
Genre | : Mathematics |
ISBN | : 1000153436 |
This book presents theoretical results, including an extension of constant rank and implicit function theorems, continuity and stability bounds results for infinite dimensional problems, and the interrelationship between optimal value conditions and shadow prices for stable and unstable programs.
Author | : Evgenij S. Levitin |
Publisher | : |
Total Pages | : 416 |
Release | : 1994-09-06 |
Genre | : Mathematics |
ISBN | : |
Presents the author's research of local parametric optimization in the finite-dimensional case. This book provides a clear and complete formulation of the main perturbation theory problems for finite-dimensional optimization as well as new mathematical methods to analyze these problems. Using a unified approach, the author has developed a general perturbation theory for finite-dimensional extremum problems. Within the framework of this theory, methods for studying perturbed problems in zero-, first- and second-order approximations have been developed.