Structure Of Optimal Policies For Large Scale Stochastic Systems
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Structure Of Optimal Policies For Large Scale Stochastic Systems
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Author : Chelsea C. White
language : en
Publisher:
Release Date : 1979
Structure Of Optimal Policies For Large Scale Stochastic Systems written by Chelsea C. White and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with categories.
Stability Analysis And Optimal Control Of Large Scale Stochastic Systems
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Author : Hassan Hmedi
language : en
Publisher:
Release Date : 2022
Stability Analysis And Optimal Control Of Large Scale Stochastic Systems written by Hassan Hmedi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.
In the past years, large-scale stochastic networks have been an intense subject of study due to their use in modelling a variety of systems including telecommunications, service and data centers, patient flows, etc. The optimal control of such systems has found numerous applications such as, but not limited to, finance and cognitive neuroscience. This thesis focuses on the stability analysis and optimal control of stochastic systems. In particular, we study: (1) the ergodic properties of multiclass multi-pool networks in the Halfin-Whitt regime; and (2) the optimal control of stochastic networks assuming a structural property relating the running cost to the solution of the Hamilton-Jacobi-Bellman (HJB) equation. In the first part of this thesis, we introduce a "system-wide safety staffing" (SWSS) parameter for multiclass multi-pool networks in the Halfin-Whitt regime which have any tree topology. This parameter can be regarded as the optimal reallocation of the capacity fluctuations (positive or negative) when each server pool employs a square-root staffing rule. First, we provide an explicit form of the SWSS as a function of the system parameters, which is derived using a graph theoretic approach based on Gaussian elimination. In addition, we give an equivalent characterization of the SWSS parameter via the drift parameters of the limiting diffusion. Then, we show that if the SWSS parameter is negative, the limiting diffusion and the diffusion-scaled queueing processes are transient under any Markov control, and cannot have a stationary distribution when this parameter is zero. If it is positive, we show that the diffusion-scaled queueing processes are stabilizable, that is, there exists a scheduling policy under which the stationary distributions of the controlled processes are tight over the size of the network. Finally, we show that there exists a control under which the limiting controlled diffusion is exponentially ergodic. Thus, we have identified a necessary and sufficient condition for the stabilizability of such networks in the Halfin-Whitt regime. In the second part of this thesis, we examine two problems related to the general topic of optimal control of stochastic systems. In the first problem, we consider a linear system with Gaussian noise observed by multiple sensors which transmit measurements over a dynamic lossy network. We assume that the system is stabilizable, that is, there exists a control such that all states variables are bounded during system's behavior. First, we characterize the stationary optimal sensor scheduling policy for the finite horizon, discounted, and long-term average cost problems. Then, we show that there exists a structural property relating the running cost to the value function which is the solution of the average cost problem. In addition, we show that the value iteration algorithm converges to this solution. Further, we show that the suboptimal policies provided by the rolling horizon truncation of the value iteration also guarantee stability and provide near-optimal average cost. Lastly, we provide qualitative characterizations of the multidimensional set of measurement loss rates for which the system is stabilizable for a static network, thus extending earlier results on intermittent observations. In the second problem and motivated by the results from the previous problem, a multiplicative relative value iteration algorithm (RVI) for infinite-horizon risk-sensitive control of controlled diffusions in [doublestruck R][superscript d] is studied. We assume that the running cost is near-monotone and that it is related to the solution of the multiplicative HJB equation through a structural assumption. We show that this structural assumption implies the existence of a control under which the ground state diffusion is exponentially ergodic. In addition, we show that the multiplicative RVI algorithm converges globally to the solution of the multiplicative dynamic programming equation starting from any positive initial condition; thus extending upon the results in the literature
Stochastic Large Scale Engineering Systems
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Author : Tzafestas
language : en
Publisher: CRC Press
Release Date : 1992-04-24
Stochastic Large Scale Engineering Systems written by Tzafestas and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-04-24 with Technology & Engineering categories.
This book focuses on the class of large-scale stochastic systems, which has dominated the attention of many academic and research groups. It discusses distributed-sensor networks, decentralized detection theory, and econometric models with integrated and decentralized policymakers.
Optimization Control And Applications Of Stochastic Systems
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Author : Daniel Hernández-Hernández
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-15
Optimization Control And Applications Of Stochastic Systems written by Daniel Hernández-Hernández 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 2012-08-15 with Science categories.
This volume provides a general overview of discrete- and continuous-time Markov control processes and stochastic games, along with a look at the range of applications of stochastic control and some of its recent theoretical developments. These topics include various aspects of dynamic programming, approximation algorithms, and infinite-dimensional linear programming. In all, the work comprises 18 carefully selected papers written by experts in their respective fields. Optimization, Control, and Applications of Stochastic Systems will be a valuable resource for all practitioners, researchers, and professionals in applied mathematics and operations research who work in the areas of stochastic control, mathematical finance, queueing theory, and inventory systems. It may also serve as a supplemental text for graduate courses in optimal control and dynamic games.
Practical Applications Of Large Scale Stochastic Control For Learning And Optimization
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Author : Eli Gutin
language : en
Publisher:
Release Date : 2018
Practical Applications Of Large Scale Stochastic Control For Learning And Optimization written by Eli Gutin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
This thesis explores a variety of techniques for large-scale stochastic control. These range from simple heuristics that are motivated by the problem structure and are amenable to analysis, to more general deep reinforcement learning (RL) which applies to broader classes of problems but is trickier to reason about. In the first part of this thesis, we explore a less known application of stochastic control in Multi-armed bandits. By assuming a Bayesian statistical model, we get enough problem structure so that we can formulate an MDP to maximize total rewards. If the objective involved total discounted rewards over an infinite horizon, then the celebrated Gittins index policy would be optimal. Unfortunately, the analysis there does not carry over to the non-discounted, finite-horizon problem. In this work, we propose a tightening sequence of 'optimistic' approximations to the Gittins index. We show that the use of these approximations together with the use of an increasing discount factor appears to offer a compelling alternative to state-of-the-art algorithms. We prove that these optimistic indices constitute a regret optimal algorithm, in the sense of meeting the Lai-Robbins lower bound, including matching constants. The second part of the thesis focuses on the collateral management problem (CMP). In this work, we study the CMP, faced by a prime brokerage, through the lens of multi-period stochastic optimization. We find that, for a large class of CMP instances, algorithms that select collateral based on appropriately computed asset prices are near-optimal. In addition, we back-test the method on data from a prime brokerage and find substantial increases in revenue. Finally, in the third part, we propose novel deep reinforcement learning (DRL) methods for option pricing and portfolio optimization problems. Our work on option pricing enables one to compute tighter confidence bounds on the price, using the same number of Monte Carlo samples, than existing techniques. We also examine constrained portfolio optimization problems and test out policy gradient algorithms that work with somewhat different objective functions. These new objectives measure the performance of a projected version of the policy and penalize constraint violation.
Fundamentals Of Stochastic Models
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Author : Zhe George Zhang
language : en
Publisher: CRC Press
Release Date : 2023-05-18
Fundamentals Of Stochastic Models written by Zhe George Zhang and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-18 with Technology & Engineering categories.
Stochastic modeling is a set of quantitative techniques for analyzing practical systems with random factors. This area is highly technical and mainly developed by mathematicians. Most existing books are for those with extensive mathematical training; this book minimizes that need and makes the topics easily understandable. Fundamentals of Stochastic Models offers many practical examples and applications and bridges the gap between elementary stochastics process theory and advanced process theory. It addresses both performance evaluation and optimization of stochastic systems and covers different modern analysis techniques such as matrix analytical methods and diffusion and fluid limit methods. It goes on to explore the linkage between stochastic models, machine learning, and artificial intelligence, and discusses how to make use of intuitive approaches instead of traditional theoretical approaches. The goal is to minimize the mathematical background of readers that is required to understand the topics covered in this book. Thus, the book is appropriate for professionals and students in industrial engineering, business and economics, computer science, and applied mathematics.
Knowledge You Can Act On
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Author : Alexandar Angelus
language : en
Publisher:
Release Date : 2017
Knowledge You Can Act On written by Alexandar Angelus and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.
We consider a nonstationary, stochastic, multi-stage supply system with a general assembly structure, in which customers can place orders in advance of their future demand requirements. This advance demand information is now recognized in both theory and practice as an important strategy for managing the mismatch between supply and demand. In conjunction, we allow expediting of components and partially completed subassemblies in the system in order to provide the supply chain with the means to manage the stockout risk and significantly enhance cost savings realized through advance demand information. To solve the resulting assembly system, we develop a new method based on identifying local properties of optimal decisions. This new method allows us to solve assembly systems with multiple product flows. We derive the structure of the optimal policy, which represents a double-tiered echelon basestock policy whose basestock levels depend on the state of advance demand information. This form of the optimal policy allows us to: (i) provide actionable policies for firms to manage large-scale assembly systems with expediting and advance demand information; (ii) prove that advance demand information and expediting of stock both reduce the amount of inventory optimally held in the system; and (iii) numerically solve such assembly systems, and quantify the savings realized. In contrast to the conventional wisdom, we discover that advance demand information and expediting of stock are complementary under short demand information horizons. They are substitutes only under longer information horizons.
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.
Handbook Of Stochastic Analysis And Applications
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Author : D. Kannan
language : en
Publisher: CRC Press
Release Date : 2001-10-23
Handbook Of Stochastic Analysis And Applications written by D. Kannan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-10-23 with Mathematics categories.
An introduction to general theories of stochastic processes and modern martingale theory. The volume focuses on consistency, stability and contractivity under geometric invariance in numerical analysis, and discusses problems related to implementation, simulation, variable step size algorithms, and random number generation.
Grants And Awards For The Fiscal Year Ended
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Author : National Science Foundation (U.S.)
language : en
Publisher:
Release Date : 1977
Grants And Awards For The Fiscal Year Ended written by National Science Foundation (U.S.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Federal aid to research categories.