A Smoothing Framework for Stochastic Continuous-time Reinforcement Learning Problem

A Smoothing Framework for Stochastic Continuous-time Reinforcement Learning Problem
Author: Bowen Hu
Publisher:
Total Pages: 0
Release: 2021
Genre:
ISBN:

Download A Smoothing Framework for Stochastic Continuous-time Reinforcement Learning Problem Book in PDF, Epub and Kindle

Reinforcement learning problem embraces many breakthroughs in stochastic discrete-time and deterministic continuous-time systems. Stochastic continuous-time reinforcement learning is an important yet under studied area. In this dissertation, I present a framework to adapt deterministic continuous time temporal difference learning method to stochastic continuous time systems. I first review the temporal difference methods of discrete time and deterministic continuous time. Then I discuss a popular method that solves optimal control problem and verify its accuracy with Merton's problem. Motivated by the fact that the stochastic system and corresponding deterministic system can be as close as possible as the variance term decreases to zero, I introduce a new nonparametric smoothing method that generalizes deterministic continuous time method to stochastic problem by shrinking the variance term of the stochastic process. I demonstrate that the smoothing method outperforms traditional deterministic continuous time temporal difference method in our numerical study of the stochastic pendulum. In the end, I provide the proof of the convergence of the solution of the proposed framework to a corresponding deterministic continuous time solution. If the optimal value function and optimal policy can be obtained by traditional deterministic algorithms, then applying kernel smoothing framework with continuous TD guarantees convergence to the optimal value or policy for stochastic process.

Reinforcement Learning and Stochastic Optimization

Reinforcement Learning and Stochastic Optimization
Author: Warren B. Powell
Publisher: John Wiley & Sons
Total Pages: 1090
Release: 2022-04-25
Genre: Mathematics
ISBN: 1119815053

Download Reinforcement Learning and Stochastic Optimization Book in PDF, Epub and Kindle

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.

First-order and Stochastic Optimization Methods for Machine Learning

First-order and Stochastic Optimization Methods for Machine Learning
Author: Guanghui Lan
Publisher: Springer Nature
Total Pages: 591
Release: 2020-05-15
Genre: Mathematics
ISBN: 3030395685

Download First-order and Stochastic Optimization Methods for Machine Learning Book in PDF, Epub and Kindle

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.

Reinforcement Learning, second edition

Reinforcement Learning, second edition
Author: Richard S. Sutton
Publisher: MIT Press
Total Pages: 549
Release: 2018-11-13
Genre: Computers
ISBN: 0262352702

Download Reinforcement Learning, second edition Book in PDF, Epub and Kindle

The significantly expanded and updated new edition of a widely used text on reinforcement learning, one of the most active research areas in artificial intelligence. Reinforcement learning, one of the most active research areas in artificial intelligence, is a computational approach to learning whereby an agent tries to maximize the total amount of reward it receives while interacting with a complex, uncertain environment. In Reinforcement Learning, Richard Sutton and Andrew Barto provide a clear and simple account of the field's key ideas and algorithms. This second edition has been significantly expanded and updated, presenting new topics and updating coverage of other topics. Like the first edition, this second edition focuses on core online learning algorithms, with the more mathematical material set off in shaded boxes. Part I covers as much of reinforcement learning as possible without going beyond the tabular case for which exact solutions can be found. Many algorithms presented in this part are new to the second edition, including UCB, Expected Sarsa, and Double Learning. Part II extends these ideas to function approximation, with new sections on such topics as artificial neural networks and the Fourier basis, and offers expanded treatment of off-policy learning and policy-gradient methods. Part III has new chapters on reinforcement learning's relationships to psychology and neuroscience, as well as an updated case-studies chapter including AlphaGo and AlphaGo Zero, Atari game playing, and IBM Watson's wagering strategy. The final chapter discusses the future societal impacts of reinforcement learning.

Control Systems and Reinforcement Learning

Control Systems and Reinforcement Learning
Author: Sean Meyn
Publisher: Cambridge University Press
Total Pages: 453
Release: 2022-06-09
Genre: Business & Economics
ISBN: 1316511960

Download Control Systems and Reinforcement Learning Book in PDF, Epub and Kindle

A how-to guide and scientific tutorial covering the universe of reinforcement learning and control theory for online decision making.

Efficient Reinforcement Learning Using Gaussian Processes

Efficient Reinforcement Learning Using Gaussian Processes
Author: Marc Peter Deisenroth
Publisher: KIT Scientific Publishing
Total Pages: 226
Release: 2010
Genre: Electronic computers. Computer science
ISBN: 3866445695

Download Efficient Reinforcement Learning Using Gaussian Processes Book in PDF, Epub and Kindle

This book examines Gaussian processes in both model-based reinforcement learning (RL) and inference in nonlinear dynamic systems.First, we introduce PILCO, a fully Bayesian approach for efficient RL in continuous-valued state and action spaces when no expert knowledge is available. PILCO takes model uncertainties consistently into account during long-term planning to reduce model bias. Second, we propose principled algorithms for robust filtering and smoothing in GP dynamic systems.

Numerical Integration of Stochastic Differential Equations

Numerical Integration of Stochastic Differential Equations
Author: G.N. Milstein
Publisher: Springer Science & Business Media
Total Pages: 178
Release: 2013-03-09
Genre: Computers
ISBN: 9401584559

Download Numerical Integration of Stochastic Differential Equations Book in PDF, Epub and Kindle

This book is devoted to mean-square and weak approximations of solutions of stochastic differential equations (SDE). These approximations represent two fundamental aspects in the contemporary theory of SDE. Firstly, the construction of numerical methods for such systems is important as the solutions provided serve as characteristics for a number of mathematical physics problems. Secondly, the employment of probability representations together with a Monte Carlo method allows us to reduce the solution of complex multidimensional problems of mathematical physics to the integration of stochastic equations. Along with a general theory of numerical integrations of such systems, both in the mean-square and the weak sense, a number of concrete and sufficiently constructive numerical schemes are considered. Various applications and particularly the approximate calculation of Wiener integrals are also dealt with. This book is of interest to graduate students in the mathematical, physical and engineering sciences, and to specialists whose work involves differential equations, mathematical physics, numerical mathematics, the theory of random processes, estimation and control theory.

Algorithms for Reinforcement Learning

Algorithms for Reinforcement Learning
Author: Csaba Grossi
Publisher: Springer Nature
Total Pages: 89
Release: 2022-05-31
Genre: Computers
ISBN: 3031015517

Download Algorithms for Reinforcement Learning Book in PDF, Epub and Kindle

Reinforcement learning is a learning paradigm concerned with learning to control a system so as to maximize a numerical performance measure that expresses a long-term objective. What distinguishes reinforcement learning from supervised learning is that only partial feedback is given to the learner about the learner's predictions. Further, the predictions may have long term effects through influencing the future state of the controlled system. Thus, time plays a special role. The goal in reinforcement learning is to develop efficient learning algorithms, as well as to understand the algorithms' merits and limitations. Reinforcement learning is of great interest because of the large number of practical applications that it can be used to address, ranging from problems in artificial intelligence to operations research or control engineering. In this book, we focus on those algorithms of reinforcement learning that build on the powerful theory of dynamic programming. We give a fairly comprehensive catalog of learning problems, describe the core ideas, note a large number of state of the art algorithms, followed by the discussion of their theoretical properties and limitations. Table of Contents: Markov Decision Processes / Value Prediction Problems / Control / For Further Exploration

Applied Stochastic Differential Equations

Applied Stochastic Differential Equations
Author: Simo Särkkä
Publisher: Cambridge University Press
Total Pages: 327
Release: 2019-05-02
Genre: Business & Economics
ISBN: 1316510085

Download Applied Stochastic Differential Equations Book in PDF, Epub and Kindle

With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.

Chemical Production Scheduling

Chemical Production Scheduling
Author: Christos T. Maravelias
Publisher: Cambridge University Press
Total Pages: 459
Release: 2021-05-06
Genre: Mathematics
ISBN: 1107154758

Download Chemical Production Scheduling Book in PDF, Epub and Kindle

Understand common scheduling as well as other advanced operational problems with this valuable reference from a recognized leader in the field. Beginning with basic principles and an overview of linear and mixed-integer programming, this unified treatment introduces the fundamental ideas underpinning most modeling approaches, and will allow you to easily develop your own models. With more than 150 figures, the basic concepts and ideas behind the development of different approaches are clearly illustrated. Addresses a wide range of problems arising in diverse industrial sectors, from oil and gas to fine chemicals, and from commodity chemicals to food manufacturing. A perfect resource for engineering and computer science students, researchers working in the area, and industrial practitioners.