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 when interacting with a complex, uncertain environment. In Reinforcement Learning, Richard Sutton and Andrew Barto provide a clear and simple account of the key ideas and algorithms of reinforcement learning. Their discussion ranges from the history of the field's intellectual foundations to the most recent developments and applications. The only necessary mathematical background is familiarity with elementary concepts of probability. The book is divided into three parts. Part I defines the reinforcement learning problem in terms of Markov decision processes. Part II provides basic solution methods: dynamic programming, Monte Carlo methods, and temporal-difference learning. Part III presents a unified view of the solution methods and incorporates artificial neural networks, eligibility traces, and planning; the two final chapters present case studies and consider the future of reinforcement learning.

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Reinforcement Learning: An Introduction

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A New Approach to Linear Filtering and Prediction Problems

From the Publisher:
This is the first comprehensive treatment of feed-forward neural networks from the perspective of statistical pattern recognition. After introducing the basic concepts, the book examines techniques for modelling probability density functions and the properties and merits of the multi-layer perceptron and radial basis function network models. Also covered are various forms of error functions, principal algorithms for error function minimalization, learning and generalization in neural networks, and Bayesian techniques and their applications. Designed as a text, with over 100 exercises, this fully up-to-date work will benefit anyone involved in the fields of neural computation and pattern recognition.

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Neural networks for pattern recognition

Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems. For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. The authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.

Numerical Optimization

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Pattern Recognition with Fuzzy Objective Function Algorithms

By decision-making in a fuzzy environment is meant a decision process in which the goals and/or the constraints, but not necessarily the system under control, are fuzzy in nature. This means that the goals and/or the constraints constitute classes of alternatives whose boundaries are not sharply defined.

An example of a fuzzy constraint is: “The cost of A should not be substantially higher than α,” where α is a specified constant. Similarly, an example of a fuzzy goal is: “x should be in the vicinity of x0,” where x0 is a constant. The italicized words are the sources of fuzziness in these examples.

Fuzzy goals and fuzzy constraints can be defined precisely as fuzzy sets in the space of alternatives. A fuzzy decision, then, may be viewed as an intersection of the given goals and constraints. A maximizing decision is defined as a point in the space of alternatives at which the membership function of a fuzzy decision attains its maximum value.

The use of these concepts is illustrated by examples involving multistage decision processes in which the system under control is either deterministic or stochastic. By using dynamic programming, the determination of a maximizing decision is reduced to the solution of a system of functional equations. A reverse-flow technique is described for the solution of a functional equation arising in connection with a decision process in which the termination time is defined implicitly by the condition that the process stops when the system under control enters a specified set of states in its state space.

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Decision-making in a fuzzy environment

The Mathematical Theory of Optimal Processes

Foreword Preface to the Second Edition Preface 1. Maximization, Minimization, and Motivation 2. Vectors and Matrices 3. Diagonalization and Canonical Forms for Symmetric Matrices 4. Reduction of General Symmetric Matrices to Diagonal Form 5. Constrained Maxima 6. Functions of Matrices 7. Variational Description of Characteristic Roots 8. Inequalities 9. Dynamic Programming 10. Matrices and Differential Equations 11. Explicit Solutions and Canonical Forms 12. Symmetric Function, Kronecker Products and Circulants 13. Stability Theory 14. Markoff Matrices and Probability Theory 15. Stochastic Matrices 16. Positive Matrices, Perron's Theorem, and Mathematical Economics 17. Control Processes 18. Invariant Imbedding 19. Numerical Inversion of the Laplace Transform and Tychonov Regularization Appendix A. Linear Equations and Rank Appendix B. The Quadratic Form of Selberg Appendix C. A Method of Hermite Appendix D. Moments and Quadratic Forms Index.

Introduction to Matrix Analysis

The description for this book, Adaptive Control Processes: A Guided Tour, will be forthcoming.

Adaptive Control Processes: A Guided Tour

: Given a set of N cities, with every two linked by a road, and the times required to traverse these roads, we wish to determine the path from one given city to another given city which minimizes the travel time. The times are not directly proportional to the distances due to varying quality of roads, and v varying quantities of traffic. The functional equation technique of dynamic programming, combined with approximation in policy space, yield an iterative algorithm which converges after at most (N-1) iterations.

Richard Bellman

Papers

Decision-making in a fuzzy environment

The Mathematical Theory of Optimal Processes

Introduction to Matrix Analysis

Adaptive Control Processes: A Guided Tour

On a routing problem