Learning Algorithms Theory and Applications: Theory and Applications

ISBN-13: 9780387906409 / Angielski / Miękka / 1981 / 280 str.

S. Lakshmivarahan

Opis

Learning constitutes one of the most important phase of the whole psychological processes and it is essential in many ways for the occurrence of necessary changes in the behavior of adjusting organisms. In a broad sense influence of prior behavior and its consequence upon subsequent behavior is usually accepted as a definition of learning. Till recently learning was regarded as the prerogative of living beings. But in the past few decades there have been attempts to construct learning machines or systems with considerable success. This book deals with a powerful class of learning algorithms that have been developed over the past two decades in the context of learning systems modelled by finite state probabilistic automaton. These algorithms are very simple iterative schemes. Mathematically these algorithms define two distinct classes of Markov processes with unit simplex (of suitable dimension) as its state space. The basic problem of learning is viewed as one of finding conditions on the algorithm such that the associated Markov process has prespecified asymptotic behavior. As a prerequisite a first course in analysis and stochastic processes would be an adequate preparation to pursue the development in various chapters.

Spis treści

1.Theory.- 1. Introduction.- 1.1. Various Approaches to Learning.- 1.2. A Learning Algorithm.- 1.3. Performance Measures and Statement of Problem.- 1.4. Classification of Learning Algorithms.- 1.5. Organization of the Book.- 1.6. Comments and Historical Remarks.- 1.7. Exercises.- 2. Ergodic Learning Algorithms.- 2.1. Introduction.- 2.2. NER?P — Algorithm.- 2.3. Analysis.- 2.4. An Alternate Characterization of z(k).- 2.5. Simulations (M = 2).- 2.6. Analysis and Simulations: General Case M ? 2.- 2.7. Comments and Historical Remarks.- 2.8. Appendix.- 2.9. Exercises.- 3. Absolutely Expedient Learning Algorithms.- 3.1. Introduction.- 3.2. NAR?P Algorithm.- 3.3. Conditions for Absolute Expediency.- 3.4. Analysis of Absolutely Expedient Algorithms.- 3.5. An Algorithm to ComDute Bounds.- 3.6. Absolute Expediency and ?-Optimality.- 3.7. Simulations.- 3.8. Comments and Historical Remarks.- 3.9. Appendix 9.- 3.10. Exercises.- 4. Time Varying Leading Algorithms.- 4.1. Introduction.- 4.2. A Time Varying Learning Algorithm.- 4.3. Kushner’s Method of Asymptotic Analysis.- A. Convergence with Probability One.- B. Weak Convergence.- 4.4. Comments and Historical Remarks.- 4.5. Appendix.- 4.6. Exercises.- II. Applications.- 5. Two-Person Zero-Sum Sequential, Stochastic Games with Imperfect and Incomplete Information-Game Matrix with Saddle-Point in Pure Strategies.- 5.1. Introduction.- 5.2. The LAR?P — Algorithm and Statement of Results.- 5.3. Analysis of Games.- 5.4. Special Case — Dominance.- 5.5. Simulations.- 5.6. Comments and Historical Remarks.- 5.7. Appendix.- 5.8. Exercises.- 6. Two-Person Zero-Sum Sequential, Stochastic Games with Imperfect and Incomplete Information — General Case.- 6.1. Introduction.- 6.2. LER?P Algorithm.- 6.3. Analysis of Game.- 6.4. Extensions.- 6.5. Simulations.- 6.6. Comments and Historical Remarks.- 6.7. Appendix.- 6.8. Exercises.- 7. Two-Person Decentralised Team Problem with Incomplete Information.- 7.1. Introduction.- 7.2. Analysis of Decentralised Team Problem LER?P Algorithm.- 7.3. Analysis of Decentralised Team Problem LAR?IAlgorithm.- 7.4. Simulations.- 7.5. Comments and Historical Remarks.- 7.6. Exercises.- 8. Control of a Markov Chain with Unknown Dynamics and Cost-Structure.- 8.1. Introduction.- 8.2. Definitions and Statement of Problem.- 8.3. Learning Algorithm.- 8.4. Analysis.- 8.5 Simulations.- 8.6. Extension to Delayed State Observations.- 8.7. Comments and Historical Remarks.- 8.8. Exercises.- Epilogue.- Epilogue.- References.