Introduction to a learning general theory
Cybernetics and Systems
Mathematical theory of neural learning
New Generation Computing - Selected papers from the international workshop on algorithmic learning theory,1990
Algorithms: main ideas and applications
Algorithms: main ideas and applications
Elements of machine learning
An introduction to genetic algorithms
An introduction to genetic algorithms
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Dynamic Programming and Optimal Control
Dynamic Programming and Optimal Control
Introduction to Reinforcement Learning
Introduction to Reinforcement Learning
Neuro-Dynamic Programming
Hi-index | 0.00 |
The number of studies related to natural and artificial mechanisms of learning rapidly increases. However, there is no general theory of learning that could provide a unifying basis for exploring different directions in this growing field. For a long time the development of such a theory has been hindered by nativists' belief that the development of a biological organism during ontogeny should be viewed as parameterization of an innate, encoded in the genome structure by an innate algorithm, and nothing essentially new is created during this process. Noam Chomsky has claimed, therefore, that the creation of a non-trivial general mathematical theory of learning is not feasible, since any algorithm cannot produce a more complex algorithm. This study refutes the above argumentation by developing a counter-example based on the mathematical theory of algorithms and computable functions. It introduces a novel concept of a Universal Learning System (ULS) capable of learning to control in an optimal way any given constructive system from a certain class. The necessary conditions for the existence of a ULS and its main functional properties are investigated. The impossibility of building an algorithmic ULS for a sufficiently complex class of controlled objects is shown, and a proof of the existence of a nonalgorithmic ULS based on the axioms of classical mathematics is presented. It is argued that a non-algorithmic ULS is a legitimate object of not only mathematics, but also the world of nature. These results indicate that an algorithmic description of the organization and adaptive development of biological systems in general is not sufficient. At the same time, it is possible to create a rigorous non-algorithmic general theory of learning as a theory of ULS. The utilization of this framework for integrating learning-related studies is discussed.