GA-Based Learning of kDNFns Boolean Formulas

The number of samples needed to learn an instance of the representation class kDNFns of Boolean formulas is predicted using some tolerance parameters by the PAC framework. When the learning machine is a simple genetic algorithm, the initial population is an issue. Using PAC-learning we derive the population size that has at least one individual at some given Hamming distance from the optimum. Then we show that the population does not need to be close to the optimum in order to learn the concept.

[1]  Mathukumalli Vidyasagar,et al.  A Theory of Learning and Generalization: With Applications to Neural Networks and Control Systems , 1997 .

[2]  Paul J. Layzell,et al.  Explorations in design space: unconventional electronics design through artificial evolution , 1999, IEEE Trans. Evol. Comput..

[3]  Leslie G. Valiant,et al.  A theory of the learnable , 1984, STOC '84.

[4]  Zbigniew Michalewicz,et al.  Evolutionary Computation 1 , 2018 .

[5]  Heinz Mühlenbein,et al.  The Science of Breeding and Its Application to the Breeder Genetic Algorithm (BGA) , 1993, Evolutionary Computation.

[6]  Erick Cantú-Paz,et al.  Efficient and Accurate Parallel Genetic Algorithms , 2000, Genetic Algorithms and Evolutionary Computation.

[7]  David E. Goldberg,et al.  Sizing Populations for Serial and Parallel Genetic Algorithms , 1989, ICGA.

[8]  Heinz Mühlenbein,et al.  Predictive Models for the Breeder Genetic Algorithm I. Continuous Parameter Optimization , 1993, Evolutionary Computation.

[9]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[10]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[11]  Arturo Hernández Aguirre,et al.  The probably approximately correct (PAC) population size of a genetic algorithm , 2000, Proceedings 12th IEEE Internationals Conference on Tools with Artificial Intelligence. ICTAI 2000.

[12]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms in Engineering Applications , 1997, Springer Berlin Heidelberg.

[13]  Peter J. W. Rayner,et al.  Generalization and PAC learning: some new results for the class of generalized single-layer networks , 1995, IEEE Trans. Neural Networks.

[14]  Martin Anthony,et al.  Computational learning theory: an introduction , 1992 .

[15]  Hitoshi Iba,et al.  Machine Learning Approach to Gate-Level Evolvable Hardware , 1996, ICES.

[16]  Hitoshi Iba,et al.  Gate-Level Evolvable Hardware: Empirical Study and Application , 1997 .

[17]  Colin R. Reeves,et al.  Using Genetic Algorithms with Small Populations , 1993, ICGA.

[18]  David Haussler,et al.  Learnability and the Vapnik-Chervonenkis dimension , 1989, JACM.

[19]  Michael Kearns,et al.  Computational complexity of machine learning , 1990, ACM distinguished dissertations.

[20]  Tatiana Kalganova.  Evolvable hardware design of combinational logic circuits , 2000 .