The Fundamental Learning Problem that Genetic Algorithms with Uniform Crossover Solve Efficiently and Repeatedly As Evolution Proceeds
Abstract
This paper establishes theoretical bonafides for implicit concurrent multivariate effect evaluation--implicit concurrency for short---a broad and versatile computational learning efficiency thought to underlie general-purpose, non-local, noise-tolerant optimization in genetic algorithms with uniform crossover (UGAs). We demonstrate that implicit concurrency is indeed a form of efficient learning by showing that it can be used to obtain close-to-optimal bounds on the time and queries required to approximately correctly solve a constrained version (k=7, \eta=1/5) of a recognizable computational learning problem: learning parities with noisy membership queries. We argue that a UGA that treats the noisy membership query oracle as a fitness function can be straightforwardly used to approximately correctly learn the essential attributes in O(log^1.585 n) queries and O(n log^1.585 n) time, where n is the total number of attributes. Our proof relies on an accessible symmetry argument and the use of statistical hypothesis testing to reject a global null hypothesis at the 10^-100 level of significance. It is, to the best of our knowledge, the first relatively rigorous identification of efficient computational learning in an evolutionary algorithm on a non-trivial learning problem.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2013
- DOI:
- 10.48550/arXiv.1307.3824
- arXiv:
- arXiv:1307.3824
- Bibcode:
- 2013arXiv1307.3824B
- Keywords:
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- Computer Science - Neural and Evolutionary Computing;
- Computer Science - Artificial Intelligence;
- Computer Science - Computational Complexity;
- Computer Science - Discrete Mathematics;
- Computer Science - Machine Learning;
- I.2.8;
- I.2.6;
- F.2
- E-Print:
- For an easy introduction to implicit concurrency (with animations), visit http://blog.hackingevolution.net/2013/03/24/implicit-concurrency-in-genetic-algorithms/