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Evolvability of Real Functions

Evolvability of Real Functions We formulate a notion of evolvability for functions with domain and range that are real-valued vectors, a compelling way of expressing many natural biological processes. We show that linear and fixed-degree polynomial functions are evolvable in the following dually-robust sense: There is a single evolution algorithm that, for all convex loss functions, converges for all distributions. It is possible that such dually-robust results can be achieved by simpler and more-natural evolution algorithms. Towards this end, we introduce a simple and natural algorithm that we call wide-scale random noise and prove a corresponding result for the L2 metric. We conjecture that the algorithm works for a more general class of metrics. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computation Theory (TOCT) Association for Computing Machinery

Evolvability of Real Functions

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References (22)

Publisher
Association for Computing Machinery
Copyright
Copyright © 2014 ACM
ISSN
1942-3454
eISSN
1942-3462
DOI
10.1145/2633598
Publisher site
See Article on Publisher Site

Abstract

We formulate a notion of evolvability for functions with domain and range that are real-valued vectors, a compelling way of expressing many natural biological processes. We show that linear and fixed-degree polynomial functions are evolvable in the following dually-robust sense: There is a single evolution algorithm that, for all convex loss functions, converges for all distributions. It is possible that such dually-robust results can be achieved by simpler and more-natural evolution algorithms. Towards this end, we introduce a simple and natural algorithm that we call wide-scale random noise and prove a corresponding result for the L2 metric. We conjecture that the algorithm works for a more general class of metrics.

Journal

ACM Transactions on Computation Theory (TOCT)Association for Computing Machinery

Published: Jul 1, 2014

Keywords: Evolvability

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