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Distribution Free Evolvability of Polynomial Functions over all Convex Loss Functions
| Citations: | 2 - 0 self |
BibTeX
@MISC{Valiant_distributionfree,
author = {Paul Valiant},
title = {Distribution Free Evolvability of Polynomial Functions over all Convex Loss Functions},
year = {}
}
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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. In the second part of the paper 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 more general classes of metrics. 1.
Keyphrases
distribution free evolvability convex loss function polynomial function second part real-valued vector fixed-degree polynomial function single evolution algorithm compelling way robust sense many natural biological process wide-scale random noise convex loss function converges corresponding result robust result natural algorithm natural evolution algorithm general class
