Distribution free evolvability of polynomial functions over all convex loss functions

  • Authors:

  • Paul Valiant

  • Affiliations:

  • UC Berkeley, Berkeley, California

  • Venue:
  • Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
  • Year:
  • 2012

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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.