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.
- K. Ball. 1997. An elementary introduction to modern convex geometry. MSRI Pub. 31.Google Scholar
- V. Feldman. 2008. Evolvability from learning algorithms. In Proceedings of the 40th Annual ACM Symposium on Theory of Computing (STOC’08). 619--628. Google Scholar
Digital Library
- V. Feldman. 2009a. A complete characterization of statistical query learning with applications to evolvability. In Proceedings of the 50th Annual Symposium on Foundations of Computer Science (FOCS’09). Google Scholar
Digital Library
- V. Feldman. 2009b. Robustness of evolvability. In Proceedings of the 22nd Conference on Learning Theory (COLT’09).Google Scholar
- V. Feldman. 2011. Distribution-independent evolvability of linear threshold functions. In Proceedings of the 24th Annual Conference on Learning Theory (COLT’11).Google Scholar
- D. Haussler. 1992. Decision theoretic generalizations of the PAC model for neural net and other learning applications. Inform. Computat. 100, 1, 78--150. Google Scholar
Digital Library
- A. Kalai and S. Vempala. 2006. Simulated annealing for convex optimization. Math. Oper. Res. 31, 2, 253--266. Google Scholar
Digital Library
- V. Kanade. 2011. Evolution with recombination. In Proceedings of the 52nd Annual Symposium on Foundations of Computer Science (FOCS’11). Google Scholar
Digital Library
- V. Kanade, L. Valiant, and J. Vaughan. 2010. Evolution with drifting targets. In Proceedings of the 23rd Conference on Learning Theory (COLT’10).Google Scholar
- M. Kearns. 1998. Efficient noise-tolerant learning from statistical queries. J. ACM 25, 6, 983--1006. Google Scholar
Digital Library
- A. Livnat, C. Papadimitriou, J. Dushoff, and M. Feldman. 2008. A mixability theory for the role of sex in evolution. Proc. Nat. Acad. Sci. 105, 50.Google Scholar
Cross Ref
- A. Livnat, C. Papadimitriou, N. Pippenger, and M. Feldman. 2009. Sex, mixability, and modularity. Proc. Nat. Acad. Sci. 107, 4.Google Scholar
- L. Lovász. 1986. An Algorithmic Theory of Numbers, Graphs, and Convexity. SIAM, Chapter 2. Google Scholar
Digital Library
- L. Michael. 2012. Evolvability via the Fourier tranform. Theor. Comput. Sci. 462, 88--98. Google Scholar
Digital Library
- Y. Nesterov and B. Polyak. 2009. Cubic regularization of Newton method and its global performance. Math. Program. 108, 1, 177--205. Google Scholar
Digital Library
- L. Valiant. 2009. Evolvability. J. ACM 56, 1. Google Scholar
Digital Library
Index Terms
Evolvability of Real Functions
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