Evolution with Recombination

Abstract

Valiant (2007) introduced a computational model of evolution and suggested that Darwinian evolution be studied in the framework of computational learning theory. Valiant describes evolution as a restricted form of learning where exploration is limited to a set of possible mutations and feedback is received through the survival of the fittest mutation. In subsequent work Feldman (2008) showed that evolvability in Valiant's model is equivalent to learning in the correlational statistical query (CSQ) model. We extend Valiant's model to include genetic recombination and show that in certain cases, recombination can significantly speed-up the process of evolution in terms of the number of generations, though at the expense of population size. This follows via a reduction from parallel-CSQ algorithms to evolution with recombination. This gives an exponential speed-up (in terms of the number of generations) over previous known results for evolving conjunctions and half spaces with respect to restricted distributions.