evolvability from learning algorithms
Valiant has recently introduced a framework for analyzing the capabilities and the limitations of the evolutionary process of random change guided by selection. In his framework the process of acquiring a complex functionality is viewed as a substantially restricted form of PAC learning of an unknown function from a certain set of functions. Valiant showed that classes of functions evolvable in his model are also learnable in the statistical query (SQ) model of Kearns and asked whether the converse is true. We show that evolvability is equivalent to learnability by a restricted form of statistical queries. Based on this equivalence we prove that for any fixed distribution D over the instance space, every class of functions learnable by SQs over D is evolvable over D. Previously, only the evolvability of monotone conjunctions of Boolean variables over the uniform distribution was known. On the other hand, we prove that the answer to Valiant's question is negative when distribution-independent evolvability is considered. To demonstrate this, we develop a technique for proving lower bounds on evolvability and use it to show that decision lists and linear threshold functions are not evolvable in a distribution-independent way. This is in contrast to distribution-independent learnability of decision lists and linear threshold functions in the statistical query model.
evolvability pac learning statistical query