  Statistical query (SQ) learning model of Kearns (1993) is a natural
restriction of the PAC learning model in which a learning algorithm is allowed
to obtain estimates of statistical properties of the examples but cannot see
the examples themselves. We describe a new and simple characterization of the
query complexity of learning in the SQ learning model. Unlike the previously
known bounds on SQ learning our characterization preserves the accuracy and the
efficiency of learning. The preservation of accuracy implies that that our
characterization gives the first characterization of SQ learning in the
agnostic learning framework. The preservation of efficiency is achieved using a
new boosting technique and allows us to derive a new approach to the design of
evolutionary algorithms in Valiant's (2006) model of evolvability. We use this
approach to demonstrate the existence of a large class of monotone evolutionary
learning algorithms based on square loss performance estimation. These results
differ significantly from the few known evolutionary algorithms and give
evidence that evolvability in Valiant's model is a more versatile phenomenon
than there had been previous reason to suspect.
