A Complete Characterization of Statistical Query Learning with Applications to Evolvability

TL;DR

This paper provides a new characterization of statistical query learning complexity that maintains accuracy and efficiency, enabling advances in agnostic learning and evolutionary algorithms within Valiant's evolvability framework.

Contribution

It introduces a simple, accurate, and efficient characterization of SQ learning, leading to novel evolutionary algorithms based on square loss performance estimation.

Findings

First SQ learning characterization in agnostic setting

Development of new boosting technique for efficiency

Existence of versatile evolutionary algorithms based on square loss

Abstract

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.