Learning by Smooth Simultaneous Estimation of the Error of Hypotheses

We consider the Probably Approximately Correct (PAC) model of "learning," introduced in [1]. Given data that consists of labeled samples, the problem is to select a "hypothesis" (a function) that will accurately label new samples. We investigate an approach, different from the usual one, that first estimates the error of each candidate hypothesis and then selects the hypothesis with the least estimated error.