Learning with confidence

Abstract

Herein we investigate learning in the limit where confidence in the current conjecture accrues with time. Confidence levels are given by rational numbers between 0 and 1. The traditional requirement that for learning in the limit is that a device must converge (in the limit) to a correct answer. We further demand that the associated confidence in the answer (monotonically) approach 1 in the limit. In addition to being a more realistic model of learning, our new notion turns out to be a more powerful as well. In addition, we give precise characterizations of the classes of functions that are learnable in our new model(s).