Apple tasting and nearly one-sided learning

Abstract

In the standard on-line model the learning algorithm tries to minimize the total number of mistakes made in a series of trials. On each trial the learner sees an instance, either accepts or rejects that instance, and then is told the appropriate response. The authors define a natural variant of this model ('apple tasting') where the learner gets feedback only when the instance is accepted. They use two transformations to relate the apple tasting model to an enhanced standard model where false acceptances are counted separately from false rejections. They present a strategy for trading between false acceptances and false rejections in the standard model. From one perspective this strategy is exactly optimal, including constants. They apply the results to obtain a good general purpose apple tasting algorithm as well as nearly optimal apple tasting algorithms for a variety of standard classes, such as conjunctions and disjunctions of n boolean variables. They also present and analyze a simpler transformation useful when the instances are drawn at random rather than selected by an adversary.