Apple tasting

In the standard on-line model the learning algorithm tries to minimizethe total number of mistakes made in a series of trials. On each trial the learner sees an instance, makes a prediction of its classification, then finds out the correct classification. We define a natural variant of this model (“apple tasting”) where u • the classes are interpreted as the good and bad instances, • the prediction is interpreted as accepting or rejecting the instance, and • the learner gets feedback only when the instance is accepted. We use two transformations to relate the apple tasting model to an enhanced standard model where false acceptances are counted separately from false rejections. We apply our 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. We also present and analyze a simpler transformation useful when the instances are drawn at random rather than selected by an adversary.

Authors

• David P. Helmbold
• Nicholas Littlestone
• Philip M. Long

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