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A 2-stage classification model is presented in which the first stage is a quick, computerized Bayes rule decision device, and the second a slow, but perfectly accurate, classifier. A stationary stream of elements or objects to be classified into one of several mutually exclusive categories is fed into the model. The conditional probabilities associated with the Bayes device are assumed unknown at the outset, except up to an initial probability distribution. The a posteriori probabilities from the first stage are treated as information that can speed up or slow down the processing time in the second stage. The latter, after a delay time, feeds back accurate classification information to the first stage to update the conditional probabilities. It is shown that, as the classification process unfolds, any updating scheme that causes the Bayes classifier ultimately to learn the true values of the conditional probabilities also minimizes the expected processing time in the second stage. The learning rate of the system is discussed as a function of the updating scheme. An example of a simple system is presented and the learning rate is derived specifically for that case.