The Use of Being Stubborn and Introspective 1

We give a simple example of a learning process in an artiicial neural network: a perceptron learning by noisy training examples, i.e. a \student" learning from an unreliable \teacher." A \gullible novice," who takes for granted everything the teacher says, does in the end far worse than this teacher. Being more \stubborn," i.e. by neglecting some of the teacher's answers, particularly the ones that the student is conndent about, the student can indeed outperform the teacher. We present an algorithm for on-line tuning of the \acceptance threshold," the fraction of the teacher's advice that the student takes into account. With this algorithm the student will always become wiser than the unreliable teacher, independent of the fraction of his errors. This is an \introspective" algorithm, in the sense that the student's own learning behavior is used to update the acceptance threshold. Introspection makes the algorithm applicable in environments that are both noisy and nonstationary. By focussing on the concepts and keeping the algorithms simple and lucid, the consequences of stubbornness and introspection can be calculated in great analytical detail. 1 In this paper, we will sometimes use rather colloquial language, hoping that this helps to elucidate some of the concepts. We sincerely apologize to any readers who do not like this style and advise them to skip the remaining footnotes.