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Frank J. Balbach

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2 papers

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I&C Journal 2011 Journal Article

Teaching randomized learners with feedback

Frank J. Balbach
Thomas Zeugmann

The present paper introduces a new model for teaching randomized learners. Our new model, though based on the classical teaching dimension model, allows to study the influence of the learner’s memory size and of the presence or absence of feedback. Moreover, in the new model the order in which examples are presented may influence the teaching process. The resulting models are related to Markov decision processes, and characterizations of optimal teachers for memoryless learners with feedback and for learners with infinite memory and feedback are shown. Furthermore, in the new model it is possible to investigate new aspects of teaching like teaching from positive data only or teaching with inconsistent teachers. Characterization theorems for teachability from positive data for both ordinary teachers and inconsistent teachers with and without feedback are provided.

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TCS Journal 2008 Journal Article

Measuring teachability using variants of the teaching dimension

Frank J. Balbach

In a typical algorithmic learning model, a learner has to identify a target object from partial information. Conversely, in a teaching model a teacher has to give information that allows the learners to identify a target object. We devise two variants of the classical teaching model for Boolean concept classes, based on the teaching dimension, and describe them by teaching-dimension-like combinatorial parameters. In the first model, the learners choose consistent hypotheses with least complexity. We show that 1-decision lists are the harder to teach the longer they are and that 2-term DNFs are the harder to teach the more terms they have. This contrasts with the teachability results for these classes in the teaching-dimension model. In our second model, the learners choose consistent hypotheses based on the assumption that the teacher is optimal. We show that monomials can be taught with a linear number of examples, whereas some 1-decision lists need exponentially many.

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