Variations on U-shaped Learning
No Thumbnail Available
Files
Date
2005-08-02
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
The paper deals with the following problem: is returning to wrong conjectures necessary to achieve full power of learning? Returning to wrong conjectures complements the paradigm of U-shaped learning when a learner returns to old correct conjectures. We explore our problem for classical models of learning in the limit: explanatory learning -- when a learner stabilizes on a correct conjecture and behaviourally correct learning -- when a learner stabilizes on a sequence of grammars representing the target concept. In both cases, we show that, surprisingly, returning to wrong conjectures is necessary to achieve full power of learning. On the other hand it is neither necessary to resort to an inverted-U-shaped behaviour (a wrong-correct-wrong pattern) nor to return to old ``overgeneralizing'' conjectures containing elements not belonging to the target language. We also consider our problem in the context of so-called vacillatory learning when a learner stabilizes to a finite number of cor...