TRA 8 / 0 5 Variations on U - shaped Learning

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 [3,7,9,23,27] when a learner returns to old correct conjectures. We explore our problem for classical models of learning in the limit: TxtEx-learning – when a learner stabilizes on a correct conjecture, and TxtBc-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 correct grammars. In this case we show that returning to old wrong conjectures, using an inverted-U-shaped strategy as well as returning to old “overgeneralizing” conjectures is necessary for full learning power. We also show that, surprisingly, learners consistent with the input seen so far can be made decisive [3,24] – they do not have to return to any old conjectures – wrong or right. Email addresses: [email protected] (LorenzoCarlucci), [email protected] (Sanjay Jain), [email protected] (EfimKinber), [email protected] (FrankStephan). 1 Supported in part by NSF grant number NSF CCR-0208616. 2 Supported in part by NUS grant number R252–000–127–112. 3 Supported in part by NUS grant number R252–000–212–112.