On Exact Learning Halfspaces with Random Consistent Hypothesis Oracle

We study the learnability of representation classes in Angluin's exact learning model. In particular, we consider the following three query types: equivalence queries, equivalence and membership queries, and membership queries only. We show in all three cases that polynomial query complexity implies already polynomial-time learnability, provided that the learner additionally has access to an oracle in [Formula: see text]. It follows that boolean circuits are polynomial-time learnable with equivalence queries and the help of an oracle in [Formula: see text].a

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LEARNING RECURSIVE LANGUAGES WITH BOUNDED MIND CHANGES

International Journal of Foundations of Computer Science ◽

10.1142/s0129054193000110 ◽

1993 ◽

Vol 04 (02) ◽

pp. 157-178 ◽

Cited By ~ 21

Author(s):

STEFFEN LANGE ◽

THOMAS ZEUGMANN

Keyword(s):

Language Learning ◽

Learning Algorithms ◽

New Method ◽

Negative Data ◽

Finite Sets ◽

Exact Learning ◽

Bounded Number ◽

Positive Data ◽

Open Question

In the present paper we study the learnability of enumerable families ℒ of uniformly recursive languages in dependence on the number of allowed mind changes, i.e. with respect to a well-studied measure of efficiency. We distinguish between exact learnability (ℒ has to be inferred w.r.t. ℒ) and class preserving learning (ℒ has to be inferred w.r.t. some suitable chosen enumeration of all the languages from ℒ) as well as between learning from positive and from both, positive and negative data. The measure of efficiency is applied to prove the superiority of class preserving learning algorithms over exact learning. In particular, we considerably improve results obtained previously and establish two infinite hierarchies. Furthermore, we separate exact and class preserving learning from positive data that avoids overgeneralization. Finally, language learning with a bounded number of mind changes is completely characterized in terms of recursively generable finite sets. These characterizations offer a new method to handle overgeneralizations and resolve an open question of Mukouchi.1

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