Problem Definition
This problem concerns the query complexity of proper learning in a widely studied learning model: exact learning with membership and equivalence queries. Hellerstein et al. [8] showed that the number of (polynomially sized) queries required to learn a concept class in this model is closely related to the size of certain certificates associated with that class. This relationship gives a combinatorial characterization of the concept classes that can be learned with polynomial query complexity. (Similar results were shown by Hegedüs[7], based on the work of Moshkov [11].)
The Exact Learning Model
Concepts are functions \( { f:X \rightarrow Y } \) where X is an arbitrary domain, and \( { Y = \{0,1\} } \). In exact learning, there is a hidden concept f from a known class of concepts C, and the problem is to exactly identify the function f.
Algorithms in the exact learning model obtain information about f, the target concept, by querying two oracles, a membership oracle...
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Hellerstein, L. (2008). Certificate Complexity and Exact Learning. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_66
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