Learning with the Aid of an Oracle

Keywords and Synonyms

Oracles and queries that are sufficient for exact learning      

Problem Definition

In the exact learning model of Angluin [1], a learning algorithm A must discover an unknown function $\mathsf{f} \colon \{0,1\}^{n} \rightarrow \{0,1\}$ that is a member of a known class C of Boolean functions. The learning algorithm can make at least one of the following types of queries about f:

• Equivalence query ${ \mathsf{EQ}_{\mathsf{f}}(\mathsf{g}) }$, for a candidate function g: The reply is either “yes”, if ${ \mathsf{g} \Leftrightarrow \mathsf{f} }$, or a counterexample a with ${ \mathsf{g}(a) \neq \mathsf{f}(a) }$, otherwise.

• Membership query ${ \mathsf{MQ}_{\mathsf{f}}(a) }$, for some ${ a \in \{0,1\}^{n} }$: The reply is the Boolean value ${ \mathsf{f}(a) }$.

• Subset query ${ \mathsf{SubQ}_{\mathsf{f}}(\mathsf{g}) }$, for a candidate function g: The reply is “yes”, if ${ \mathsf{g} \Rightarrow \mathsf{f} }$, or a counterexample a with \( {...