Learning with the Aid of an Oracle

Years and Authors of Summarized Original Work

• 1996; Bshouty, Cleve, Gavaldà, Kannan, Tamon

Problem Definition

In the exact learning model of Angluin [2], a learning algorithm A must discover an unknown function $\mathsf{f} : \{0,1\}^{n} \rightarrow \{0,1\}$ that is a member of a known classC of Boolean functions.The learning algorithm can make at least one of the following types of queries aboutf:

• Equivalence query EQ _f (g), for a candidate function g:

  The reply is either “yes,” if $\mathsf{g} \Leftrightarrow \mathsf{f}$, or a counterexample a with g(a) ≠ f(a), otherwise.

• Membership query MQ _f (a), for some a ∈ {0, 1}ⁿ:

  The reply is the Boolean value f(a).

• Subset query SubQ _f (g), for a candidate function g:

  The reply is “yes,” if $\mathsf{g} \Rightarrow \mathsf{f}$, or a counterexample a with f(a) < g(a), otherwise.

• Superset query SupQ _f (g), for a candidate function g:

  The reply is “yes,” if $\mathsf{f} \Rightarrow \mathsf{g}$, or a counterexample a with g(a) < f(a),...