On the Power of Membership Queries in Agnostic Learning

We study the properties of the agnostic learning framework of Haussler [Hau92] and Kearns, Schapire and Sellie [KSS94]. In particular, we address the question: is there any situation in which membership queries are useful in agnostic learning? Our results show that the answer is negative for distribution-independent agnostic learning and positive for agnostic learning with respect to a specific marginal distribution. Namely, we give a simple proof that any concept class learnable agnostically by a distribution-independent algorithm with access to membership queries is also learnable agnostically without membership queries. This resolves an open problem posed by Kearns et al. [KSS94]. For agnostic learning with respect to the uniform distribution over {0, 1}n we show a concept class that is learnable with membership queries but computationally hard to learn from random examples alone (assuming that one-way functions exist).

• Type: Conference
• Year: 2008
• Where: COLT
• Authors: Vitaly Feldman
• Keywords: Agnostic Learning, Agnostic Learning Framework, COLT 2008, Machine Learning, Membership Queries