We study the properties of the agnostic learning framework of Haussler (1992)and Kearns, Schapire and Sellie (1992). 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 ... more >>>

We prove lower bounds on the redundancy necessary to represent a set $S$ of objects using a number of bits close to the information-theoretic minimum $\log_2 |S|$, while answering various queries by probing few bits. Our main results are: \begin{itemize} \item To represent $n$ ternary values $t \in \zot^n$ in ... more >>>