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# Average-Case Information Complexity of Learning

*Proceedings of the 30th International Conference on Algorithmic Learning Theory*, PMLR 98:633-646, 2019.

#### Abstract

How many bits of information are revealed by a learning algorithm for a concept class of VC-dimension $d$? Previous works have shown that even for $d=1$
the amount of information may be unbounded (tend to $\infty$ with the universe size). Can it be that all concepts in the class require leaking a large amount of information? We show that typically concepts do not require leakage. There exists a proper learning algorithm that reveals $O(d)$ bits of information for most concepts in the class.
This result is a special case of a more general phenomenon we explore.
If there is a low information learner when the algorithm \emph{knows} the underlying distribution on inputs, then there is a learner that reveals little information on an average concept \emph{without knowing} the distribution on inputs.