We exhibit a family of computably enumerable sets which can be learned within polynomial resource bounds given access only to a teacher but which requires exponential resources to be learned given access only to a membership oracle. In general, we compare the families that can be learned with and without teachers and oracles for four measures of efficient learning.
"Teachers, Learners, and Oracles." Notre Dame J. Formal Logic 60 (1) 13 - 26, 2019. https://doi.org/10.1215/00294527-2018-0021