The complexity of properly learning simple concept classes

@article{Alekhnovich2008TheCO,
title={The complexity of properly learning simple concept classes},
author={Michael Alekhnovich and Mark Braverman and Vitaly Feldman and Adam R. Klivans and Toniann Pitassi},
journal={J. Comput. Syst. Sci.},
year={2008},
volume={74},
pages={16-34}
}

We consider the complexity of properly learning concept classes, i.e. when the learner must output a hypothesis of the same form as the unknown concept. We present the following new upper and lower bounds on well-known concept classes: • We show that unless NP = RP, there is no polynomial-time PAC learning algorithm for DNF formulas where the hypothesis is an OR-of-thresholds. Note that as special cases, we show that neither DNF nor OR-of-thresholds are properly learnable unless NP = RP… CONTINUE READING