An Equivalence Between Private Classification and Online Prediction
arXiv:2003.00563
Abstract
We prove that every concept class with finite Littlestone dimension can be learned by an (approximate) differentially-private algorithm. This answers an open question of Alon et al. (STOC 2019) who proved the converse statement (this question was also asked by Neel et al.~(FOCS 2019)). Together these two results yield an equivalence between online learnability and private PAC learnability. We introduce a new notion of algorithmic stability called "global stability" which is essential to our proof and may be of independent interest. We also discuss an application of our results to boosting the privacy and accuracy parameters of differentially-private learners.
An earlier version of this manuscript claimed an upper bound over the sample complexity that is exponential in the Littlestone dimension. The argument was erranous, and the current version contains a correction, which leads to double-exponential dependence in the Littlestone-dimension