On the Equivalence between Online and Private Learnability beyond Binary Classification
Abstract
Alon et al. [2019] and Bun et al. [2020] recently showed that online learnability and private PAC learnability are equivalent in binary classification. We investigate whether this equivalence extends to multi-class classification and regression. First, we show that private learnability implies online learnability in both settings. Our extension involves studying a novel variant of the Littlestone dimension that depends on a tolerance parameter and on an appropriate generalization of the concept of threshold functions beyond binary classification. Second, we show that while online learnability continues to imply private learnability in multi-class classification, current proof techniques encounter significant hurdles in the regression setting. While the equivalence for regression remains open, we provide non-trivial sufficient conditions for an online learnable class to also be privately learnable.
Cite
@article{arxiv.2006.01980,
title = {On the Equivalence between Online and Private Learnability beyond Binary Classification},
author = {Young Hun Jung and Baekjin Kim and Ambuj Tewari},
journal= {arXiv preprint arXiv:2006.01980},
year = {2021}
}
Comments
An earlier version of this manuscript claimed an upper bound over the sample complexity that is exponential in the Littlestone dimension. The argument contained a technical mistake, and the current version presents a correction that deteriorates the dependence on the Littlestone dimension from exponential to doubly exponential. arXiv admin note: text overlap with arXiv:2003.00563 by other authors