We provide a lowerbound on the sample complexity of distribution-free parity learning in the realizable case in the shuffle model of differential privacy. Namely, we show that the sample complexity of learning d-bit parity functions is Ω(2d/2). Our result extends a recent similar lowerbound on the sample complexity of private agnostic learning of parity functions in the shuffle model by Cheu and Ullman. We also sketch a simple shuffle model protocol demonstrating that our results are tight up to poly(d) factors.
@article{arxiv.2103.15690,
title = {The Sample Complexity of Distribution-Free Parity Learning in the Robust Shuffle Model},
author = {Kobbi Nissim and Chao Yan},
journal= {arXiv preprint arXiv:2103.15690},
year = {2021}
}