The Sample Complexity of Distribution-Free Parity Learning in the Robust Shuffle Model

03/29/2021

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by   Kobbi Nissim, et al.

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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(2^d/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.