The Sample Complexity of Distribution-Free Parity Learning in the Robust Shuffle Model
This work addresses the fundamental limits of privacy-preserving learning for parity functions, which is an incremental extension of prior results in the shuffle model.
The paper establishes a lower bound of Ω(2^{d/2}) on the sample complexity for distribution-free parity learning in the realizable case under the shuffle model of differential privacy, and sketches a protocol showing this bound is tight up to polynomial factors.
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.