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 $\Omega(2^{d/2})$. 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.

翻译：在不同的隐私打字模式中,在可实现的案例中,我们提供了关于免分配平等学习的抽样复杂性的较低范围。也就是说,我们表明,学习美元-比特等功能的抽样复杂性为$\Omega(2 ⁇ d/2}美元。我们的结果对Cheu和Ullman在打字模式中私人不可知性学习平等功能的抽样复杂性也进行了类似的较低范围。我们还勾画了一个简单的打字示范协议,表明我们的成果接近于$(d)因素。