奇偶性的计算高效可复现学习及其应用
Computationally Efficient Replicable Learning of Parities and Applications
AI总结：
本文提出首个计算高效的奇偶性可复现学习算法，证明可复现学习在一般分布上严格超越SQ学习，并揭示其与差分隐私在样本复杂度上的分离。
摘要：
我们研究了可复现性（Impagliazzo等 [STOC `22], Ghazi等 [NeurIPS `21]）与其他稳定性概念之间的计算关系。具体而言，我们关注可复现PAC学习及其与差分隐私（Dwork等 [TCC 2006]）和统计查询（SQ）模型（Kearns [JACM `98]）的联系。从统计角度看，已知差分隐私学习和可复现学习是等价的，并且严格强于SQ学习。然而，在计算上，所有先前已知的高效（即多项式时间）可复现学习算法都局限于SQ可学习任务或受限分布，这与差分隐私学习形成对比。我们的主要贡献是第一个计算高效的可复现算法，用于在任意分布上可实现地学习奇偶性，这一任务在SQ模型中是困难的，但在差分隐私下是可能的。这一结果首次证明，在一般分布上的高效可复现学习严格扩展了高效SQ学习，并且在能力上更接近高效差分隐私学习，尽管可复现性与隐私之间存在计算分离。此外，我们利用我们的奇偶性学习器证明，假设$RP \neq NP$，将可复现性转化为纯差分隐私需要样本复杂度的严格损失。我们的主要构建模块是一个新的、高效且可复现的算法，给定一组向量，该算法输出其线性张成的一个子空间，该子空间覆盖了大部分向量。
英文摘要：
We study the computational relationship between replicability (Impagliazzo et al. [STOC `22], Ghazi et al. [NeurIPS `21]) and other stability notions. Specifically, we focus on replicable PAC learning and its connections to differential privacy (Dwork et al. [TCC 2006]) and to the statistical query (SQ) model (Kearns [JACM `98]). Statistically, it was known that differentially private learning and replicable learning are equivalent and strictly more powerful than SQ-learning. Yet, computationally, all previously known efficient (i.e., polynomial-time) replicable learning algorithms were confined to SQ-learnable tasks or restricted distributions, in contrast to differentially private learning. Our main contribution is the first computationally efficient replicable algorithm for realizable learning of parities over arbitrary distributions, a task that is known to be hard in the SQ-model, but possible under differential privacy. This result provides the first evidence that efficient replicable learning over general distributions strictly extends efficient SQ-learning, and is closer in power to efficient differentially private learning, despite computational separations between replicability and privacy. Additionally, we leverage our parity learner to prove that, assuming $RP \neq NP$, converting replicability to pure differential privacy requires a strict loss in sample complexity. Our main building block is a new, efficient, and replicable algorithm that, given a set of vectors, outputs a subspace of their linear span that covers most of them.
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