arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2007.09371cs.LGcs.CRstat.ML

Tighter Generalization Bounds for Iterative Differentially Private Learning Algorithms

UBTECH Sydney AI Centre, School of Computer Science, Faculty of Engineering, the University of Sydney(悉尼大学工程学院计算机科学学院优必选悉尼人工智能中心);University of Science and Technology of China(中国科学技术大学)

Fengxiang He, Bohan Wang, Dacheng Tao

英文摘要:

This paper studies the relationship between generalization and privacy preservation in iterative learning algorithms by two sequential steps. We first establish an alignment between generalization and privacy preservation for any learning algorithm. We prove that $(\varepsilon, δ)$-differential privacy implies an on-average generalization bound for multi-database learning algorithms which further leads to a high-probability bound for any learning algorithm. This high-probability bound also implies a PAC-learnable guarantee for differentially private learning algorithms. We then investigate how the iterative nature shared by most learning algorithms influence privacy preservation and further generalization. Three composition theorems are proposed to approximate the differential privacy of any iterative algorithm through the differential privacy of its every iteration. By integrating the above two steps, we eventually deliver generalization bounds for iterative learning algorithms, which suggest one can simultaneously enhance privacy preservation and generalization. Our results are strictly tighter than the existing works. Particularly, our generalization bounds do not rely on the model size which is prohibitively large in deep learning. This sheds light to understanding the generalizability of deep learning. These results apply to a wide spectrum of learning algorithms. In this paper, we apply them to stochastic gradient Langevin dynamics and agnostic federated learning as examples.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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