Differentially Private Stochastic Gradient Descent with Low-Noise
This work addresses privacy concerns in machine learning for applications requiring fine-grained data analysis, offering incremental improvements in theoretical bounds and algorithm design.
The paper tackles the trade-off between privacy and utility in machine learning by analyzing differentially private stochastic gradient descent (SGD) algorithms, deriving sharper excess risk bounds in low-noise settings and proposing a new algorithm for pairwise learning that achieves optimal rates even for non-smooth losses.
Modern machine learning algorithms aim to extract fine-grained information from data to provide accurate predictions, which often conflicts with the goal of privacy protection. This paper addresses the practical and theoretical importance of developing privacy-preserving machine learning algorithms that ensure good performance while preserving privacy. In this paper, we focus on the privacy and utility (measured by excess risk bounds) performances of differentially private stochastic gradient descent (SGD) algorithms in the setting of stochastic convex optimization. Specifically, we examine the pointwise problem in the low-noise setting for which we derive sharper excess risk bounds for the differentially private SGD algorithm. In the pairwise learning setting, we propose a simple differentially private SGD algorithm based on gradient perturbation. Furthermore, we develop novel utility bounds for the proposed algorithm, proving that it achieves optimal excess risk rates even for non-smooth losses. Notably, we establish fast learning rates for privacy-preserving pairwise learning under the low-noise condition, which is the first of its kind.