Near Optimal Private and Robust Linear Regression

• URL: http://arxiv.org/abs/2301.13273v1
• Date: Mon, 30 Jan 2023 20:33:26 GMT
• Title: Near Optimal Private and Robust Linear Regression
• Authors: Xiyang Liu, Prateek Jain, Weihao Kong, Sewoong Oh, Arun Sai Suggala
• Abstract summary: We propose a variant of the popular differentially private gradient descent (DP-SGD) algorithm with two innovations. Under label-corruption, this is the first efficient linear regression algorithm to guarantee both $(varepsilon,delta)$-DP and robustness.
• Score: 47.2888113094367
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the canonical statistical estimation problem of linear regression from $n$ i.i.d.~examples under $(\varepsilon,\delta)$-differential privacy when some response variables are adversarially corrupted. We propose a variant of the popular differentially private stochastic gradient descent (DP-SGD) algorithm with two innovations: a full-batch gradient descent to improve sample complexity and a novel adaptive clipping to guarantee robustness. When there is no adversarial corruption, this algorithm improves upon the existing state-of-the-art approach and achieves a near optimal sample complexity. Under label-corruption, this is the first efficient linear regression algorithm to guarantee both $(\varepsilon,\delta)$-DP and robustness. Synthetic experiments confirm the superiority of our approach.

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