Near Optimal Private and Robust Linear Regression

Xiyang Liu, Prateek Jain, Weihao Kong, Sewoong Oh, Arun Suggala

Keywords: differential privacy, private estimation, linear regression, label corruption

TL;DR: We provide a private gradient descent with adaptive clipping that achieves near optimal error rate and robustness against label noise.

Abstract: We study the canonical statistical estimation problem of linear regression from $n$ i.i.d. examples under $(\varepsilon,\delta)$-differential privacy when a fraction of 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 near optimal sample complexity. Under label-corruption, this is the first efficient linear regression algorithm to provably guarantee both $(\epsilon,\delta)$-DP and robustness. Synthetic experiments confirm the superiority of our approach.

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