Differentially Private Linear Regression over Fully Decentralized Datasets

Abstract

This paper presents a differentially private algorithm for linear regression learning in a decentralized fashion. Under this algorithm, privacy budget is theoretically derived, in addition to that the solution error is shown to be bounded by $O(t)$ for $O(1/t)$ descent step size and $O(\exp (t^{1-e}))$ for $O(t^{-e})$ descent step size.