Private Gradient Descent for Linear Regression: Tighter Error Bounds and Instance-Specific Uncertainty Estimation

arXiv:2402.13531v1 Announce Type: new
Abstract: We provide an improved analysis of standard differentially private gradient descent for linear regression under the squared error loss. Under modest assumptions on the input, we characterize the distribution of the iterate at each time step.
Our analysis leads to new results on the algorithm's accuracy: for a proper fixed choice of hyperparameters, the sample complexity depends only linearly on the dimension of the data. This matches the dimension-dependence of the (non-private) ordinary least squares …

abstract analysis arxiv assumptions cs.cr cs.lg distribution error gradient instance iterate leads linear linear regression loss regression standard type uncertainty