  Stochastic Gradient Descent (SGD) is a widely used tool in machine learning.
In the context of Differential Privacy (DP), SGD has been well studied in the
last years in which the focus is mainly on convergence rates and privacy
guarantees. While in the non private case, uncertainty quantification (UQ) for
SGD by bootstrap has been addressed by several authors, these procedures cannot
be transferred to differential privacy due to multiple queries to the private
data. In this paper, we propose a novel block bootstrap for SGD under local
differential privacy that is computationally tractable and does not require an
adjustment of the privacy budget. The method can be easily implemented and is
applicable to a broad class of estimation problems. We prove the validity of
our approach and illustrate its finite sample properties by means of a
simulation study. As a by-product, the new method also provides a simple
alternative numerical tool for UQ for non-private SGD.
