Differentially private Riemannian optimization. (arXiv:2205.09494v1 [math.OC])

In this paper, we study the differentially private empirical risk
minimization problem where the parameter is constrained to a Riemannian
manifold. We introduce a framework of differentially private Riemannian
optimization by adding noise to the Riemannian gradient on the tangent space.
The noise follows a Gaussian distribution intrinsically defined with respect to
the Riemannian metric. We adapt the Gaussian mechanism from the Euclidean space
to the tangent space compatible to such generalized Gaussian distribution. We
show that this strategy presents …

arxiv math optimization