Abstract 

In this talk, we discuss a recent preprint that introduces a new algorithm, called RFedSVRG, to perform federated learning on Riemannian manifolds.
After recalling the basics of federated learning problems, we review some fundamental ideas and tools needed to perform numerical optimization on Riemannian manifolds. Particular emphasis is given to parallel transport and tangent space average, which are the main components of the newly proposed algorithm. We present the high-level algorithm and provide some ideas on how to prove the convergence results.
Numerical experiments on synthetic and real data demonstrate that RFedSVRG outperforms the straightforward manifold extension of two existing algorithms.