  In the recent paper FLECS (Agafonov et al, FLECS: A Federated Learning
Second-Order Framework via Compression and Sketching), the second-order
framework FLECS was proposed for the Federated Learning problem. This method
utilize compression of sketched Hessians to make communication costs low.
However, the main bottleneck of FLECS is gradient communication without
compression. In this paper, we propose the modification of FLECS with
compressed gradient differences, which we call FLECS-CGD (FLECS with Compressed
Gradient Differences) and make it applicable for stochastic optimization.
Convergence guarantees are provided in strongly convex and nonconvex cases.
Experiments show the practical benefit of proposed approach.
