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In the recent paper FLECS (Agafonov et al, FLECS: A Federated LearningSecond-Order Framework via Compression and Sketching), the second-orderframework FLECS was proposed for the Federated Learning problem. This methodutilize compression of sketched Hessians to make communication costs low.However, the main bottleneck of FLECS is gradient communication withoutcompression. In this paper, we propose the modification of FLECS withcompressed gradient differences, which we call FLECS-CGD (FLECS with CompressedGradient 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.

FLECS-CGD: A Federated Learning Second-Order Framework via Compression and Sketching with Compressed Gradient Differences