Abstract
This paper introduces \texttt{FedMPDD} (\textbf{Fed}erated Learning via \textbf{M}ulti-\textbf{P}rojected \textbf{D}irectional \textbf{D}erivatives), a novel algorithm that simultaneously optimizes bandwidth utilization and enhances privacy in Federated Learning. The core idea of \texttt{FedMPDD} is to encode each client's high-dimensional gradient by computing its directional derivatives along multiple random vectors. This compresses the gradient into a much smaller message, significantly reducing uplink communication costs from to , where . The server then decodes the aggregated information by projecting it back onto the same random vectors. Our key insight is that averaging multiple projections overcomes the dimension-dependent convergence limitations of a single projection. We provide a rigorous theoretical analysis, establishing that \texttt{FedMPDD} converges at a rate of , matching the performance of FedSGD. Furthermore, we demonstrate that our method provides some inherent privacy against gradient inversion attacks due to the geometric properties of low-rank projections, offering a tunable privacy-utility trade-off controlled by the number of projections. Extensive experiments on benchmark datasets validate our theory and demonstrates our results.