  This paper investigates the use of the cubic-regularized Newton method within
a federated learning framework while addressing two major concerns that
commonly arise in federated learning: privacy leakage and communication
bottleneck. We introduce a federated learning algorithm called Differentially
Private Federated Cubic Regularized Newton (DP-FCRN). By leveraging
second-order techniques, our algorithm achieves lower iteration complexity
compared to first-order methods. We also incorporate noise perturbation during
local computations to ensure privacy. Furthermore, we employ sparsification in
uplink transmission, which not only reduces the communication costs but also
amplifies the privacy guarantee. Specifically, this approach reduces the
necessary noise intensity without compromising privacy protection. We analyze
the convergence properties of our algorithm and establish the privacy
guarantee. Finally, we validate the effectiveness of the proposed algorithm
through experiments on a benchmark dataset.
