  Federated learning is a machine learning approach where multiple devices
collaboratively learn with the help of a parameter server by sharing only their
local updates. While gradient-based optimization techniques are widely adopted
in this domain, the curvature information that second-order methods exhibit is
crucial to guide and speed up the convergence. This paper introduces a scalable
second-order method, allowing the adoption of curvature information in
federated large models. Our method, coined Fed-Sophia, combines a weighted
moving average of the gradient with a clipping operation to find the descent
direction. In addition to that, a lightweight estimation of the Hessian's
diagonal is used to incorporate the curvature information. Numerical evaluation
shows the superiority, robustness, and scalability of the proposed Fed-Sophia
scheme compared to first and second-order baselines.
