Fed-Sophia: A Communication-Efficient Second-Order Federated Learning Algorithm

TL;DR

Fed-Sophia is a scalable second-order federated learning algorithm that efficiently incorporates curvature information to accelerate convergence in large models, outperforming existing methods.

Contribution

It introduces a novel second-order federated learning method combining gradient averaging, clipping, and Hessian diagonal estimation for improved scalability and robustness.

Findings

Fed-Sophia outperforms first and second-order baselines.

It demonstrates robustness across various scenarios.

The method scales well with large models.

Abstract

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.