DP-FedSOFIM: Differentially Private Federated Stochastic Optimization using Regularized Fisher Information Matrix

Differentially private federated learning (DP-FL) often suffers from slow convergence under tight privacy budgets because the noise required for privacy preservation degrades gradient quality. Although second-order optimization can accelerate training, existing approaches for DP-FL face significant scalability limitations: Newton-type methods require clients to compute Hessians, while feature covariance methods scale poorly with model dimension. We propose DP-FedSOFIM, a simple and scalable Hessian approximation-based second-order optimization method for DP-FL. The method constructs a regularized proxy for the Fisher information matrix at the server using only privatized aggregated gradients, capturing useful curvature information without requiring full Hessian computations or feature covariance estimation. Efficient rank-one updates based on the Sherman-Morrison formula enable communication costs proportional to the model size and require only O(d) client-side memory. Because all curvature and preconditioning operations are performed at the server on already privatized gradients, DP-FedSOFIM introduces no additional privacy cost beyond the underlying privatized gradient release mechanism. Experiments on CIFAR-10 and PathMNIST demonstrate that DP-FedSOFIM converges faster and consistently achieves higher accuracy than several competitive differentially private federated learning baselines across a wide range of privacy budgets.