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

Abstract: Differentially private federated learning (DP-FL) suffers from slow convergence under tight privacy budgets due to the overwhelming noise introduced to preserve privacy. While adaptive optimizers can accelerate convergence, existing second-order methods such as DP-FedNew require O(d^2) memory at each client to maintain local feature covariance matrices, making them impractical for high-dimensional models. We propose DP-FedSOFIM, a server-side second-order optimization framework that leverages the Fisher Information Matrix (FIM) as a natural gradient preconditioner while requiring only O(d) memory per client. By employing the Sherman-Morrison formula for efficient matrix inversion, DP-FedSOFIM achieves O(d) computational complexity per round while maintaining the convergence benefits of second-order methods. Our analysis proves that the server-side preconditioning preserves (epsilon, delta)-differential privacy through the post-processing theorem. Empirical evaluation on CIFAR-10 demonstrates that DP-FedSOFIM achieves superior test accuracy compared to first-order baselines across multiple privacy regimes.