In this study, we consider nonconvex federated learning problems with the existence of Byzantine workers. We propose a new simple Byzantine robust algorithm called Momentum Screening. The algorithm is adaptive to the Byzantine fraction, i.e., all its hyperparameters do not depend on the number of Byzantine workers. We show that our method achieves the best optimization error of $O(\delta^2\zeta_\mathrm{max}^2)$ for nonconvex smooth local objectives satisfying $\zeta_\mathrm{max}$-uniform gradient heterogeneity condition under $\delta$-Byzantine fraction, which can be better than the best known error rate of $O(\delta\zeta_\mathrm{mean}^2)$ for local objectives satisfying $\zeta_\mathrm{mean}$-mean heterogeneity condition when $\delta \leq (\zeta_\mathrm{max}/\zeta_\mathrm{mean})^2$. Furthermore, we derive an algorithm independent lower bound for local objectives satisfying $\zeta_\mathrm{max}$-uniform gradient heterogeneity condition and show the minimax optimality of our proposed method on this class. In numerical experiments, we validate the superiority of our method over the existing robust aggregation algorithms and verify our theoretical results.

A novel algorithm is proposed for highly privacy-preserving decentralized federated learning (FL). Several studies have reported security risks in decentralized FL by reconstructing data even from model update differences. A common approach to overcome this issue is to use the diffusion process following differential privacy (DP), i.e., message passing between nodes is hidden by noise. However, this often makes the learning process unstable, leading to degraded results compared to without using DP diffusion process. In this paper, we propose a primal-dual DP algorithm with denoising normalization (DP-Norm) for less sensitivity to noise/interference, such as DP diffusion and heterogeneous data allocation. For DP-Norm, privacy analysis to determine minimal noise level and convergence analysis are conducted. Through image classification benchmark tests, we confirmed that DP-Norm performed close to the single-node reference score, even when statistically heterogeneous data was allocated on six nodes.