We scrutinize the resilience of the partial-sharing online federated learning
(PSO-Fed) algorithm against model-poisoning attacks. PSO-Fed reduces the
communication load by enabling clients to exchange only a fraction of their
model estimates with the server at each update round. Partial sharing of model
estimates also enhances the robustness of the algorithm against model-poisoning
attacks. To gain better insights into this phenomenon, we analyze the
performance of the PSO-Fed algorithm in the presence of Byzantine clients,
malicious actors who may subtly tamper with their local models by adding noise
before sharing them with the server. Through our analysis, we demonstrate that
PSO-Fed maintains convergence in both mean and mean-square senses, even under
the strain of model-poisoning attacks. We further derive the theoretical mean
square error (MSE) of PSO-Fed, linking it to various parameters such as
stepsize, attack probability, number of Byzantine clients, client participation
rate, partial-sharing ratio, and noise variance. We also show that there is a
non-trivial optimal stepsize for PSO-Fed when faced with model-poisoning
attacks. The results of our extensive numerical experiments affirm our
theoretical assertions and highlight the superior ability of PSO-Fed to
counteract Byzantine attacks, outperforming other related leading algorithms.

评估了部分共享在线联邦学习（PSO-Fed）算法对抗模型投毒攻击的韧性。通过分析 PSO-Fed 在存在拜占庭客户端的情况下的表现，我们证明 PSO-Fed 在遭受模型投毒攻击的压力下仍能保持收敛性。通过推导理论均方误差（MSE），我们将其与步长、攻击概率、拜占庭客户端数量、客户端参与率、部分共享比率和噪声方差等各种参数相关联。我们还展示了 PSO-Fed 面对模型投毒攻击时存在一个非平凡的最优步长。我们广泛的数值实验结果证实了我们的理论断言，并凸显了 PSO-Fed 对抗拜占庭攻击的卓越能力，优于其他相关的领先算法。