  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.
