  Federated Learning (FL) has garnered widespread adoption across various
domains such as finance, healthcare, and cybersecurity. Nonetheless, FL remains
under significant threat from backdoor attacks, wherein malicious actors insert
triggers into trained models, enabling them to perform certain tasks while
still meeting FL's primary objectives. In response, robust aggregation methods
have been proposed, which can be divided into three types: ex-ante, ex-durante,
and ex-post methods. Given the complementary nature of these methods, combining
all three types is promising yet unexplored. Such a combination is non-trivial
because it requires leveraging their advantages while overcoming their
disadvantages. Our study proposes a novel whole-process certifiably robust
aggregation (WPCRA) method for FL, which enhances robustness against backdoor
attacks across three phases: ex-ante, ex-durante, and ex-post. Moreover, since
the current geometric median estimation method fails to consider differences
among clients, we propose a novel weighted geometric median estimation
algorithm (WGME). This algorithm estimates the geometric median of model
updates from clients based on each client's weight, further improving the
robustness of WPCRA against backdoor attacks. We also theoretically prove that
WPCRA offers improved certified robustness guarantees with a larger certified
radius. We evaluate the advantages of our methods based on the task of loan
status prediction. Comparison with baselines shows that our methods
significantly improve FL's robustness against backdoor attacks. This study
contributes to the literature with a novel WPCRA method and a novel WGME
algorithm. Our code is available at https://github.com/brick-brick/WPCRAM.
