Client-level fair federated learning, in the form of $q$-fair federated learning ($q$-FFL), agnostic federated learning, or tilted empirical risk minimization, has emerged as an attractive solution to equalize utility across heterogeneous clients. This paradigm grants high-loss clients greater relative influence, while a central server aggregates their loss-weighted updates into a single shared model. Yet, the Byzantine robustness of $q$-fair federated learning has been largely neglected, leaving the server unable to tell legitimate fairness-induced amplification from malicious update scaling. To address this critical gap, we formalize the problem of Byzantine-robust $q$-fair federated learning under an \emph{update-only interface}, in which the server observes nothing but the fairness-scaled client updates. Our analysis under shared class-conditional label skew shows that fairness scaling preserves the nonnegative class-mixture structure of honest updates, while replacing their unit-sum constraint by a client-dependent radial scale. Moving beyond magnitude-based screening, we show that this warped geometry supplies two complementary tests, one radial and one structural, that a single norm cannot provide. We then introduce FUSE, a structure-aware robust aggregator that uses a small trusted labeled dataset for coefficient recovery, scale and cone-consistency screening, and post-screening step-size control. Across four benchmarks and seven Byzantine attacks, FUSE improves seed-wise worst-attack accuracy over the strongest baseline on each benchmark by 3.9--30.1 percentage points, while largely preserving the influence of the high-loss honest clients that fairness is meant to protect.

翻译：暂无翻译