FalOTS: Orthogonal Target-Aware SAM for Federated Active Learning Under Global Class Imbalance

Federated active learning (FAL) reduces annotation costs by selectively labeling data distributed across clients. However, under global class imbalance, the class proportions in the aggregate labeled data may differ substantially from those desired for evaluation (target prior), limiting the global model's performance. Existing FAL methods mainly improve sample acquisition, leaving this mismatch insufficiently addressed during local training. Sharpness-aware minimization (SAM) offers a promising foundation for local training by seeking parameters whose loss remains low under nearby perturbations. Yet, its empirical-gradient perturbation does not explicitly account for the mismatch between global labeled and target class priors. To address this limitation, we propose $\text{FalOTS}$, a target-aware SAM optimizer for local training within FAL loop. At each acquisition phase, $\text{FalOTS}$ constructs class weights from the ratio between the target prior and current global labeled prior. It computes a target-aware gradient on each labeled mini-batch and adds its normalized orthogonal residual to SAM perturbation. This correction preserves SAM empirical-gradient component while adding a complementary direction. The subsequent descent step uses the original unweighted loss. Our analysis characterizes the correction's geometric properties and provides sufficient conditions for a lower target risk after one update than SAM. $\text{FalOTS}$ improves global model accuracy under limited labeling budgets, outperforming FAL baselines using SGD- and SAM-based optimizers across diverse benchmarks and settings.