  Data privacy and long-tailed distribution are the norms rather than the
exception in many real-world tasks. This paper investigates a federated
long-tailed learning (Fed-LT) task in which each client holds a locally
heterogeneous dataset; if the datasets can be globally aggregated, they jointly
exhibit a long-tailed distribution. Under such a setting, existing federated
optimization and/or centralized long-tailed learning methods hardly apply due
to challenges in (a) characterizing the global long-tailed distribution under
privacy constraints and (b) adjusting the local learning strategy to cope with
the head-tail imbalance. In response, we propose a method termed
$\texttt{Fed-GraB}$, comprised of a Self-adjusting Gradient Balancer (SGB)
module that re-weights clients' gradients in a closed-loop manner, based on the
feedback of global long-tailed distribution evaluated by a Direct Prior
Analyzer (DPA) module. Using $\texttt{Fed-GraB}$, clients can effectively
alleviate the distribution drift caused by data heterogeneity during the model
training process and obtain a global model with better performance on the
minority classes while maintaining the performance of the majority classes.
Extensive experiments demonstrate that $\texttt{Fed-GraB}$ achieves
state-of-the-art performance on representative datasets such as CIFAR-10-LT,
CIFAR-100-LT, ImageNet-LT, and iNaturalist.
