  As federated learning gains increasing importance in real-world applications
due to its capacity for decentralized data training, addressing fairness
concerns across demographic groups becomes critically important. However, most
existing machine learning algorithms for ensuring fairness are designed for
centralized data environments and generally require large-sample and
distributional assumptions, underscoring the urgent need for fairness
techniques adapted for decentralized and heterogeneous systems with
finite-sample and distribution-free guarantees. To address this issue, this
paper introduces FedFaiREE, a post-processing algorithm developed specifically
for distribution-free fair learning in decentralized settings with small
samples. Our approach accounts for unique challenges in decentralized
environments, such as client heterogeneity, communication costs, and small
sample sizes. We provide rigorous theoretical guarantees for both fairness and
accuracy, and our experimental results further provide robust empirical
validation for our proposed method.
