FAIRVAR: Fair Federated Learning via Variance Regularization

Federated learning is an emerging distributed paradigm that addresses the challenges posed by heterogeneous, privacy-sensitive data. It enables multiple clients to train a model collaboratively by aggregating their local updates at a server. However, conventional aggregation schemes typically use fixed weights that fail to reflect unequal and time-varying client contributions, leading to biased and unstable learning. To improve fairness and stability, we propose the Trajectory Shapley Value (TSV), a contribution metric that evaluates how each client influences the optimization trajectory of the global model using a validation-based, temporally consistent utility. Building on TSV, we design FedTSV, an adaptive aggregation method that converts per-round evaluations into dynamic client weights, allowing the server to respond to heterogeneous and adversarial participation in real time. Experiments on benchmark datasets show that FedTSV accelerates convergence, improves robustness, and yields more equitable contribution assessments, thereby providing a principled foundation for fairness-aware federated optimization.

Federated Learning enables collaborative model training across decentralized data sources without data transfer. Averaging-based FL is limited by the presence of non-IID data, which negatively impacts convergence speed and final model accuracy. Conventional alternatives suffer from significant inefficiency. Clients with noisy or highly heterogeneous data contribute expensive gradient computations that are either discarded or heavily down-weighted before aggregation. These reactive approaches waste computational resources, require more communication rounds and result in unnecessary privacy exposure. In this paper, we propose a proactive client selection framework that aims to find an optimal federation of clients whose combined data match utility and fairness requirements before training begins. Our method relies on mutual information computed from differentially private contingency tables to quantify the relevance of cross-feature correlations in the union dataset. We introduce a Potential Federation Loss (PFL) over the set of fixed-size federations, which balances two objectives. Maximizing collective data utility while ensuring fair cross-features correlations to prevent group unfairness. Client selection is expressed as an optimal subset search problem over the PFL objective, which we solve using simulated annealing under strong differential privacy guarantees for clients' local statistics. Experimental results on four benchmarks show faster, fairer, and more accurate models trained on optimally found federations, compared to uniform sampling, even when state-of-the-art adaptive aggregation or sampling strategies are employed.

Federated Learning (FL) is fundamentally challenged by statistical heterogeneity, where non-identically distributed (non-IID) data induces client drift that severely hampers global convergence. While existing approaches attempt to mitigate this drift through spatial-domain gradient correction or regularization, they overlook the intrinsic spectral structure of optimization signals. In this work, we revisit client drift from a novel frequency-domain perspective and uncover a critical Spectral Bias of Drift: inter-client gradient divergence is predominantly concentrated in low-frequency components which encode client-specific distributional shifts, while high-frequency components representing fine-grained features remain relatively consistent. Motivated by this, we propose SpecGradFilter, a unified Spectral Gradient Filtering Framework that tames heterogeneity by suppressing discordant low-frequency signals. Crucially, we demonstrate that SpecGradFilter is a generalizable principle, effective not only via precise FFT-based truncation but also through spatial approximations like Gaussian detrending. Extensive experiments on benchmarks such as CIFAR-10/100 and Tiny-ImageNet demonstrate that SpecGradFilter significantly performs better performance in highly Non-IID settings with negligible communication overhead, establishing a new paradigm for robust federated optimization.