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Life sciences · Preprint
arXiv · September 9, 2026
Early or partial results. Treat as a signal, not a conclusion.
HiFedProx, a federated learning optimization method using higher-order power-type regularization (p ≥ 2), shows improved robustness to synthetic stress in controlled experiments on a single frozen FEMNIST dataset subset compared to standard quadratic regularization (p = 2). The work is a preprint and has not undergone peer review; results are limited to one small benchmark and do not establish real-world federated learning performance or generalizability.
Controlled algorithmic experiments with grid search over hyperparameter p. Frozen 60-writer FEMNIST dataset subset (handwriting recognition); no real federated clients or heterogeneous data distribution simulation beyond stress injection.. Intervention: HiFedProx with power-type regularizer indexed by p ≥ 2, combined with finite-budget stochastic client optimization and Armijo backtracking. Compared with: FedProx (quadratic regularization, p = 2).
Moderate-stress loss improved over p=2 by 11.44% at p=7 Severe-stress loss improved over p=2 by 23.16% at p=6 Displacement-tail ratios continue to decrease through p=8, but predictive performance peaks in intermediate range p=5–7
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Early-stage algorithmic development with controlled experiments on a single frozen dataset subset; no peer review, no clinical or real-world validation, and results limited to a narrow federated learning benchmark.
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Federated clients that perform several local optimization steps can return parameter displacements with widely different magnitudes. The quadratic regularization of FedProx grows linearly with displacement and therefore offers limited control over the contrast between ordinary and unusually large client movements. We here introduce HiFedProx, which replaces the quadratic penalty with a scale-matched power-type regularizer indexed by $p\geq2$. All powers have the same regularization-gradient magnitude at a reference displacement $R$, while every $p>2$ gives a weaker response below $R$ and a stronger response above it. An exact affine reference calculation shows that increasing $p$ compresses relative displacement disparities, although very large powers approach fixed-radius behavior and increase local curvature. HiFedProx combines this geometry with finite-budget stochastic client optimization and same-minibatch Armijo backtracking. In paired five-seed experiments on a frozen 60-writer FEMNIST subset, a common-parameter study over $p\in\{2,3,4,5,6,7,8\}$ shows similar clean-training performance but substantial gains under composite stress. The lowest moderate- and severe-stress losses occur at $p=7$ and $p=6$, improving over $p=2$ by $11.44\%$ and $23.16\%$, respectively. Although displacement-tail ratios continue to decrease through $p=8$, predictive performance peaks in an intermediate range and Armijo trial cost increases with $p$. These results indicate that the exponent should be calibrated rather than maximized. In our experiments, $p=5$--$7$ provides the most useful range.
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