FedEHD: Entropic High-Order Descent for Robust Federated Multi-Source Environmental Monitoring

We propose Federated Entropic High-Order Descent (FedEHD), a drop-in client optimizer that augments local SGD with (i) an entropy (sign) term and (ii) quadratic and cubic gradient components for drift control and implicit clipping. Across non-IID CIFAR-10 and CIFAR-100 benchmarks (100 clients, 10% sampled per round), FedEHD achieves faster and higher convergence than strong baselines including FedAvg, FedProx, SCAFFOLD, FedDyn, MOON, and FedAdam. On CIFAR-10, it reaches 70% accuracy in approximately 80 rounds (versus 100 for MOON and 130 for SCAFFOLD) and attains a final accuracy of 72.5%. On CIFAR-100, FedEHD surpasses 60% accuracy by about 150 rounds (compared with 250 for MOON and 300 for SCAFFOLD) and achieves a final accuracy of 68.0%. In an environmental monitoring case study involving four distributed air-quality stations, FedEHD yields the highest macro AUC/F1 and improved calibration (ECE 0.183 versus 0.186–0.210 for competing federated methods) without additional communication and with only O(d) local overhead. The method further provides scale-invariant coefficients with optional automatic adaptation, theoretical guarantees for surrogate descent and drift reduction, and convergence curves that illustrate smooth and stable learning dynamics.