Abstract—Federated learning lets Internet of Things devices train a shared model without transmitting raw data, but its energy cost on battery-powered hardware remains a barrier to deployment. That cost has two components, local computation and parameter exchange, and the number of local epochs performed between synchronizations trades one against the other. This paper formulates the trade-off as a normalized multi-objective problem and derives a closed-form expression for the epoch count that minimizes it. The expression depends on one measurable quantity, the fraction of total energy attributable to communication, and is embedded in a Lyapunov drift-plus-penalty controller that adapts the epoch count online under a long-run energy budget, with proven mean-rate stability and an O(1/V) optimality gap. Experiments on the CICIoT2023 intrusion-detection dataset support the prediction: the optimal epoch count rises with the communication energy fraction, confirmed through two independent mechanisms, varying the uplink rate and the quantization width. Against federated averaging at a fixed two local epochs, the controller improves accuracy significantly at three levels of statistical heterogeneity. Against federated averaging tuned over a grid of fixed epoch counts it is less energy-efficient in a single run; its advantage is reaching a comparable operating point without that search, an 81.4% reduction in total energy once the search is counted. The framework yields negative savings in high-bandwidth settings, which the theory predicts. All energy figures reported are outputs of an analytical energy model rather than hardware measurements.

Index Terms—adaptive optimization, communication-energy trade-off, energy-efficient computing, federated learning, Internet of Things, Lyapunov optimization

Cite: Almamoon Alauthman and Feras Alfaqih , "Energy-aware Adaptive Federated Optimization for Sustainable IoT: A Unified  Energy-communication-accuracy Trade-off Framework," International Journal of Electrical and Electronic Engineering & Telecommunications, vol. 15, no. 5, pp. 406-420, 2026. doi: 10.18178/ijeetc.15.5.406-420

Copyright © 2026 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).