Energy-Efficient Federated Edge Learning For Small-Scale Datasets in Large IoT Networks

Haihui Xie; Wenkun Wen; Shuwu Chen; Zhaogang Shu; Minghua Xia

cs.LGApr 12, 2026

Energy-Efficient Federated Edge Learning For Small-Scale Datasets in Large IoT Networks

Authors: Haihui Xie, Wenkun Wen, Shuwu Chen, Zhaogang Shu, Minghua Xia

Organizations: College of Computer and Information Sciences, Fujian Agriculture and Forestry University, and also with the Engineering Research Center of Smart Sensing and Agricultural Chip Technology, Fujian Province University, Fuzhou 350002, China · R&D Department, Techphant Technologies Company Ltd., Guangzhou 510310, China · School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou 510006, China

Abstract

Large-scale Internet of Things (IoT) networks enable intelligent services such as smart cities and autonomous driving, but often face resource constraints. Collecting heterogeneous sensory data, especially in small-scale datasets, is challenging, and independent edge nodes can lead to inefficient resource utilization and reduced learning performance. To address these issues, this paper proposes a collaborative optimization framework for energy-efficient federated edge learning with small-scale datasets. We first derive an expected learning loss to quantify the relationship between the number of training samples and learning objectives. A stochastic online learning algorithm is then designed to adapt to data variations, and a resource optimization problem with a convergence bound is formulated. Finally, an online distributed algorithm efficiently solves large-scale optimization problems with high scalability. Extensive simulations and autonomous navigation case studies with collision avoidance demonstrate that the proposed approach significantly improves learning performance and resource efficiency compared to state-of-the-art benchmarks.

Figures & tables

Symbol	Definition
$\mathcal{K},\,\mathcal{K}_{i}$	User set; user set at edge node $i$
$\mathcal{X}(t),\,\mathcal{X}_{i}(t)$	Collected dataset (all devices); dataset at node $i$
$\bm{w}(t),\,\bm{w}_{i}(t+1)$	Global model; local model at node $i$
$A(t),\,A_{i}(t)$	Initial number of collected samples at epoch $t$ (all nodes; node $i$ )
$F(\bm{w}),\,F_{i}(\bm{w})$	Global loss; local loss at node $i$
$\mathcal{D},\,\mathcal{D}_{i}$	The whole data distribution, data distribution at edge node $i$

TABLE I: Summary of main notations.

Fig. 1: The cloud-edge-end collaborative system in resource-constrained large-scale IoT networks.

	$\displaystyle\widetilde{\Phi}(\bm{p}\mid\bm{p}^{*})\triangleq{}$	$\displaystyle{}\left(\dfrac{BT}{V\ln 2}\sum_{k=1}^{K}\left(\ln\left(\sum_{\ell=1}^{K}\dfrac{G_{k,\ell}p_{\ell}}{\sigma^{2}}+1\right)-\ln\left(\sum_{\ell=1,\,\ell\neq k}^{K}\dfrac{G_{k,\,\ell}p_{\ell}^{*}}{\sigma^{2}}+1\right)+1\right.\right.$
		$\displaystyle{}-\left.\left.\left(\sum_{\ell=1,\,\ell\neq k}^{K}\dfrac{G_{k,\,\ell}p_{\ell}^{*}}{\sigma^{2}}+1\right)^{-1}\times\left(\sum_{\ell=1,\,\ell\neq k}^{K}\dfrac{G_{k,\,\ell}p_{\ell}}{\sigma^{2}}+1\right)\right)+A-D\right)^{2},$		(19)

Table 3


$\displaystyle\mathcal{P}_{4}:\min_{\bm{p}}\$	$\displaystyle\widetilde{\Phi}(\bm{p}\mid\bm{p}(t))$	(20a)
$\displaystyle{\rm s.t.}\$	$\displaystyle\widetilde{\Phi}(\bm{p}\mid\bm{p}(t))\leq\dfrac{1}{2}D^{2},$	(20b)
	$\displaystyle\dfrac{BT}{V\ln 2}\sum_{k\in\mathcal{K}_{i}}\left(\ln\left(\sum_{\ell=1}^{K}\dfrac{G_{k,\ell}p_{\ell}}{\sigma^{2}}+1\right)-\ln\left(\sum_{\ell=1,\,\ell\neq k}^{K}\dfrac{G_{k,\,\ell}p_{\ell}(t)}{\sigma^{2}}+1\right)+1\right.$
	$\displaystyle{}\left.-\left(\sum_{\ell=1,\,\ell\neq k}^{K}\dfrac{G_{k,\,\ell}p_{\ell}(t)}{\sigma^{2}}+1\right)^{-1}\times\left(\sum_{\ell=1,\,\ell\neq k}^{K}\dfrac{G_{k,\,\ell}p_{\ell}}{\sigma^{2}}+1\right)\right)+A_{i}-D_{i}\leq 0,$	(20c)
	$\displaystyle\eqref{S2-EQ6d}.$	(20d)

Table 4

Fig. 2: Block diagram of the centralized MM-based algorithm.

	$\displaystyle\phi_{i}(\bm{p}_{i})\triangleq{}$	$\displaystyle\dfrac{BT}{V\ln 2}\sum_{k\in\mathcal{K}_{i}}\left({}\ln\left(\sum_{\ell\in\mathcal{K}_{i}}\dfrac{G_{k,\ell}p_{\ell}}{\sigma^{2}}+\sum_{\ell\in\mathcal{K}\setminus\mathcal{K}_{i}}\dfrac{G_{k,\ell}p_{\ell}(t)}{\sigma^{2}}+1\right)+1-\ln\left(\sum_{\ell\in\mathcal{K},\,\ell\neq k}\dfrac{G_{k,\,\ell}p_{\ell}(t)}{\sigma^{2}}+1\right)\right.$
		$\displaystyle\left.{}-\left(\sum_{\ell\in\mathcal{K},\,\ell\neq k}\dfrac{G_{k,\,\ell}p_{\ell}(t)}{\sigma^{2}}+1\right)^{-1}\times\left(\sum_{\ell\in\mathcal{K}_{i},\,\ell\neq k}\dfrac{G_{k,\,\ell}p_{\ell}}{\sigma^{2}}+\sum_{\ell\in\mathcal{K}\setminus\mathcal{K}_{i},\,\ell\neq k}\dfrac{G_{k,\,\ell}p_{\ell}(t)}{\sigma^{2}}+1\right){}\right)+A_{i}-D_{i}.$		(21e)

Table 6

Panel of Figure 7 — Fig. 3: Learning loss vs. the number of training samples.

Panel of Figure 8 — Fig. 4: Expected learning loss/Power utilization ratio vs. the number of edge nodes.

Panel of Figure 9 — Fig. 5: Learning loss vs. the transmission time.

Panel of Figure 10 — Fig. 6: Mean squared errors (MSE) vs. the number of iterations, with the learning step $\eta=1\times 10^{-3}$ .

Panel of Figure 11 — Fig. 7: Average CPU time vs. the number of edge nodes, with $|\mathcal{K}_{1}|=|\mathcal{K}_{2}|=\cdots=|\mathcal{K}_{I}|=10$ .

Panel of Figure 12 — Fig. 8: The training behavior in autonomous navigation.

Panel of Figure 13 — Fig. 9: Visualization of autonomous navigation in the CARLA simulator. Each subfigure pair displays the navigation trajectories (main panels) and final states (top-right panels) of the autonomous vehicles. Black and red vehicles indicate agents and obstacles, gray regions represent roads, red dashed lines show trajectories, blue polygons denote obstacles, and white circular markers indicate vehicle positions.

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