# D2D-Assisted Adaptive Federated Learning in Energy-Constrained Edge Computing
## 4 Partite Graph-Based FL Scheme with Adaptive D2D Pairing and Aperiodic Local Iterations
We use the these two datasets instead of IoT images collected through camera sensors to test our designed schemes. The learning task is to identify the objects showing in the dataset images. Moreover, to make the datasets follow non-IID distribution, we sort and divide the datasets into subsets and then randomly assign a number of these shards to each edge server, according to [PERSON], [PERSON] et al. [36]. Figure 4 compares the training loss of dataset-uncorrelated FL schemes using the MNIST and CIFAR-10 datasets. The benchmarks selected for this performance comparison are the energy budget-oriented D2D pairing FL scheme, the transmission distance-oriented D2D pairing FL scheme, and the FedYogi FL scheme [37]. Compared with these benchmark schemes, our proposed partite graph-based FL scheme yields the lowest loss expectation when applied to both datasets. Although FedYogi can flexibly adjust the learning rate, its aggregation process does not consider the energy budget constraints and the communication topology of the edge servers participating in the FL. Thus, due to the energy exhaustion caused by intensive model training and long-distance parameter transfer, some servers may exit the FL model aggregation process prematurely and, finally, produce the highest model training loss. The energy budget-oriented FL allocates both local model training and parameter data relay tasks to the servers with the most remaining energy but ignores the impact of communication topology on the transmission energy overhead. It wastes part of the energy available for model training on unnecessary remote data delivery. Contrary to the energy budget-oriented FL, the transmission distance-oriented FL scheme only pays attention to the difference in transmission energy consumption affected by the geographical location of the servers in the designing of its operation process. Therefore, it fails to fully utilize the training capabilities of energy-constrained servers. Unlike the

above two D2D-assisted FL mechanisms, our proposed partite graph-based FL jointly matches the edge servers in the training process, in terms of energy budget, computing power, and communication topology. Moreover, we exploit the differential effect of server computing power on model accuracy in different FL iterations, and we further optimize the server computing power allocation, thereby improving server-training energy efficiency and obtaining the lowest loss expectation. Figure 5 shows the training loss of FL performed in networks with different numbers of wireless channels. Given the number of channels used for direct delivery between client servers and aggregation servers, which is denoted as \(Z_{1}\), the training loss decreases as the number of D2D communication channels \(Z_{2}\) increases, but this decreasing trend

Figure 4: Comparison of training loss with different FL schemes. Figure 3: Deployment of servers in an edge computing network. gradually weakens as \(Z_{2}\) increases. When Z2 increases from 2 to 4, although the D2D communication capacity between the FL servers has improved, due to the densely deployed 30 servers, only four channels still have difficulty supporting the complete spatial-division multiplexing of the spectrum resources. However, with six channels, spectrum spatial-division multiplexing in server-dense areas can be achieved, thereby supporting more concurrent D2D model aggregation between servers, thereby reducing the training loss. In contrast to the above phenomenon, when \(Z_{2}\) is fixed, the training loss does not show an obvious changing trend with the increase of \(Z_{1}\), and the loss value fluctuates. Since the increase of \(Z_{2}\) can promote D2D aggregation between client servers, the results of this figure demonstrate that distributed model aggregation has better training improvement than simply adjusting the central aggregation number. Figure 6 presents the number of local training iterations for the servers with different energy budgets.