# FedCO: Communication-Efficient Federated Learning via Clustering Optimization +
## 4 Proposed Approach

Table 5: The number of communication rounds to reach a certain accuracy level for the two compared FL algorithms on each LEAF dataset. rounds for FedAvg and 80 rounds for FedAvg and 80 rounds for FedProx. CMFL considerably minimizes this cost to 60; see Figure (b)b. Finally, for the CIFAR-10 IID data, the required communication costs of the FedAvg and FedProx to achieve 85% accuracy is 150 rounds, while CMFL obtains the same result for 75 rounds. Our FedCO algorithm outperforms the others, needing only nine rounds to reach this accuracy value (cf. Figure (a)a). In the case of the CIFAR-10 Non-IID data (see Figure (b)b), in 25 communication rounds, FedCO obtains an accuracy of 85%, while FedAvg and FedProx reach 79% and 80%, respectively. On the other hand, CMFL achieves a close result 82% of accuracy in the same number of rounds. Figure 5: Learning accuracy versus the number of communication rounds for MNIST data. The top plot presents the results produced in the case of the IID data distribution scenario, while the bottom plot depicts the results generated in the case of the Non-IID data distribution scenario. (**a**) IID; (**b**) Non-IID. Figure 6: Learning accuracy versus communication rounds for FashionMNIST data. The top plot presents the results produced in the case of the IID data distribution scenario, while the bottom plot depicts the results generated in the case of the Non-IID data distribution scenario. (**a**) IID; (**b**) Non-IID. Figure 7: Learning accuracy versus communication rounds for the CIFAR-10 data. The top plot presents the results produced in the case of the IID data distribution scenario, while the bottom plot depicts the results generated in case of the Non-IID data distribution scenario. (**a**) IID; (**b**) Non-IID. FedCO differs from the Federated Learning baseline FedAvg as follows: our algorithm uses a much smaller number of nodes while the aggregation procedure is the same. Thus, if we have a smaller number of workers, convergence is reached faster than in FedAvg, where all the available workers are used. At each round, FedCO selects and uses a different set of workers, and each worker is a representative that achieves the highest accuracy in each cluster. Hence, the accuracy is not sacrificed. Table 4 shows the number of communication rounds to achieve the maximum model accuracy (i.e., to converge) for the datasets considered. Specifically, the target accuracy values are 90% for MNIST and FashionMNIST and 85% for CIFAR-10. FedAvg is the baseline benchmark, and the iterations saved for algorithm \(X\) (\(X\) = FedProx, CMFL, or FedCO) is computed as

\[1-\frac{num\_of\_iteration\_X}{num\_of\_iteration\_FedAvg}.\]

FedCO saves from 75% to 86% of iterations to converge with respect to FedAvg for IID data distribution setting, and it saves from 65% to 82% iterations for the Non-IID data distribution scenario. Moreover, FedCO always converges with at least half of the iteration rounds needed by CMFL. In more detail, one can observe that the model on the MNIST IID data distribution setting converges to an accuracy of 90% in 190 rounds with the FedAvg algorithm, and in 25 rounds for our FedCO algorithm, providing savings of 86%, and in 185 rounds for FedProx, and in 50 rounds for CMFL, providing savings of 26% and 73%, respectively. The model trained on the FashionMNIST IID data distribution scenario converges to a target accuracy of 90% in 200 rounds for FedAvg, and in 50 rounds for FedCO, saving 75% of communication rounds, while it requires 190 and 60 rounds for FedProx (5% saving) and CMFL (70% saving), respectively. Furthermore, in the FashionMNIST Non-IID data distribution scenario, the model converges to an accuracy of 90% in 200 rounds for the FedAvg algorithm, and in 186 rounds for FedProx, saving only 7%. In contrast, it requires 70 and 150 communication rounds for FedCO and CMFL, with savings of 65% and 25%, respectively.