## 2 The Rise of the Federated Learning Approach
### Delving into Decentralized Federated Learning (DFL)
#### 2.3.1 Communication Reduction
Plenty of experiments have been conducted, using well-known datasets (Mnist [46], FMnist [47], Cifar-10 and Cifar-100 [43], Tiny-Imagenet [48]) and both DeProFL and centralized SOTA algorithms, and the proposed method achieves comparable results regarding accuracy (accuracy degradation approximately from 0.4% to 5%), while it was proved to converge faster under non-convex loss function assumptions. After [PERSON] et al. 's work [8], [PERSON] et al. in [49] introduced a federated learning approach based on collaborative learning among one-hop connected devices (fully decentralized federated learning--DFL), taking advantage of their own localized personal data. The proposed scheme is completely server-aware, since no centralized control is required in order for the training procedure to be performed. While the collaboratively learned model functions as a Bayesian-like model, the authors explored the potential for extending it to deep neural networks (DNNs). The efficiency of the aforementioned algorithm was tested in [38], in which the results of a linear regression task, being performed on both Bayesian-like and DNNs models, showed that DFL provides better results compared to the cases in which nodes learn only from their own data. In [50], the authors provide up-to-date information about the evolution of the decentralized federated learning algorithm (DSGD), taking stochastic gradient descent (SGD)for granted in the proposed implementations. They provide theoretical analysis and convergence rates in both convex and non-convex [51], fashion [52], taking network topology adaptivity and data heterogeneity into consideration. For example, they offer an improved version of theoretical proofs regarding the cases of parameters-abundant models, Local SGD [52] and cooperative SGD. It is worth highlighting that DSGD paves the way for large-scale machine learning implementations in a D2D topology fashion. Plenty of variations, presented in this section, have been introduced in order to cope with the challenges that a peer-to-peer topology brings, e.g., communication cost, convergence speed (reaching consensus), etc. However, DSGD has been proved to converge to the optimal level when assumptions regarding convexity are applied. [PERSON] et al. [53] proposed a server-less dynamic peer-to-peer environment, namely _BrainTorrent_ (see Table 2 for more frameworks) with the aim of alleviating data privacy concerns while decentralized topology approaches are used on training deep neural networks with medical images (which are very sensitive personal data). It is one of the first frameworks to implement server-less approaches in collaborative learning. The results of the experimental evaluation showed that this server-less peer-to-peer framework with a range of 5 to 7 participating clients performs about 1-2% better than centralized federated learning approaches, while it reaches almost the same accuracy (86.3%) as the _pooled_ model (86.6%). In [37], the authors were the first to implement the DSGD algorithm to edge networks. They used a D2D network topology in order for the nodes to collaboratively train a shared ML model. In order to meet the transmission standards of the network, each device prunes the trainable model to align with the device's lowest data rate (limited bandwidth). Experiments were conducted, using both digital (D-DSGD) and analog (A-DSGD) schemes. In the latter one, Over-The-Air (OTA) SGD-based approaches are used like the one mentioned in [54], which seemed to have a better performance than DSGD only in cases where a conventional star-like topology is used, given the Fashion-Mnist dataset as a training set in a classification task. In their work [55], [PERSON] et al. present a DFL framework that involves both local updates and inter-node communication. They also propose a compressed algorithm, C-DFL, to address communication overhead and facilitate cross-device convergence.