Robust Client Selection Strategy Using an Improved Federated Random High Local Performance Algorithm to Address High Non-IID Challenges

Abstract

This paper introduces an improved version of the Federated Random High Local Performance (Fed-RHLP) algorithm, specifically aimed at addressing the difficulties posed by Non-IID (Non-Independent and Identically Distributed) data within the context of federated learning. The refined Fed-RHLP algorithm implements a more targeted client selection approach, emphasizing clients based on the size of their datasets, the diversity of labels, and the performance of their local models. It employs a biased roulette wheel mechanism for selecting clients, which improves the aggregation of the global model. This approach ensures that the global model is primarily influenced by high-performing clients while still permitting contributions from those with lower performance during the model training process. Experimental findings indicate that the improved Fed-RHLP algorithm significantly surpasses existing methodologies, including FederatedAveraging (FedAvg), Power of Choice (PoC), and FedChoice, by achieving superior global model accuracy, accelerated convergence rates, and decreased execution times, especially under conditions of high Non-IID data. Furthermore, the improved Fed-RHLP algorithm exhibits resilience even when the number of clients participating in local model updates and aggregation is diminished in each communication round. This characteristic positively influences the conservation of limited communication and computational resources.

1. Introduction

In the context of Federated Learning (FL), the process of client selection plays a pivotal role in determining the most suitable participants for model training. Effective client selection contributes to accelerated convergence, improved global model accuracy, optimal utilization of heterogeneous data, and enhanced computational capabilities across various devices, ultimately leading to superior model performance [1]. Concurrently, it is essential to ensure communication efficiency and minimize computational resource consumption.

Engaging all clients can present significant challenges, including the potential unavailability of certain clients at specific times and communication bottlenecks arising from network infrastructure limitations. Consequently, an efficient client selection strategy focuses on identifying a smaller subset of clients for participation, which offers multiple advantages, such as reduced communication costs, improved resource efficiency, and enhanced model generalization [2].

A significant challenge in FL relates to suboptimal client selection and excessive diversity in model aggregation. Client heterogeneity can arise from statistical disparities, such as imbalanced datasets or substantial variations in data volume across clients, which may lead to diminished model accuracy and prolonged convergence times [3]. Furthermore, the non-independent and identically distributed (Non-IID) characteristics of the data compound this challenge. Each client possesses training samples from a limited range of classes and demonstrates imbalanced sample distributions during the training process. The Non-IID challenge can be categorized into two distinct levels: high-level and low-level issues. High-level issues emerge when each client is assigned only a few labels for local model training. Conversely, low-level issues occur when clients have access to a broader range of labels, albeit not the complete set.

The challenges associated with heterogeneous client selection and low-quality data are particularly evident in the random client selection mechanism employed by the Federated Averaging algorithm (FedAvg). As previous research has indicated [4], FedAvg may result in suboptimal global model aggregation [5,6], leading to increased delays and diminished model accuracy, especially when addressing Non-IID data across clients [7,8,9]. In response to the issues arising from random client selection, various strategies have been developed that incorporate bias values to select clients based on their number of training samples and elevated local loss. One such strategy, as highlighted in [10], proposed the Power-of-Choice algorithm (PoC), which prioritizes clients exhibiting higher local loss values to enhance convergence rates. Nevertheless, the PoC approach may deviate from the optimal central loss function, potentially compromising overall model accuracy due to its singular focus on accelerating convergence. To refine the PoC methodology, the FedChoice algorithm was introduced [11]. This algorithm aims to improve global model convergence by favoring clients with higher loss values, thereby increasing their likelihood of participating in local model training and subsequent integration into the global model.

This study presents an improved version of the Federated Random High Local Performance (Fed-RHLP) algorithm, building upon the initial iteration introduced in [12]. The primary objective of this improvement is to refine the process of robust client selection by identifying a more suitable and reduced subset of clients, thereby addressing the challenges posed by significant Non-IID issues. The improved Fed-RHLP algorithm prioritizes the selection of clients with three key characteristics: a substantial number of samples, demonstrated label diversity, and high local model performance across both local updates and global aggregation. Concurrently, the algorithm allows for the inclusion of lower-quality clients, enabling them to contribute their local datasets during the training and aggregation phases. The implementation of this algorithm results in accelerated convergence and improved accuracy, particularly in scenarios characterized by high Non-IID conditions. Moreover, it ensures fairness by facilitating proportional participation from the majority of clients.

2. Materials and Methods

2.1. Exploring Issues of Client Selection Methods

In the context of Federated Learning (FL), the selection of diverse clients, combined with limited data samples and suboptimal data quality, can impede convergence rates and contribute to the development of an inaccurate global model. Numerous studies have proposed client selection methodologies designed to address the statistical discrepancies encountered during the global model aggregation process. The challenge of statistical heterogeneity originates from multiple sources, including variations in data distributions, inconsistent sampling practices, and Non-IID data or imbalanced datasets [13]. To manage this heterogeneity, it is crucial to implement client selection strategies during the training process that ensure convergence across the system, considering the diversity of statistical heterogeneity [14]. Furthermore, additional complexities arise from variations in model architectures, network conditions, and hardware capabilities among participating clients. These factors collectively exacerbate the existing challenges, diminishing the server’s ability to perform effective model aggregation and resulting in a global model with compromised precision [15]. A comprehensive review and analysis of the challenges and limitations associated with these algorithms can be conducted as follows:

FedAvg represents a straightforward approach that involves the random selection of clients for local model updates, specifically employing Convolutional Neural Networks (CNNs) to distribute computational tasks among clients and address challenges associated with centralized machine learning. This method applies gradient descent to perform local updates on the models of a randomly selected subset of clients, which are subsequently aggregated to create a global model. Although FedAvg averages the updates from individual client models, it may encounter significant divergence from the optimal model, particularly when the training data distribution of a single client markedly differs from the heterogeneous and non-IID data distribution [16,17].

The ideal model equation for FedAvg can be decomposed into two primary components: (1) Local Updates: Each client k refines its model ${\mathrm{w}}_{\mathrm{t}+1}^{\mathrm{k}}$ through gradient descent, employing a step size determined by η, (the learning rate). This process is influenced by the client’s local dataset and the gradient ${\mathrm{g}}_{\mathrm{k}}$ of the loss function. (2) Global aggregation: The locally updated models from the clients are amalgamated to form the global model ${\mathrm{w}}_{\mathrm{t}+1 }$, with the aggregation weighted proportionally to the size of each client’s dataset ${\mathrm{n}}_{\mathrm{k}}$ relative to the total dataset size n, as shown in Equation (1).

$$\begin{gathered} \forall k, w_{t+1}^k\leftarrow w_t-n{g}_k \\ {\mathrm{w}}_{\mathrm{t}+1 }\leftarrow {\displaystyle \sum }_{\mathrm{k}=1}^{\mathrm{K}}{\displaystyle \frac{{\mathrm{n}}_{\mathrm{k}}}{\mathrm{n}}}{\mathrm{w}}_{\mathrm{t}+1}^{\mathrm{k}} \end{gathered}$$

(1)

The problems with FedAvg can be demonstrated through the following example, as shown in Figure 1.

In Figure 1, it is assumed that three clients (K = 3), represented as k₁, k₂, and k₃, are each responsible for updating their local models (w_k1, w_k2, and w_k3) with a local dataset (d_k) and then contribute to aggregating a global model (W_t) in the communication round (t). In the random client selection process, the probability of selecting a client (p_k) for local updates is equally distributed, with a probability value of p_k = 1/K (0.33). We assume that k₁ has 100 samples with 3 labels (n_k = 100, L_k = 3), k₂ has 50 samples with 1 label (n_k = 50, L_k = 2), and k₃ has 20 samples with 1 label (n_k = 20, L_k =1). If clients with low data quantity and few labels (k₂ and k₃) are frequently selected for updates, this can cause significant divergence.

Upon examining client selection methodologies, such as the Power-of-Choice (PoC) algorithm and the FedChoice algorithm, it becomes evident that bias values are allocated to clients based on the volume of training samples and elevated local loss. A significant concern emerges when a client with a substantial number of samples is selected, particularly if these samples are predominantly from a single label. This scenario detrimentally affects the diversity of datasets utilized in model updates and global aggregation [18]. The issue of label scarcity further compounds this challenge, as certain clients may lack adequate labeled data due to resource constraints or insufficient motivation for labeling tasks. Such complications contribute to suboptimal model performance and impede the development of a well-generalized model across varied datasets. Ideally, client selection should encompass a range of labels alongside a considerable number of samples [19,20]. This approach ensures that local model training effectively captures diverse patterns, thereby enhancing the global model’s generalization [21]. When addressing the bias gap arising from an exclusive reliance on large sample sizes for client selection in local loss estimation and model updates within the PoC and FedChoice frameworks, as well as the conventional practice of utilizing all clients for local model performance assessment in Fed-RHLP, it becomes apparent that these approaches may result in a deficiency of local dataset diversity and significant execution time delays. This issue is evident, as shown in Figure 2.

In Figure 2, a comparison of client selection methods for local model updates in the PoC, FedChoice, and traditional Fed-RHLP algorithms is shown. In the example, there are three clients (k₁, k₂, and k₃).

The PoC and FedChoice algorithms assume that the server selects only two clients as candidates for local loss estimation in each communication round. These algorithms prioritize clients with larger local datasets for participation. The probability of selecting each client (k) based on its local dataset size is calculated as ${\mathrm{P}}_{\mathrm{k}}={\displaystyle \frac{{\mathrm{n}}_{\mathrm{k}}}{{{\displaystyle \sum }}_{\mathrm{k}=1}^{\mathrm{K}}{\mathrm{n}}_{\mathrm{k}}}}$. For k₁, with a local dataset size of n_k1 = 300, the probability is calculated as P_k1 = 300/700 = 0.43. For k₂, with n_k2 = 250, P_k2 = 250/700 = 0.36. Finally, for k₃, with n_k3 = 150, P_k3 = 150/700 = 0.21. As a result, k₁ has the highest probability of being selected, followed by k₂, which has a higher probability than k₃. This selection process often leads to clients with a single label, such as k₁ and k₂, being selected repeatedly for local model training. Consequently, this reduces the diversity of the aggregated global model.

The traditional Fed-RHLP algorithm, proposed in [12], uses all clients (k₁, k₂, and k₃) to estimate the clients’ local model performance (LP_k) by sending the global model (W) to each client for estimating with the local dataset (d_k). Subsequently, the LP_k of each client is converted into a weight for local model performance (${\mathrm{WLP}}_{\mathrm{k}}$), which is added to a biased roulette wheel for randomly selecting model updates and aggregation based on clients’ local model performance, as shown in Equations (2)–(4).

$${\mathrm{LP}}_{\mathrm{k}}=\mathrm{f}\left(\mathrm{W}; {\mathrm{d}}_{\mathrm{k}}\right)$$

(2)

$$\mathrm{TotalLP}={\displaystyle \sum }_{\mathrm{k}=1}^{\mathrm{N}}{\mathrm{LP}}_{\mathrm{k}}$$

(3)

$${\mathrm{WLP}}_{\mathrm{k}}={\displaystyle \frac{{\mathrm{LP}}_{\mathrm{k}}}{\mathrm{TotalLP}}}$$

(4)

The conventional Fed-RHLP algorithm is marked by significant computational demands, particularly in situations where certain clients are unavailable for processing at specific times. Additionally, the random selection of a large number of clients complicates the identification of those with high-quality datasets. This scenario may lead to missed processing opportunities and impede the accurate identification of clients eligible for participation.

The utilization of a biased roulette wheel for client selection and aggregation aims to enhance the performance of the Fed-RHLP algorithm. The calculations presented in Equations (2)–(4) can be elucidated and implemented in a two-step process as follows.

Step 1: Involves determining the probability for each candidate client, which is based on the quantity of data samples and the diversity of labels. This probability is subsequently normalized by dividing it by the cumulative total of these values across all candidate clients, thereby establishing the probability for each individual client.

Step 2: Focuses on calculating the probability derived from the assessed local model performance of the candidate clients, giving precedence to those exhibiting superior local model performance.

The resultant combined probability, which integrates both dataset size and model performance, is constrained within the range of 0 to 1. This probability dictates the representation of each client within the biased roulette wheel.

During each communication round, a seed is randomly assigned without replacement, ensuring that client selection corresponds with their designated probabilities and that a distinct set of clients is chosen in every round. The local models selected are then amalgamated into the global model, thereby facilitating a balanced and efficient client selection process.

2.2. Developing the Improved Federated RHLP Algorithm for Efficient Client Selection

The Improved Federated RHLP algorithm exhibits enhanced efficiency by increasing the accuracy of global model aggregation and accelerating the convergence rate. The subsequent key assumptions underpin the analysis:

(1) The selection of a predominant number of clients possessing extensive data samples and varied labels contributes positively to the updates of local models.

(2) The identification of candidate clients that exhibit superior local model performance alongside a substantial and diverse dataset significantly improves the efficacy of global model aggregation.

(3) The application of a dual-biased strategy in the roulette wheel selection process enhances the accuracy of the global model, expedites the convergence rate, and minimizes execution duration.

This improvement is achieved through its dual-bias approach, consisting of Module 1 and Module 2. These modules incorporate factors such as the number of samples, label diversity, and the high performance of local models from clients into the processes of model updates and aggregation, as shown in Figure 3.

In Figure 3, the architecture of the Improved RHLP algorithm is developed in two modules:

Module 1: Candidate client selection

The client selection process requires improvement to more effectively select a smaller set of candidate clients (Ct) in each communication round, prioritizing based on the number of samples (n_k) and label diversity (L_k). In the example (Figure 4), the probability of choosing each client (k) is calculated as ${\mathrm{P}}_{\mathrm{k} }$= ${\displaystyle \frac{{\mathrm{n}}_{\mathrm{k} \times { \mathrm{L}}_{\mathrm{k}}}}{{{\displaystyle \sum }}_{\mathrm{k}=1}^{\mathrm{K}}{\mathrm{n}}_{\mathrm{k} \times { \mathrm{L}}_{\mathrm{k}}}}}$ For k₁, P_k1 = (300 × 1)/1000 = 0.3; for k₂, P_k2 = (250 × 1)/1000 = 0.25; for k₃, P_k3 = (150 × 3)/1000 = 0.45. Consequently, k₃ exhibits the greatest probability of selection for local model updates and performance assessment, with k₁ following closely, possessing a higher likelihood than k₂. This proposed selection process ensures that clients with more diverse labels and larger datasets are prioritized, leading to a more diverse and robust aggregated global model.

Module 2: High local model performance updates and aggregation

The local model performance is measured in the algorithm by splitting each candidate’s local dataset (d_k) into training samples (d_train_k), where (d_train_k) is further split into batches of size B for locally updating the model (w_k) by using the Stochastic Gradient Descent (SGD) technique, and small test samples (d_test_k), which are used for testing local model performance of each client (LP_k) with LP_k = ʄ(w_k;d_test_k). High-performing local models, calculated from $\mathrm{TotalLP}={\displaystyle \sum }_{{\mathrm{k} \in \mathrm{C}}_{\mathrm{t}}}{\mathrm{LP}}_{\mathrm{k}}$ and using Equation (4) to determine the weight of local model performance (${\mathrm{WLP}}_{\mathrm{k}}$), are then randomly selected using a biased roulette wheel mechanism for global model aggregation.

In the example of local model aggregation involving candidate clients (k₁, k₃, and k_x), let us consider that client k₁ possesses local model parameters (w_k) in the structural layers, which have been trained with d_train_k1 = 1,1,1,. In contrast, k₃ has structural layer parameters that are trained using d_train_k3 = (2,2,2), while client k_x has structural layer parameters trained with d_train_kx = (1,2,1).

The revised local model for the chosen candidate clients is assessed utilizing their corresponding test datasets (d_test_k). Subsequently, the accuracy of each local model is computed and transformed into a probability value (fitness) that falls within the interval of 0 to 1, employing the established method for determining the performance probability of the local model, as detailed below.

The predicted accuracies for the models are as follows: k₁ exhibits an accuracy of 88%, k₃ shows an accuracy of 83%, and k_x has an accuracy of 86.5%. The local model performance probabilities for each candidate client are computed as follows: P_k1 = 88/257.5 = 0.34, P_k3 = 83/257.5 = 0.32, and P_kx = 86.5/257.5 = 0.34. The cumulative probability for all candidate clients totals 1. These probabilities are subsequently allocated to a roulette wheel mechanism, where k₁ spans the interval 0.000–0.340, k₃ covers the interval 0.341–0.660 (noting that 0.341 = 0.340 + 0.001), and k_x ranges from 0.661 to 1.000.

A random number is subsequently generated within the interval of 0 to 1, and the client is chosen in accordance with the designated probability ranges. This selection process occurs without replacement during each round of communication.

By assigning biased values on the roulette wheel in accordance with the performance of local models, k₁ and k_x may be randomly selected. Upon selection, these models will transmit their parameters, specifically (w_k1 = 1,1,1) and (w_kx = 1,2,1) for the purpose of averaging. The revised global model parameters will be determined by the calculation ${\displaystyle \frac{1,1,1+1,2,1 }{2}}=\left({\mathrm{W}}_{\mathrm{t}}=1,1.5,1\right)$ prior to their transmission for the forthcoming local model updates in the subsequent communication round.

The details of the improved RHLP algorithm are presented in the pseudocode in Algorithm 1.

Algorithm 1: Improved Federated RHLP algorithm.
1:	ServerExecute:
2:	${\mathrm{W}}_0$ = Initial parameters of the CNNs model
3:	N = Total number of clients
4:	C1 = Fraction of candidate clients
5:	C2 = Fraction of selected clients
6:	m1 = Number of candidate clients
7:	m2 = Number of selected clients
8:	nk = Number of samples of client k
9:	lk = Label diversity of client k
10:	d_train_proportion = Proportion of local training samples
11:	d_test_proportion = Proportion of local testing samples
12:	For t = 1 to T do
13:	m1 = N·C1
14:	Ct = {random set of candidate (m1) clients based on ${\mathrm{P}}_{\mathrm{k}}$= ${\displaystyle \frac{{\mathrm{n}}_{\mathrm{k}·{\mathrm{l}}_{\mathrm{k}}}}{\sum _{\mathrm{k}=1}^{\mathrm{K}}{\mathrm{n}}_{\mathrm{k}·{\mathrm{l}}_{\mathrm{k}}}}}$, $\mathrm{r}\mathrm{e}\mathrm{p}\mathrm{l}\mathrm{a}\mathrm{c}\mathrm{e}=\mathrm{F}\mathrm{a}\mathrm{l}\mathrm{s}\mathrm{e}$}
15:	For k ∈ Ct in Parallel do
16:	${\mathrm{w}}_{\mathrm{t}+1}^{\mathrm{k}},{\mathrm{L}\mathrm{P}}_{\mathrm{t}}^{\mathrm{k}}=\mathrm{C}\mathrm{l}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{U}\mathrm{p}\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{e}\_\mathrm{T}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{L}\mathrm{P}(\mathrm{k},{\mathrm{W}}_{\mathrm{t}})$
17:	${\mathrm{TotalLP}}_{\mathrm{t}}+={\mathrm{L}\mathrm{P}}_{\mathrm{t}}^{\mathrm{k}}$
18:	End for
19:	For k ∈ Ct do
20:	${\mathrm{W}\mathrm{L}\mathrm{P}}_{\mathrm{t}}^{\mathrm{k}}$= ${\displaystyle \frac{{\mathrm{L}\mathrm{P}}_{\mathrm{t}}^{\mathrm{k}}}{{\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{L}\mathrm{P}}_{\mathrm{t}}}}$
21:	${\mathrm{L}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{W}\mathrm{L}\mathrm{P}}_{\mathrm{t}}$.append(${\mathrm{W}\mathrm{L}\mathrm{P}}_{\mathrm{t}}^{\mathrm{k}}$)
22:	End for
23:	St = {random set of higher local performance (m2) clients based on ${\mathrm{L}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{W}\mathrm{L}\mathrm{P}}_{\mathrm{t}}$     ,$\mathrm{r}\mathrm{e}\mathrm{p}\mathrm{l}\mathrm{a}\mathrm{c}\mathrm{e}=\mathrm{F}\mathrm{a}\mathrm{l}\mathrm{s}\mathrm{e}$}
24:	${\mathrm{W}}_{\mathrm{t}+1}={\displaystyle \frac{1}{\mathrm{m}2}}\sum _{\mathrm{k}\in {\mathrm{S}}_{\mathrm{t}}}{\mathrm{w}}_{\mathrm{t}+1}^{\mathrm{k}}$
25:	End for
26:	ClientUpdate_TestLP(k, w):
27:	d_train, d_test = TrainTestSplit(dk, d_train_proportion, d_test_proportion)
28:	B = (Split d_train into batches)
29:	For i = 1 to E do
30:	For b ∈ B do
31:	$\mathit{w}\leftarrow \mathit{w}-\mathit{n}\mathtt{\nabla }\mathcal{l}(\mathit{w};\mathit{b})$
32:	End for
33:	End for
34:	$\mathrm{L}\mathrm{P}=\mathrm{ƒ}\left(\mathrm{w};\mathrm{d}\_\mathrm{t}\mathrm{e}\mathrm{s}\mathrm{t}\right)$
35:	Return w, LP to the server

The comprehensive examination presented in Figure 3 and Figure 4 illustrates the advantages of the enhanced Fed-RHLP algorithm, particularly through an analysis of the selection of random biasing factors utilized in both client selection and model aggregation procedures. Additionally, the algorithm offers substantial security measures against potential network attacks, as detailed in the subsequent sections:

1. Large Datasets: Selecting data repositories that contain extensive datasets has a beneficial impact on the performance of global models. The Law of Large Numbers (LLN) serves as a core tenet in probability theory, underpinning the consistent behavior of sample averages as the size of the sample grows [22]. By augmenting the number of samples, the model is better equipped to represent the actual data distribution, resulting in enhanced accuracy.

2. Label Diversity: The presence of diverse data types within each data repository is essential for the effective training of models, particularly in the context of Federated Learning, where data distribution may not be independent and identically distributed (Non-IID). A heterogeneous dataset enables the model to learn from various data types, thereby enhancing its adaptability and overall performance. From a statistical perspective, increased label diversity contributes positively to model efficacy by providing a more comprehensive understanding of the problem and facilitating a balance between bias and variance. This approach mitigates bias and helps to avoid overfitting, ultimately resulting in improved performance. In Reference [23], a technique was introduced in which clients share their label distributions to allocate biased weights for model updates and aggregation, thereby further optimizing model efficiency.

3. Local Model Performance: The precision of the model developed from the local dataset of each data repository is of paramount importance. A repository that excels in assimilating knowledge from its own data is likely to contribute positively to the overall performance of the model when updates are made. Therefore, selecting repositories that demonstrate strong local performance will significantly enhance both the accuracy and efficiency of global model training within the Federated Learning (FL) framework. In the context of Genetic Algorithms (GA), the process of choosing solutions with high fitness is essential for fostering the development of optimal solutions by selecting and refining the most advantageous genes across generations [24]. The application of a fitness function to assess the quality of each solution facilitates an ongoing pursuit of the most effective outcomes.

4. Robust Security Against Attacks on the Network: Concentrating on a reduced subset of clients while ensuring the overall accuracy of the global model can enhance the detection and validation of adversarial attacks or clients exhibiting harmful behavior. This strategy proves to be more effective than the inclusion of all clients for model updates and communications within the network. The enhanced Fed-RHLP algorithm refrains from transmitting raw data or values that are directly associated with the actual dataset, thereby increasing its resilience against adversarial threats or malicious clients that may arise in practical situations.

Furthermore, Algorithm 1 illustrates the pseudocode of the Enhanced RHLP algorithm, highlighting its scalability in relation to the increasing number of clients. As additional clients engage in local model updates, the algorithm is capable of concurrently assessing the probability of each candidate client by considering various factors, including the volume of data samples, diversity of labels, local model training, and performance evaluation of the local model. The efficacy of parallel processing within the proposed algorithm is particularly noticeable in Lines 15–18 and 26–35.

2.3. Experiment Setup

This study employs CNNs, recognized as a highly effective deep learning algorithm suitable for tasks involving image classification [25]. The experimental procedure is organized into three distinct phases, which are outlined in the following sections.

2.3.1. Dataset Preparation

In this study, we address the challenge posed by imbalanced and Non-IID datasets that are distributed among clients, a critical concern in the realm of FL [26]. Such imbalances have a profound impact on the efficacy of model training [27]. The effectiveness of the improved Fed-RHLP algorithm was evaluated through comparisons with FedAvg, PoC, and FedChoice, specifically focusing on Non-IID scenarios utilizing the MNIST and Fashion-MNIST (FMNIST) datasets.

The structures of these datasets are described and illustrated in Figure 5.

Figure 5 shows the use of two datasets: (a) the MNIST dataset and (b) the FMNIST dataset. Both datasets contain a total of 70,000 images, each being a 28 × 28 grayscale image. The MNIST dataset consists of handwritten digit images (ranging from 0 to 9) [28], while the FMNIST dataset contains fashion item images categorized into 10 classes [29]. Both datasets are split into 60,000 training images and 10,000 test images.

To demonstrate the resilience of the improved Federated RHLP algorithm, we constructed Non-IID challenges to assess the algorithm’s robustness at two distinct levels: (1) High Non-IID Challenge: Each client was assigned 1–2 classes for local model updates, and (2) Low Non-IID Challenge: Each client was assigned 5–6 classes for local model updates. The datasets were distributed among 100 clients, with each client receiving a varying proportion of data samples, ranging from 10% to 30%, to support the training of their local models.

2.3.2. Setting up Algorithms, CNN Model Structures, and Hardware Specifications

• Setting Up Algorithms

The algorithms will be executed over 200 communication rounds to consolidate the global model. The SGD optimization technique is employed within the CNNs framework for local model updates across five local epochs (E). The batch size is established at 64, with a learning rate of 0.01 for the SGD [30,31,32,33].

During each communication iteration, the Improved Federated RHLP, PoC, and FedChoice algorithms select a subset of candidate clients (Ct), which constitutes 10% (C = 0.1) of the overall pool of 100 clients. Following this, a smaller group of clients (St) is chosen in varying proportions of 2%, 4%, 6%, 8%, and 10% [34]. When the selection for St reaches 10%, the number of candidate clients is augmented by 15% (adding 15 additional candidates) to facilitate a sufficiently random selection process. Furthermore, in the Improved Federated RHLP methodology, each client’s local dataset is partitioned into local testing samples, randomly varying between 3% and 5%, while the remaining data is designated for training during local model updates and performance assessment. In contrast, the FedAvg method does not predefine candidate clients but instead directly selects fractions of 2%, 4%, 6%, 8%, and 10% of clients for the purpose of model training.

2.

Setting Up CNN Model Structures

The structure of the CNN model is configured for training on the MNIST and FMNIST datasets, as outlined below:

(1) MNIST Dataset:

The CMM model architecture comprises two convolutional layers. In the first layer, 10 feature maps are produced using 5 × 5 filters. The second layer increases the number of feature maps to 20, also employing 5 × 5 filters. To reduce the risk of overfitting, a dropout layer with a rate of 0.5 is applied after the second convolutional layer. The network architecture further includes two fully connected layers: the first layer reduces 320 features to 50 neurons, and the second layer maps these 50 neurons to 10 output classes, representing the digits 0 to 9.

(2) FMNIST Dataset:

The CNN model architecture comprises two convolutional layers. The initial layer generates 32 feature maps using 3 × 3 filters with a padding of 1. A max pooling layer with a 2 × 2 kernel and a stride of 2 follows this first layer. The subsequent convolutional layer increases the number of feature maps to 64, again employing a 3 × 3 filter size. This is followed by another max pooling layer, utilizing the same 2 × 2 kernel and stride of 2. The model further incorporates three fully connected layers: The first layer transforms 2304 features into 600 neurons. A dropout layer with a rate of 0.25 is introduced after this layer to mitigate the risk of overfitting. The second fully connected layer reduces the 600 features to 120 neurons. The final layer maps the 120 features to 10 output classes, representing various fashion items.

3.

Setting Up Hardware Component Specifications

This experiment prepares the hardware specifications for setting up and executing the algorithms, as outlined in

Table 1. Hardware specifications for executing the algorithms.

Device	Specification
Central Processing Unit	11th Gen Intel(R) Core(TM) i5-11400F 2.59 GHz
Graphics Processing Unit	Radeon (TM) RX 480 Graphics
Random Access Memory	32.0 GB
Operating System	Windows 11
Software Environment	Python 3.7.2 with the Pytorch framework

.

2.3.3. Algorithm Performance Evaluation

The global model of the algorithms was evaluated 3 times over 200 communication rounds to ensure the stable reporting of its performance, using 10,000 global test samples from the MNIST and FMNIST datasets. The formula for evaluating the Improved RHLP algorithm, compared with other benchmark algorithms, involves measuring prediction accuracy, convergence speed, and reduced execution time [11]. The calculation methods for these three performance metrics are shown in Equations (5)–(7).

$$\mathrm{Accuracy} \left(\%\right)={\displaystyle \frac{\left(\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{test} \mathrm{samples} - \mathrm{Number} \mathrm{of} \mathrm{incorrectly} \mathrm{predicted} \mathrm{samples}\right)\times 100}{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{test} \mathrm{samples}}}$$

(5)

$$\mathrm{Convergence} \mathrm{speed} \left(\%\right)={\displaystyle \frac{\left(\mathrm{Higher} \mathrm{round} - \mathrm{Lower} \mathrm{round}\right)\times 100}{\mathrm{Higher} \mathrm{round}}}$$

(6)

$$\mathrm{Educed} \mathrm{execution} \mathrm{time} \left(\%\right)={\displaystyle \frac{\left(\mathrm{Higher} \mathrm{execution} \mathrm{time} - \mathrm{Lower} \mathrm{execution} \mathrm{time}\right)\times 100}{\mathrm{Higher} \mathrm{execution} \mathrm{time}}}$$

(7)

3. Results

The Improved Fed-RHLP was assessed for its overall model accuracy and benchmarked against various algorithms across different ratios of selected clients. This evaluation was conducted using the MNIST and FMNIST datasets, which respectively represent high and low degrees of Non-IID challenges. The results are shown below.

The data depicted in Figure 6 demonstrate that the improved Fed-RHLP exhibits superior global model accuracy compared to alternative client selection algorithms, irrespective of the severity of Non-IID challenges, as substantiated by the results derived from the MNIST and FMNIST datasets. In scenarios characterized by high Non-IID issues, the improved Fed-RHLP significantly outperforms its competitors across all client selection proportions. Conversely, under conditions of low Non-IID challenges, the algorithm provides a modest advantage over alternative approaches.

In scenarios characterized by high Non-IID challenges within the MNIST dataset, the improved Fed-RHLP achieves a peak global model accuracy of 96.49% when employing a selection proportion of 10%. This performance demonstrates notable improvements: 10.31% higher than FedAvg (highest accuracy: 86.18% at a 10% selection proportion), 3.06% higher than PoC (highest accuracy: 93.43% at a 2% selection proportion), and 6.27% higher than FedChoice (highest accuracy: 90.22% at a 2% selection proportion). Similarly, in the context of high Non-IID issues within the FMNIST dataset, the improved Fed-RHLP attains a global model accuracy of 89.06% at a selection proportion of 10%. This represents performance improvements of 4.02% higher than FedAvg (highest accuracy: 85.04% at an 8% selection proportion), 3.27% higher than PoC (highest accuracy: 85.79% at a 10% selection proportion), and 1.16% higher than FedChoice (highest accuracy: 87.90% at a 10% selection proportion).

In scenarios characterized by low Non-IID challenges within the MNIST dataset, the improved Fed-RHLP achieves a peak global model accuracy of 98.91% with a selection proportion of 4%. This performance demonstrates marginal improvements: 0.44% higher than FedAvg (highest accuracy: 98.47% at a 10% selection proportion), 0.08% higher than PoC (highest accuracy: 98.83% at a 10% selection proportion), and 0.14% higher than FedChoice (highest accuracy: 98.78% with a 4% selection proportion). Similarly, in the context of low Non-IID issues in the FMNIST dataset, the improved Fed-RHLP attains a maximum global model accuracy of 90.97% with a selection proportion of 8%. This represents incremental performance improvements of: 0.38% higher than FedAvg (highest accuracy: 90.59% at an 8% selection proportion), 0.20% above PoC (highest accuracy: 90.77% at an 8% selection proportion), and 0.34% greater than FedChoice (highest accuracy: 90.63% at an 8% selection proportion).

Additionally, the improved Fed-RHLP underwent assessment for its convergence speed and execution time, benchmarked against alternative algorithms across both high and low levels of Non-IID challenges. The evaluation focused on achieving the highest global model accuracy under the following parameters: High Non-IID Conditions: MNIST: 10% client selection proportion; FMNIST: 10% client selection proportion; and in Low Non-IID Conditions: MNIST: 4% client selection proportion; FMNIST: 8% client selection proportion, respectively. The results are presented as follows.

Figure 7a–d show that the improved Fed-RHLP achieves higher global model accuracy, faster convergence speed, and reduced execution time compared to FedAvg, PoC, and FedChoice when tested on MNIST and FMNIST under both high and low levels of Non-IID issues. The insights from the results are presented in

Table 2. Performance metrics for the global model of the algorithms on the Non-IID MNIST dataset.

Algorithm	Issue Level	Accuracy of Global Model	Convergence Rounds and Time (Seconds) with Different Accuracy
			60%		70%		80%		90%
			Round	Time	Round	Time	Round	Time	Round	Time
improved Fed-RHLP	High	96.49%	6	633.6	11	1161.6	19	2006.4	41	4329.6
	Low	98.91%	3	486	3	486	6	972	10	1620
FedAvg	High	86.18%	32	1747.2	74	4040.4	126	6879.6	-	-
	Low	98.03%	9	680.4	12	907.2	12	907.2	52	3931.2
PoC	High	90.31%	43	3947.4	57	5232.6	85	7803	185	16,983
	Low	98.76%	3	451.8	5	753	8	1204.8	15	2259
FedChoice	High	87.80%	40	3816	60	5724	92	8776.8	-	-
	Low	98.78%	3	464.4	5	774	8	1238.4	14	2167.2

and

Table 3. Performance metrics for the global model on the Non-IID FMNIST dataset.

Algorithm	Issue Level	Accuracy of Global Model	Convergence Rounds and Time (Seconds) with Different Accuracy
			60%		70%		80%		90%
			Round	Time	Round	Time	Round	Time	Round	Time
improved Fed-RHLP	High	89.06%	6	1288.8	11	2362.8	15	3222	-	-
	Low	90.97%	1	328.2	2	656.4	7	2297.4	48	15,753.6
FedAvg	High	83.68%	13	2386.8	23	4222.8	55	10,098	-	-
	Low	90.59%	3	747	3	747	3	747	83	20,667
PoC	High	85.79%	8	1929.6	9	2170.8	39	9406.8	-	-
	Low	90.77%	3	1072.8	5	1788	6	2145.6	85	30,396
FedChoice	High	87.90%	8	1934.4	12	2901.6	21	5077.8	-	-
	Low	90.63%	2	714	4	1428	6	2142	59	21,063

.

From Table 2 and Table 3, the testing results on the MNIST and FMNIST datasets demonstrate that the improved Fed-RHLP exhibits significant advantages in addressing high Non-IID levels compared to other algorithms.

In the context of the MNIST dataset characterized by high Non-IID challenges, the improved Fed-RHLP demonstrates exceptional performance, achieving an accuracy of 96.49%. This result surpasses that of FedAvg, PoC, and FedChoice by margins of 10.31%, 6.18%, and 8.69%, respectively. At an accuracy level of 80%, Fed-RHLP exhibits both faster convergence and reduced execution time compared to all other algorithms. Most notably, it reaches 90% accuracy within merely 41 communication rounds, which represents a 77.84% improvement over PoC, accompanied by a 74.51% reduction in execution time. In scenarios with low Non-IID levels, Fed-RHLP significantly outperforms FedAvg, achieving an 80.77% enhancement in convergence speed and a 58.79% decrease in execution time. Additionally, the algorithm marginally exceeds the performance of PoC and FedChoice.

In the context of the FMNIST dataset characterized by high Non-IID challenges, the improved Fed-RHLP demonstrates a peak accuracy of 89.06%. This performance exceeds that of FedAvg, PoC, and FedChoice by margins of 5.38%, 3.27%, and 1.16%, respectively. When achieving an accuracy of 80%, Fed-RHLP exhibits remarkable convergence characteristics: 72.73% more rapid convergence than FedAvg, 61.54% faster than PoC, and 28.57% quicker than FedChoice. Correspondingly, the algorithm achieves significant reductions in execution time: a 68.09% reduction compared to FedAvg, a 65.75% reduction compared to PoC, and a 36.55% reduction compared to FedChoice. In scenarios with low levels of Non-IID, Fed-RHLP demonstrates a marginal advantage over FedAvg, PoC, and FedChoice.

In summary, the improved Fed-RHLP exhibits greater efficiency and precision in managing elevated Non-IID levels across both datasets, showing notable advancements in convergence speed and execution duration when compared to alternative algorithms.

4. Discussion and Conclusions

This paper presents an enhanced version of the Fed-RHLP algorithm designed to address challenges posed by Non-IID data distributions. It selects a focused and diverse group of clients for training using a dual-biased strategy, considering factors such as dataset size, label variety, and local model performance. The goal is to optimize both data diversity and the quality of the global model, aligning with the approach in [35]. The Oort algorithm also tackles the participant selection challenge by considering data and system diversity to choose suitable participants.

A key feature of the enhanced version of the Fed-RHLP algorithm is the prioritization of high-performing clients while still allowing lower-performing clients to contribute. Focusing on high-performing clients during model aggregation improves global model accuracy, while including lower-performing clients ensures fairness and maintains data diversity. The equilibrium between clients with high and low performance fosters convergence and enhances the model’s ability to generalize effectively across varied data distributions. As noted in [36], it is crucial to maintain fairness in FL by carefully selecting high-quality clients and equitably distributing incentives. This assessment may involve considerations of data quality, data volume, and advancements in the model. To realize this objective, it is imperative to engage multiple clients in collaboration, rather than depending solely on a single source for the training dataset [37].

Additionally, this method reduces the computational cost of federated learning by selectively choosing clients based on dataset characteristics and local model performance. By minimizing the number of clients required for each aggregation round, execution time is reduced, which is especially beneficial in resource-constrained or large-scale scenarios. As outlined in [38], the approach improves computational efficiency and addresses communication overhead by dynamically selecting the best client models to share. This reduces unnecessary communication, lowers costs, and accelerates aggregation, making it especially valuable in federated settings with limited network bandwidth. The result is a more efficient FL framework with reduced computational load and faster model updates.

The process of aggregating the global model during each communication round of the enhanced Fed-RHLP algorithm entails computing the average of the local model parameters derived from the chosen optimal clients. This methodology significantly strengthens the robustness of global model aggregation. This strategy is consistent with the results presented in [39], which indicate that the WFA (Distance-weighted FedAvg aggregation) function achieved markedly superior accuracy and recall compared to other algorithms. While the accuracy and recall of the proposed function may experience a minor decline when faced with attacks, it still demonstrates considerable resilience against such threats.

In conclusion, the enhanced Fed-RHLP algorithm improves both accuracy and convergence, especially in Non-IID environments with significant data heterogeneity. By balancing the involvement of high- and low-performing clients, the algorithm ensures fairness and increases the diversity of contributions to the global model. This balance accelerates convergence and reduces computational costs, making it an effective solution for federated learning in diverse data environments.

5. Future Works

In future work, we aim to improve the Fed-RHLP algorithm by incorporating hierarchical FL structures. As the client pool expands, the central server faces heightened computational demands. To alleviate this, we propose dividing clients into smaller subgroups for localized aggregation before transmitting the results to the central server. This strategy will help reduce the computational load and enhance scalability, as well as decrease communication overhead and speed up the aggregation process. Additionally, we plan to adapt this hierarchical framework to handle various data distributions and model types, ensuring its effectiveness in diverse environments. Furthermore, we aim to dynamically adjust client participation in each round, considering factors such as fluctuating client participation ratios and local training epochs. This adjustment will be based on the influence of global model tuning and the contributions of client groups in each communication round, optimizing the efficiency of the global model.