Unsupervised Recurrent Federated Learning for Edge Popularity Prediction in Privacy-Preserving Mobile Edge Computing Networks

The complex and varied user interest/need poses enormous challenges for accurately predicting the dynamic popularity. To this end, many different algorithms have been proposed in the literature to predict the dynamic popularity over the recent years. Some inspiring examples include the time-series prediction method [20, 16], the social-driven prediction method [21, 22], and the statistics-based prediction method [23, 24]. Jiang et al. [20] proposed an online content popularity prediction algorithm by exploiting the content features and user preferences, where the user preferences were learned offline from the historically requested information. In [16], an auto-encoder (AE) neural network was combined with the long short-term memory module to predict the popularity by extracting time-series features from the historical requests of users. Nevertheless, the time-sequence prediction approaches in [20, 16] rely heavily on the privacy of users such as historical requests to improve the prediction accuracy, which is intolerable for those privacy-sensitive users and not appropriate for the privacy-preserving systems. Xu et al. [21] explored the dynamically changing and evolving propagation patterns of videos in social media and the content popularity could be forecasted in a timely fashion. In [22], the social relationships among a small number of users were explored to bridge the gap between prediction accuracy and small population. A social-driven propagation dynamics model was proposed therein to improve the popularity prediction accuracy. However, as the hidden features can only be extracted from massive amounts of social information accumulated over a long-term time, the timeliness and privacy concerns of the social-driven prediction methods are questioned. Statistical prediction methods based on regression analysis have also been examined. For instance, Trzcinśki et al. [23] used support vector regression based on Gaussian radial basis functions to predict the online video popularity. Similarly, a Bayesian hierarchical probabilistic model was designed [24] to regress the content popularity in an EC network. While the existing statistical approaches show potentials in achieving accurate and stable prediction, they are still far from practical use. For instance, the selection of probabilistic models in statistics-based methods [23, 24] has critical impacts on the prediction performance, but the selection criteria are unclear and impossible to be a priori given in the real world. Most importantly, they inevitably raise privacy issues due to the fact that statistics-based methods require access to the historical request log data of users for popularity prediction.

As a matter of fact, private data leakage vulnerabilities in IIoT systems, especially in the healthcare and automotive-related industries, can lead to catastrophic consequences such as endangering user safety and causing severe property loss for data providers [25]. The resultant privacy preservation constraint makes the dynamic popularity prediction in EC even trickier. Recently, the disruptive blockchain technique [26] shows superiority in enhancing data security and privacy preservation due to its anonymity, inherent decentralization, and trust properties. Nevertheless, the blockchain technique is essentially a distributed database of records and it has no interface for user behavior analysis [27]. We argue that the knotty problem of privacy-preserving popularity prediction can be tacked by leveraging the recent advances of distributed deep learning, particularly the federated learning (FL) [28]. FL has emerged as a distributed artificially intelligence (AI) approach, by coordinating multiple devices to perform AI training without sharing raw data for privacy enhancement [29].

FL incorporating deep neural networks (DNNs), which combines the capabilities of DNNs in extracting features from input data and the advantages of FL in distributed training and privacy preservation, and has become one of the main paradigms of FL [30]. Therein, convolutional neural networks (CNNs) and recurrent neural networks (RNNs) are two important types used for the incorporation with FL Literature [31] investigates the image classification problem and proposes a communication-efficient and privacy-preserving distributed machine learning framework based on the FL cooperating with CNNs. The superior classification accuracy shown in [31] demonstrates the strong ability of the FL cooperating with CNNs in image feature extraction while preserving privacy. However, the architecture of CNNs is not appropriate for the feature extraction of sequence data which is rather important to wireless communication systems. RNNs, as an efficient architecture of sequence data processing, cooperating with FL is viewed as a promising framework for privacy-preserving data processing in wireless communication systems. For instance, Liu et al. [32] provide a FL-based gated recurrent unit neural network for traffic flow prediction while providing reliable data privacy preservation. Although FL integrating with DNNs has been widely investigated, many existing works,[31, 32], adopt the supervised learning with costly manual labels which poses significant challenges to their practical applications, especially to practical popularity prediction. The spatiotemporal variability and unobservability of the content popularity lead to the difficulty in manually obtaining the popularity labels. Therefore, we extending FL to an unsupervised paradigm in this paper to address the challenges on the manual labelling of popularities. In this paper, we proposed an unsupervised FL incorporating RNNs to effectively predict popularities from sequences of historical requests without labels while preserving user privacy. Moreover, we further design a parameter aggregation to alleviate the non-i.i.d. problem which is an open challenge in the research field of FL [33].

The MEC framework enables FL in the wireless communication networks with the supply of abundant and closer computing/caching resources. A comprehensive survey of FL from the perspective of fundamentals, challenges, solutions, and applications in MEC networks can be found in [34]. Therein, FL-based privacy-preserving popularity prediction in MEC networks has been explored in many works, i.e.,[35, 36, 37, 38, 39]. Nevertheless, many challenges still remain to be addressed. In a recent work [35], the center server is prohibited from snooping on users’ private data, while only the local MEC server is permitted to collect and learn from the historical requests of users. This scheme relies on authorization management and is susceptible to unauthorized access provided by the unreliable network operator or gained by malicious cracking. In addition, the deep learning method in [35] requires manual labeling in advance, which unfortunately is costly and infeasible in real implementation. The authors in [36] proposed an FL-based method to realize the privacy-preserving EC. On the basis of literature [36], Cui et al. [37] utilized blockchain to further improve the security of FL implementation. However, the EC policies considered in [36, 37] are both built on the similarities between users and contents, which is calculated by potential features extracted from historical requests of users. The similarity calculated in these two literatures is just a rough estimation of popular contents rather than the actual popularity. Thus, the content popularity which represents the accurate requested probability of each content has not been predicted in [36, 37]. Moreover, the relationship between the client-side popularity and server-side popularity has not been explored in [36, 37]. In [38], the content popularity has been predicted while the popularity relationship between the client side and server side is preliminarily explored. Nonetheless, the explorations of the relationship between client-side and server-side popularities were sketchy and empirical in [38], which was reflected in the thoughtlessness of user request arrival rate as well as the absence of any verification for the given relationship. In this paper, we introduce the concept of local popularity at user side and global popularity at MEC server side respectively, and further derive and validate the mathematical relationship between these two popularity types.

Yu et al. [39] considered the mobility of users and proposed a mobility-aware FL method to predict the popularity while preserving user privacy. Nevertheless, the temporal variability of the popularity caused by the time-varying user interests has not been explored in [39]. Furthermore, in [39], sampling from the real popularity distribution at the MEC server side is required to generate the input of the prediction model during the local training phase. However, the real popularity distribution at the MEC server side depends on the subjective interests of users within the entire service area and thus is extremly hard to obtain a priori. In our study, we consider the local and global popularities both time-varying and unavailable so as to be more closely aligned with reality. In addition, we can further observe from [36, 37, 38, 39] that local users are supposed to share or upload their request history when making online predictions, so as to generate the input of the prediction model. Indeed, this kind of sharing or upload violates the privacy-preserving requirement. The fundamental reason why these works need to collect users’ request history for the global prediction can be attributed to the consistency requirement in the typical FL framework, which demands that the model structures and model inputs should be exactly the same between the local and global sides [33]. To mitigate the risk of privacy leakage caused by the collection of user request history, we design the input structure of the local and global models to break the consistency requirement on model inputs, and then realize the distributed training and prediction without any external access to user’s historical requests except itself.

We assume that the content library contains $N$ files, which is denoted as a set ${{\cal F}}=\{{{F}_{1}},{{F}_{2}},\ldots,{{F}_{N}}\}$, and the cloud have a complete copy of all the files. Limited by the cache capacity, the MEC server can only cache ${M_{0}}$ files and an arbitrary UE-$i$ can cache ${M_{i}}$ files. Generally, ${M_{0}}\gg{M_{i}},\forall i\in{\cal I}=\{1,2,\ldots,I\}$. We assume that a content file ${F^{i}}(t)\in\emptyset\cup{{\cal F}}$ is requested by UE-$i$ at time slot $t$, where we have ${F^{i}}(t)\in\emptyset$ when UE-$i$ does not request any contents. Then, the request will be uploaded to the MEC server if ${F^{i}}(t)$ cannot be found in UE-$i$, which is represented as $F^{i}\left(t\right)\notin\mathcal{C}_{i}(t)$, where $\mathcal{C}_{i}(t)$ is the files set cached in UE-$i$ at time slot $t$. Conversely, if ${F^{i}}(t)\in\emptyset$ or $F^{i}\left(t\right)\in\mathcal{C}_{i}(t)$ is true, UE-$i$ will not upload this request information to the MEC server. MEC server will retrieve content for the received requests in its current cache $\mathcal{C}_{0}(t)$. If $F^{i}\left(t\right)\notin\mathcal{C}_{0}(t)$ is satisfied, the MEC server will further request the absent files from the cloud. Finally, the requested files of each user will be sent back from the MEC server. In addition, it is worth to note that the users will not upload any request information in time slot $t$ unless $F^{i}\left(t\right)\notin\mathcal{C}_{i}(t)$.

As mentioned above, the content popularities on the local user side and the MEC server side are respectively termed local popularity and global popularity. Regarding the local popularity, we assume that the content popularity of each user in each time slot $t$ follows a Zipf distribution which has been wildly adopted in related works [44, 45, 46]. Moreover, the time-varying nature of the popularity is taken into account in this paper. For an arbitrary UE-$i$, the probability of demanding the $n$-th file at time slot $t$ is

where the $N$ files have been assigned with a descending ordering of popularity in each time slot $t$. The distribution parameter ${\alpha^{i}}(t)$ evolves over time. As such, the content popularity of UE-$i$ at $t$ can be denoted as ${\bf P}^{i}\left(\alpha^{i}\left(t\right),t\right)=\left\{P_{n}^{i}\left(\alpha^{i}\left(t\right),t\right)\right\}_{n=1}^{N}$. It should be noticed that the Zipf distribution is assumed for the convenience of discussion, and generalization to any other probability distribution model is straightforward.

As depicted in Fig. 2, for user $\forall i\in{\cal I}$, we model the dynamics of ${\alpha^{i}}(t)$ using a model-free Markov chain with the states $\left|{{{\cal G}_{i}}}\right|$ recorded in the set ${{\cal G}_{i}}=\{\alpha_{g}^{i}|g=1,2,\ldots,{G_{i}}\}$. Consequently, the dynamics of ${\alpha^{i}}(t)$ can be defined as

where $P_{\alpha^{i}\left(t\right)\rightarrow\alpha_{g}^{i}}^{\alpha^{i}\left(t\right)}$ denotes the transition probability of $\alpha^{i}\left(t\right)$ transits to $\forall\alpha_{g}^{i}\in\mathcal{G}_{i}$. It is worth mentioning that, neither the parameter sets nor the transition probabilities are unknown to the model-free Markov chain due to the diversity and complexity of users’ subjective interests [16]. The difference among the users are captured by the set ${{\cal G}_{i}}$ as well as the potential state transition probabilities. Besides, user behaviors are assumed to be non-i.i.d. in the system model.

At the MEC server side, the global popularity at time slot $t$ can be represented as ${{\bf{P}}^{\rm{G}}}(t)=\left\{P_{n}^{\rm{G}}(t)\right\}_{n=1}^{N}$, where $P_{n}^{\rm{G}}(t)$ is the probability that content $n$ is requested within the service area. Apparently, the global popularity depends on all the local popularities within the service area, and the MEC server as a service provider can significantly improve its caching efficiency under the guidance of accurate knowledge of the global popularity. However, as will be elaborated in Section IV, the prediction of the global popularity is much more complicated than that of the local popularity due to the different behavior patterns of different users as well as the privacy-preserving constraint.

At time slot $t$, a certain UE-$i$ requests a file $F^{i}(t)\in\emptyset\cup\mathcal{F}$, where the probability of $F^{i}(t)\in\emptyset$ follows its corresponding current request arrival rate, denoted as $\lambda_{i}\left(t\right)$. If $F^{i}(t)\in\mathcal{F}$, UE-$i$ make a request, which satisfies the present probability distribution denoted as $F^{i}\left(t\right)\sim{\rm{Zipf}}\left(\alpha^{i}\left(t\right)\right)$. According to the above description, the content request model of an arbitrary UE-$i\in\mathcal{I}$ at time slot $t$ can be expressed as

where $F_{n}\in\mathcal{F}$ and $\alpha^{i}\left(t\right)\in\mathcal{G}_{i}$. Similar to ${\alpha^{i}}\left(t\right)$, parameter $\lambda_{i}\left(t\right)$ also reflects the individual characteristics of user $i$ and should be protected from being accessed by others.

In the real world, privacy-sensitive users usually concern about the leakage of their private data such as location information, historical contents/services request, personal bank or social account information. In this paper, we readily observed from the service process that the private information of users involved in the problem under investigation is mainly the historical contents request data, and the historical request database of each user $\mathcal{D}^{i}=\left\{\left.F^{i}\left(t\right)\right|t=1,2,\cdots\right\}$ is stored only in their own UEs and is inaccessible to outsiders. Moreover, as stated in some data privacy legislations such as the European Commission’s General Data Protection Regulation (GDPR) [47], users have the right to require the responsible party to delete the individual data records about them. Thus, to respond with the implementation of GDPR, the burn-after-read principle as the privacy-preserving mechanism is implemented in the MEC servers, i.e., the request information from users must be immediately deleted from the memory of the MEC server once the contents have been scheduled. The MEC servers are not allowed to hold any historical information of any users.

In the MEC-based IIoT system under investigation, both the user and the server sides participate in the popularity prediction process. Given a popularity ${{\bf{P}}^{i}}({\alpha^{i}}(t),t)$ at time slot $t$, UE-$i$ generate a content request denoted as ${{F}^{i}}(t){|_{{{\bf{P}}^{i}}({\alpha^{i}}(t),t)}}$, which is simplified as ${{F}^{i}}(t)$ in the sequel for the convenience of discussion. Based on the request history saved in its local memory, the local popularity of user $i$ can be predicted by

where ${f^{{\Theta^{i}}}}(\cdot)$ is a predictive model inside UE-$i$ and ${\Theta^{i}}$ denotes the collection of trainable parameters therein. ${\bf R}^{i}(t)=\left[F^{i}(t-H),F^{i}(t-H+1),\cdots,F^{i}(t)\right]$ is a extractor of UE-$i$ to extract its historical request information of continuous $H$ times before time $t$. $H$ is the observation window length of the extractor. On account of the structural features of AE, we can divide ${\Theta^{i}}$ into encoder and decoder parameters sets, denoted as ${\Theta^{i}}=\left\{\Theta_{\rm{E}}^{i},\Theta_{\rm{D}}^{i}\right\}$. The implementation of ${f^{{\Theta^{i}}}}(\cdot)$ will be detailed in Section IV-B.

At time $t$, to minimize the distributed popularity prediction errors of all the users at future time $t+1$, the mean-square error (MSE) metric is adopted and the underlying optimization problem of arbitrary UE-$i$ can be formulated as

where ${\bf P}^{i}(\alpha^{i}(t+1),t+1)$ and ${\bf\hat{P}}^{i}(\alpha^{i}(t+1),t+1)$ are abbreviated as ${\bf P}^{i}(t+1)$ and ${\bf\hat{P}}^{i}(t+1)$, respectively. $\left\|\cdot\right\|$ and $\left\|\cdot\right\|_{2}$ respectively represent the $l_{0}$ and $l_{2}$ norm. Constraint (5b) ensures the observation window length of the extractor $\mathbf{R}^{i}\left(t\right)$ at time $t$ not exceed $H$. $\alpha^{i}(t-h)$ and $\lambda_{i}\left(t-h\right)$ depend on the subject interests of user $i$ at time $t-h$. $F^{i}(t-h)$ is the component of $\mathbf{R}^{i}$ and extracted from the request database $\mathbf{\mathcal{D}}^{i}$. Note that ${\bf P}^{i}(\alpha^{i}(t+1),t+1)$, $\mathcal{G}_{i}$, $\alpha^{i}(t-h)$ and $\lambda_{i}\left(t-h\right)$ are all time-varying and unknown, which poses significant challenges to solve the problem (5).

The MEC server makes the global prediction in a completely different way since there is no historical information of any users under the privacy-preserving constraint. The only data that the MEC server can provisionally acquire is ${\bf{R}}^{\rm{G}}(t)=\left\{{{F}^{i}}(t)\right\}_{i=1}^{I}$ at time slot $t$, which will be erased from the server before the next time slot. To further evaluate the difficulty in predicting the global popularity in such cases, we first give the following theorem which reveals the mathematical relationship between the local and global popularities.

The simulation validation of Theorem 1 can be found in Appendix B. According to Theorem 1, we find that ${{\bf{P}}^{\rm{G}}}(t+1)$ cannot be obtained without any a priori knowledge of $\left\{{{{\bf{P}}^{i}}({\alpha^{i}}(t),t)}\right\}_{i=1}^{N}$ and $\left\{{{\lambda_{i}}(t)}\right\}_{i=1}^{I}$. Nonetheless, the local popularity and the request-arrival rate of each user both dynamically varies over time and also cannot be acquired in the privacy-preserving system. To address this challenge, a URFL algorithm is proposed in this work to predict the global popularity without violating UEs’ data privacy. By employing the URFL algorithm, the global popularity in the next time slot $t+1$ is predicted by exploiting the newly arrived request at time slot $t$, i.e.,

where $f^{{\Theta^{\rm{G}}}}(\cdot)$ represents the predictive function at the MEC server side in the proposed global model, and ${{\Theta^{\rm{G}}}}$ is the parameters set. The implementation of $f^{{\Theta^{\rm{G}}}}(\cdot)$ and ${{\Theta^{\rm{G}}}}$ under the privacy-preserving mechanism will be detailed in Section IV-B.

At the MEC server side, the underlying optimization problem at time $t$ can be formulated as

Similar with the problem $\eqref{P_i}$, the problem (8) also evolves over time and the optimal solution $\Theta^{\textrm{G}*}$ should be valid at any time $t$. However, ${\bf P}^{\textrm{G}}(t+1)$ is unknown while $\alpha^{i}(t),\lambda_{i}\left(t\right),\mathcal{G}_{i},\mathbf{\mathcal{D}}^{i},\forall i\in\mathcal{I}$ are unavailable to the MEC server due to the subjectively of user interests as well as the privacy-preserving requirements. Thus, it is also quite challenging to solve problem (8).

This subsection presents the design of the URFL framework and its application to the privacy-preserving edge popularity prediction. The proposed architecture of URFL is illustrated in Fig. 3. Concretely, in individual UE, a moderate-scale recurrent neural network (RNN) is prepared and trained on the local request history alone. The RNN in each UE is designed as an AE, with each neuron being an LSTM cell to capture the contextual information hidden in the input data [48, 49]. Since the MSE loss of an AE is directly obtained by comparing the input and output, the troublesome training data labeling is circumvented. Then, the collaborative prediction is performed under an FL framework, where the distributed UEs periodically exchange their diverse model parameters, rather than the raw private data, with the MEC server to collectively train a global model. Note that the MEC server only needs to deploy an encoder module. We next elaborate on each key element in the designed framework.

In the numerical simulations, we compare the prediction performance of the proposed URFL method with the baseline methods. All the reference methods are simulated in a $10$-user case. In addition, $2752$ epochs are run for all the learning methods.

The prediction error measured by RMSE [35] of the proposed algorithm in predicting the local popularity is shown in Fig. 6, where the prediction loss of each local model is sampled after every $T=32$ self-training iterations. It can be observed from Fig. 6(a) and (b) that, for each user, the prediction accuracy of the local popularity and the AE loss can both stably converge to a satisfactory level with the proposed approach. In particular, we identify many regular jitters on the RMSE curves as the learning epoch increases in Fig. 6(a). The reason is that all the local AEs are forced to aggregate their parameters based on FL after every $T$ rounds of self-training. As such, the RMSE loss of each local model instantaneously increases after the parametric aggregation of multiple UEs, and it then gradually decays to a lower level within the next $T$ self-training iterations. We also readily observe from Figs. 6(a) and (b) that, there are slight differences in the convergence losses of local popularity prediction for different users, which is reasonable since all the users are non-i.i.d. and both the set ${{\cal G}_{i}}$ and the probability $\mathbf{P}_{i}$ of each UE-$i$ are randomly generated. For the complicated ${{\cal G}_{i}}$ and $\mathbf{P}_{i}$, the challenge of prediction is tougher. In fact, this difference in prediction accuracy also indicates a non-i.i.d. open problem in FL [33], which will be an important research focus in our future works.

We further take UserID 7 as an instance and examine the performance comparison of the proposed algorithm with the self-training method, which is commonly adopted in deep learning related works. In such a method, the agents train their own local models individually without any interactions with others. As shown in Fig. 7, the proposed algorithm outperforms the self-training method from an individual user perspective in terms of AE loss and prediction loss. This result suggests that proper interactions with other participants can improve the prediction accuracy, which is congenial with common sense.

We take a step forward and study the prediction performance from the perspective of global popularity. Fig. 8 implies that the proposed method is superior to all the other baseline methods in terms of the prediction accuracy. In the $10$-UE case, the proposed method yields an RMSE of around $68.7\%$ lower than those of SVD, SDAEFL, and DDAEFL, and $60.5\%$ lower than that of DRAEL. The remarkable gain suggests that the proposed method can significantly improve the prediction accuracy while grantee the data privacy of users since it only aggregates the model parameters of each user rather than the private raw data. We argue that the aggregation process of the global prediction model pushes the MEC server to deeply and accurately learn the underlying features from all the UEs towards its coverage. In contrast, the baseline methods not only need to be supplied by large amounts of private data but also are incompetent to exact features from a mass of historical requests kneaded together in time and space. In addition, we observe from Fig. 8 that the performance of SDAEFL is inferior to SVD and DDAEFL, which implies that the single dense neural network cannot effectively predict popularity. Furthermore, the $19.5\%$ gain of the DRAEL to the DDAEFL and the $60.5\%$ gain of the proposal to the DRAEL confirm that the recurrent mode realized by LSTM and the parameters aggregation realized by FL can both contribute to the reduction of prediction error considerably. We also infer from the comparison between the proposed algorithm and DRAEL in Fig. 8 that, the prediction variance can be significantly reduced using the proposal. It is interesting to note, increasing the number of UEs does not continuously improve the prediction accuracy of the proposed algorithm. As can be seen from Fig. 8, the best RMSE performance is achieved when the number of UEs $I=6$ rather than $I=10$ or $I=3$. This is because aggregation of insufficient local models can be unrepresentative of the global characteristics, while an overly large sample size will result in information redundancy.

The performance comparisons between the proposed method and all the baseline algorithms versus the number of total content files $N$ are presented in Fig. 9. It can be seen from Fig. 9 that the proposed URFL algorithm significantly outperforms all the baselines regardless of the value of $N$. The statistics of communication cost represented by the data traffic in the MEC network are listed in Table III, where $I=10,N=24,T=32$. Though we can observe from Table III that the proposed URFL algorithm generates more data traffic for its offline training than the other baseline methods, the offline training phase is often implemented when the UE is idle, i.e., dormant status, charging status, etc. Therefore, it is acceptable for the proposed method to reduce the error of popularity prediction and preserve the privacy of users by sacrificing the tolerable increase of data traffic in the idle status of the MEC network. Moreover, under the assumption that $\forall i\in\mathcal{I},C_{i}\left(t\right)=\emptyset,\lambda_{i}\left(t\right)=1$, the theoretical data traffic of all the considered methods per time slot are equal, but the proposed method can achieve the lowest prediction error. When the assumption is invalid in the real environment, the data traffic of the centralized methods still remains $40\;\rm{B}$. By contrast, the data traffic of the distributed methods will be less than $40\;\rm{B}$, which actually depends on the $\lambda_{i}\left(t\right)$, prediction errors of local/global popularities, and the cache hit rates of each cache entities.

In Fig. 10, we provide the performance evaluations of the proposed URFL algorithm on different number of samples. We can observe from Fig. 10(a) and (b) that the proposed method can achieve superior performance in both local and global popularity predictions when the sample size is more sufficient. The reason is that the prediction model generally extracts more complete features from a dataset with sufficient samples, thus achieves the lower prediction error. With the sample size increasing to a certain extent, the further performance gains will not be produced due to the feature saturation. Moreover, we also evaluate the performance of the proposed URFL algorithm on different $T$, as shown in Fig. 11. Fig. 11(a) and (b) imply that the prediction error of the local popularity decreases with increasing $T$. This is because the local prediction errors are valued under the same communication rounds. As such, the local prediction model will be trained with more epochs as $T$ increases, and thus converges to a better performance level. Straightforward, if we want to achieve the the same local prediction performance under different $T$, we should continue increasing the number of communication rounds in the case of small $T$, but which also means higher communication costs. Fig. 11 (c) illustrates that the prediction error of the global popularity will first decrease and then increase as $T$ increases. This performance trend is due to the fact that large local-training epochs pre round will bring a large bias between each local model, while few $T$ will lead to an under-optimization of each local model on their local dataset pre round.

In Fig. 13, we provide the performance evaluation of the proposed FedLWA parameter aggregation scheme. It can be observered from Fig.13(a) that, for each user, the training loss of the LSTM-AE model can converge to a lower level with the proposed FedLWA-based URFL algorithm, which demonstrates that the FedLWA parameter aggregation scheme can bring additional performance gains to the training. The reason is that the proposed FedLWA scheme can adaptively weigh the contribution of each local parameter to the global parameter on the basis of the convergence of local models at the end of each communication round, so as to obtain better aggregated parameters. Consequently, as shown in Fig. 13(b), the FedLWA-based URFL approach is superior to the URFL approach in terms of the prediction errors at both local user and MEC server sides. Hence, the non-i.i.d. problems in the investigated scenario could be alleviated by applying the proposed FedLWA parameter aggregation scheme.

The performance comparisons between the proposed methods and the baseline methods on large groups of users, i.e. $I=\left\{100,200,\cdots,700\right\}$, are presented in Fig. 12. Note that random sampling aggregation is a common approach to FL for large-scale client scenarios [54]. Herein, we randomly select $6$ local clients for each parameter aggregation in the training phase. It can be observed from Fig. 12 that, in large-scale user scenarios, the proposed URFL algorithm still outperform the baselines regardless of the value of $I$. Moreover, Fig. 12 showcases the superiority of the proposed FedLWA-based URFL algorithm, which demonstrates that the proposed FedLWA parameter aggregation scheme is also applicable to large-scale user scenarios and can bring additional performance gains regardless of the number of users.

In closing, we test the online prediction performance of the proposed URFL algorithm in the local UEs and the MEC server in $20$ consecutive time slots. In the simulations, each UE and the MEC server are deployed with their own prediction models which have entered the convergent state using the proposed URFL algorithm. During the service delivery, the trained prediction models predict the future local and global popularities in real-time to assist the equipments to effectively update caches. In each time slot for arbitrary $i$, we compute the respective absolute errors between the predicted local popularity and the true local popularity of the request probability associated with each content file, denoted as $\mathbf{e}_{i}\left(t\right)=\left\{\left|\hat{P}_{n}^{i}\left(\alpha^{i}\left(t\right),t\right)-P_{n}^{i}\left(\alpha^{i}\left(t\right),t\right)\right|\right\}_{n=1}^{N}$. The real-time prediction errors of each UE are visualized in Figs. 14(a) to (e). Likewise, we evaluate the real-time prediction errors of the global popularity by $\mathbf{e}_{\textrm{G}}\left(t\right)=\left\{\left|\hat{P}_{n}^{i}\left(\alpha^{i}\left(t\right),t\right)-P_{n}^{i}\left(\alpha^{i}\left(t\right),t\right)\right|\right\}_{n=1}^{N}$ and show the result in Fig. 14(f). We readily observe from Fig. 14 that, for both local and global popularities, the real-time prediction error for each content file is largely lower than $0.1$ and, in most of the cases, it is under $0.05$. This result shows that the convergent URFL algorithm can significantly reduce the prediction error of the local/global popularities during the online service, and this reconfirms the effectiveness of the proposed algorithm.