PPVF: An Efficient Privacy-Preserving Online Video Fetching Framework with Correlated Differential Privacy

There are three types of entities in the system, which are briefly introduced as follows:

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  Content Provider (CP): The CP is an online video service provider possessing a comprehensive set of I videos denoted by $\mathcal{I}=\{i_{1},i_{2},\cdots,i_{\text{I}}\}$. However, the CP also collects users’ request traces to enhance its services, e.g., recommendation [23, 13] and advertisement [12, 14], which is regarded as the main risk entity in our privacy model.

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  Trusted Edge Devices (EDs): In PPVF, we denote $\mathcal{E}=\{e_{1},e_{2},\cdots,e_{\text{E}}\}$ as the set of all EDs which can be trusted by users [24, 10, 11]. Each ED $e\in\mathcal{E}$ has a storage limitation $c_{e}$ in our system model. EDs play two critical roles: i) caching videos fetched from the CP to serve users’ requests with a higher quality of service (QoS), and ii) preserving video request privacy to conceal users’ real preferences¹¹1Our main focus is to design a privacy framework for trusted edge devices, which may deploy Trusted Execution Environments (TEE), such as Intel SGX, TrustZone for Cortex-M, to convince users and execute instructions reliably. .

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  Users: Users are final consumers of videos. Rather than directly exposing video requests to the CP, users in PPVF only submit their requests to corresponding trusted EDs, which act as agents to fetch videos from the CP for users.

In traditional online video systems, privacy threats related to video fetching primarily arise from the exposure of users’ video-request patterns and preferences. As users interact with the CP to access the online video services, their historical video requests and pre-fetching activities will be inadvertently exposed to the CP, which can accordingly infer sensitive information, such as age [12], gender [9], locations [2, 6], and favorites [13, 14], of users. Such threats are driven by the goal of enhancing services through caching or recommendation algorithms. CPs can exploit inferred sensitive information to gain insights into individual user preferences. Therefore, unauthorized access to user-specific information without protection poses a significant privacy threat, enabling CPs to infer personal preferences, potentially compromising users’ privacy.

Let us first consider the global video caching problem without considering privacy leakage. When requesting videos missed by the edge cache from the CP, ED $e$ also makes requests for redundant videos based on pre-fetching decisions $\bm{x}_{e}\ =[x^{k}_{e,i}]^{\text{K}_{e}\times\text{I}}$. Let $\bm{\lambda}_{e}\ =[\lambda^{k}_{e,i}]^{\text{K}_{e}\times\text{I}}$ denote all video utility values, e.g., the predicted rate to request videos by users, for any ED $e$. The problem of maximizing pre-fetching and caching utility can be formulated by:

where $h_{e}:\mathcal{I}\times\mathbb{R}^{+}\rightarrow\mathbb{R}^{+}$ can represent any prediction function for utility with model parameters $\bm{\theta}$ and historical viewing records $\mathcal{V}_{e}^{k}$ up to time $t^{k}$ at ED $e$. Besides, Eq. (1b) restricts the maximum pre-fetching capacity $f_{e}$ of ED $e$.

For traditional video streaming, the CP can collect historical video request records to infer $\bm{\lambda}_{e},\,\forall e$, which can be further used to derive optimal solution $\bm{x}_{e}^{*}$, for all EDs. In this process, the CP can exactly infer preferences exposed by EDs. To prevent privacy leakage, EDs can apply differential privacy (DP) noises to distort pre-fetching decisions $\bm{x}_{e}$, to hide both users’ original video requests and video utility. It is difficult for the CP to infer user privacy from public fetching actions, and hence user privacy is preserved. In the rest of the subsection, we extend $\mathbb{P}_{g}$ to present the privacy-preserving video pre-fetching problem.

We begin by succinctly introducing DP, avoiding any unnecessary notation. In problem $\mathbb{P}_{g}$, the pre-fetching decision variables $\bm{x}$ are primarily determined by the utility $\bm{\lambda}$, which is evaluated by the function $h$ with the parameter $\bm{\theta}$, and the set $\mathcal{V}$ of real request records. To preserve privacy, DP can be applied to distort the output of utility function $h$ to protect privacy in dataset $\mathcal{V}$.

However, in practical online video systems, cardinality I for $\mathcal{I}$ is a huge number, and users’ view preferences can be very skewed, implying that there exists a large number of cold videos with very few user requests [25, 4]. Thereby, directly applying DP noise to distort utilities for video pre-fetching confronts the following two challenges:

1. (1)

   More privacy budget will be consumed to protect privacy if there are more videos in $\mathcal{I}$. If cardinality I is a large number, the noises will be excessively large such that the video utility predicted by the function $h$ is valueless.

2. (2)

   Considering that the CP can implement collaborative filtering algorithms to infer user privacy, requesting cold videos (with scarce requests) as noises is not effective in preserving privacy since collaborative filtering algorithms can easily remove the noisy influence of cold video requests [26].

To tackle these two challenges, we consider adding DP noises to protect pre-fetching privacy by the Exponential Mechanism (EM) [27] with a candidate video set selected in an online manner. We start with a brief introduction to the EM. The EM is a classical DP mechanism satisfying $\epsilon$-DP, which can be applied to distort the output of utility function $h$, defined as follows.

Instead of applying the whole video set $\mathcal{I}$, we identify a candidate video set $\mathcal{A}_{e}^{k}\subseteq\mathcal{I}$ for ED $e$ to generate redundant requests ED $e$. Here, $k$ is the pre-fetching index for the request missed by the edge cache. The whole candidate video set $\mathcal{A}_{e}=\{\mathcal{A}_{e}^{k}\ |\ 1\leq k\leq\text{K}_{e}\}$ is obtained by solving the problem $\mathbb{P}_{e}$ subjecting to both the privacy budget and pre-fetching capacity constraint. In the problem $\mathbb{P}_{e}$, the constraint (3b) ensures that the assigned privacy budget cannot exceed the total privacy budget $\xi_{e}$ for each video, and $f_{e}$ denotes the pre-fetching capability at ED $e$.

Based on problem $\mathbb{P}_{e}$, we can illustrate the holistic optimization process of PPVF:

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  Federated Learning: EDs can jointly evaluate video utility, i.e., $\lambda_{e,i}^{k}=h_{e}(i,t^{k}\ |\ \mathcal{V}_{e}^{k},\bm{\theta})$, $\forall\,e,\,i,\,k$, via the federated learning framework. This approach allows EDs to achieve significantly more accurate video utility than those obtained solely from local traces.

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  Video Selection and Budget Allocation: With evaluated $\bm{\lambda}_{e}^{k}$, EDs can solve $\mathbb{P}_{e}$ in an online manner to obtain $\mathcal{A}_{e}^{k}$, which is the candidate set of videos to be requested from the remote CP.

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  Pre-fetching Request Generation: With $\mathcal{A}_{e}^{k}$ derived from $\mathbb{P}_{e}$ and privacy budget allocation decisions, EDs can apply the EM to distort their fetching requests with correlated differential privacy (CDP). Then, EDs contact the CP to fetch both viewing videos and redundant videos.

To better understand how users, EDs and the CP interact with each other, we present the workflow of PPVF, as shown in Fig. 1. Briefly speaking, the life cycle of each request involves five steps. ① Upon receiving a video viewing request from a user, EDs first search for that video in their edge cache. If the video is cached, EDs directly stream it to users with a shorter response latency without any privacy leakage. Otherwise, EDs assemble pre-fetching video requests, along with the viewing video, to fetch redundant videos from the CP. ② The utility predictor evaluates the videos’ utility based on the federated learning framework, which ensures that only model parameters $\bm{\theta}$ are exchanged between EDs and the CP. The process is detailed in Section IV. ③ Subsequently, the budget scheduler assesses video utility in conjunction with the privacy budget to curate a video candidate set for the subsequent pre-fetching decision, elaborated in Section III-B. ④ The request generator distorts the original utility to generate a pre-fetching decision, which navigates the trade-off between privacy and caching performance by leveraging the EM with the CDP method. After combining the pre-fetching decision with the real view video, the final fetching vector is sent to the CP. This process will be discussed in Section III-C. ⑤ When the CP returns videos, EDs perform cache replacement based on video utility and forward the viewing video to users.

Note that our main contribution is represented by three modules in green color (long dashed box) in Fig. 1, which will be introduced in the following sections in detail.

Directly solving problem $\mathbb{P}_{e}$ confronts two challenges: (1) the problem is inherently online due to the dynamic nature of request patterns and video utility, and (2) the problem $\mathbb{P}_{e}$ can be categorized as an online multiple knapsack problem, which is challenging to solve immediately and irrevocably, even if the utility $\bm{\lambda}^{k}_{e}$ is known.

To solve the challenging online problem $\mathbb{P}_{e}$, we propose a filtering mechanism [28, 29] that selects a video into $\mathcal{A}_{e}^{k}$ if the ratio of this video utility over its excepted privacy budget exceeds a threshold. Intuitively speaking, a video of a higher utility will be played by users in the future with a higher probability. Hence, the utility of EDs in caching such videos will be higher. Meanwhile, considering the limited privacy budget, PPVF only selects videos with the ratio $\lambda_{e,i}^{k}/\epsilon_{e,i}$ exceeding a threshold. This threshold is set in accordance with the fraction of the consumed privacy budget.

We can set the threshold for selecting videos as follows. Let $U_{e}$ and $L_{e}$ denote the upper and lower bound of the ratio for any video $i$ at ED $e$, which means that $L_{e}<\lambda_{e,i}^{k}/\epsilon_{e,i}<U_{e},\ \forall i\in\mathcal{I},1\leq k\leq\text{K}_{e}$. With the values of $L_{e}$ and $U_{e}$, the threshold function is defined as:

Here, $\gamma\in[0,1]$ denotes the fraction of the privacy budget that has been allocated to a video until the current time, $\Gamma_{e}=\frac{1}{1+ln(U_{e}/L_{e})}$ is the lowest threshold for assessing the privacy budget proportion $\gamma$. The intuition of our design is that the selection of a video is more conservative if the consumed privacy budget fraction $\gamma$ of that video is larger.

The detailed algorithm is presented in Alg. 1. Specifically, using the threshold function $\Theta_{e}(\cdot)$, PPVF randomly selects a video from the set $\mathcal{I}$ and checks whether its $\lambda_{e,i}^{k}/\epsilon_{e,i}$ is exceeds the threshold $\Theta_{e}(\gamma_{e,i}^{k})$. If so, the video is incorporated into candidate set $\mathcal{A}_{e}^{k}$; if not, the video remains unchosen. This stochastic selection process continues until $\mathcal{A}_{e}^{k}$ contains $f_{e}$ videos. Although Alg. 1 is a heuristic-based algorithm, we can theoretically prove that Alg. 1 can achieve an optimal competitive ratio (CR) of $\left(1+\ln(U_{e}/L_{e})\right)$ for any ED $e$.

Considering $U_{e}=\max_{\forall i,k}\lambda_{e,i}^{k}/\epsilon_{e,i}$ and $L_{e}=\min_{\forall i,k}\lambda_{e,i}^{k}/\epsilon_{e,i}$, we observe that CR is solely dependent on $\bm{\lambda}$ and $\bm{\epsilon}$ and is independent of the request quantity (i.e., $K_{e}$). As the privacy budgets $\bm{\epsilon}$ are specified by EDs for each video, while utility $\bm{\lambda}$ is often generated by upstream utility prediction algorithms, they are both within a specific range. This characteristic ensures a constant-level CR of our algorithm, independent of the total request quantity (i.e., $K_{e}$), which is a highly appealing property. Through differentiation of CR with respect to $U_{e}$ and $L_{e}$, it becomes evident that a decrease in $U_{e}$ leads to a reduction in CR, indicating an approach to the optimal offline solution in the worst-case scenario. Similarly, a larger $L_{e}$ results in a smaller value of CR. Moreover, when $U_{e}/L_{e}$ approaches 1, CR approaches 1, indicating that the performance is close to the offline optimal solution.

Directly requesting videos in $\mathcal{A}_{e}^{k}=\{i\ |\ a_{e,i}^{k}=1,\forall i\in\mathcal{I}\}$ according to video utility can expose the video utility knowledge to the CP. To preserve privacy, PPVF adopts the EM to randomly select videos based on probability shown in Eq. (5) and generate the final pre-fetching decision $\bm{x}_{e}^{k}$. Specifically, if video $i$ is selected by the EM, PPVF will set $x_{e,i}^{k}=1$ to pre-fetch that video from the CP. Otherwise, it will be set to $0$. The probability is given by

Here, $\epsilon_{e}^{k}=\frac{1}{f_{e}}\sum_{i\in\mathcal{A}^{k}_{e}}\epsilon_{e,i}$ is the averaged privacy for pre-fetching one redundant video, where $\sum_{i\in\mathcal{A}^{k}_{e}}\epsilon_{e,i}$ denotes the total privacy budget assigned by Alg. 1. Besides, $\Delta\lambda_{e,gc}^{k}$ is the global sensitivity at the time of the $k$-th pre-fetching.

In our problem, the calculation of $\Delta\lambda_{e,gc}^{k}$ is complicated because of the correlation between videos. Collaborative filtering algorithms can exploit such correlation information for inferring users’ personal interests. To factor in the influence of video correlation, we employ the correlated differential privacy (CDP) for computing sensitivity. For ED $e$, we can calculate the correlation between videos $i$ and $j$ for the $k$-th pre-fetching with $\lambda_{e,i(j)}^{k}$ predicted by utility function $h_{e}$. Suppose that EDs cache three history matrices $\bm{\psi}_{e}^{k-1}=[\psi_{e,i,j}^{k-1}]^{\text{I}\times\text{I}}$, $\bm{\alpha}_{e}^{k-1}=[\alpha_{e,i}^{k-1}]^{\text{I}}$, $\bm{\sigma}_{e}^{k-1}=[\sigma_{e,i}^{k-1}]^{\text{I}}$, where the items can be incrementally updated by $\psi_{e,i,j}^{k}=\psi_{e,i,j}^{k-1}+\lambda_{e,i}^{k}\cdot\lambda_{e,j}^{k},\ \alpha_{e,i}^{k}=\alpha_{e,i}^{k-1}+\lambda_{e,i}^{k},\ \sigma_{e,i}^{k}=\sigma_{e,i}^{k-1}+(\lambda_{e,i}^{k})^{2},$ respectively. Based on Pearson’s correlation [27], the correlation degree between videos $i$ and $j$ can be calculated with these three history matrices as follows:

Let $\bm{\Psi}_{e}^{k}=[\Psi_{e,i,j}^{k}]^{\text{I}\times\text{I}}$ denote the correlation matrix. The sensitivity of our problem can be calculated using the following two definitions.

Here, the L1 distance measures the effect on utility when deleting records related to video $j$ from $\mathcal{V}_{e}^{k}$. Parameter $\Psi_{e,i,j}^{k}$ estimates the correlated degree between videos $i$ and $j$. Correlated Video Sensitivity combines the effect of correlated records and the correlated degree together.

The correlated sensitivity lists all videos in candidate set $\mathcal{A}_{e}^{k}$ responding to utility and selects the maximal video sensitivity as the correlated sensitivity. When videos are independent or weakly correlated, the global sensitivity will only slightly increase. Particularly, if all videos are independent, the correlated video sensitivity is equal to the global sensitivity, i.e., $\max_{i\in\mathcal{A}^{k}_{e}}||h_{e}(i,t^{k}|\mathcal{V}^{k}_{e},\bm{\theta})-h_{e}(i,t^{k}|\mathcal{V}^{k}_{e,-i},\bm{\theta})||_{1}$. Additionally, given the historical matrices $\bm{\psi}_{e}^{k}$, $\bm{\alpha}_{e}^{k}$, and $\bm{\sigma}_{e}^{k}$, which can be incrementally updated prior to the $k$-th pre-fetching, the correlated degree $\Psi_{e,i,j}^{k}$ can be efficiently determined in $\text{O}(1)$, as per Eq. (6). Consequently, the computational complexity to obtain sensitivity $\Delta\lambda^{k}_{e,i}$ of video $i$ is $\text{O}(f_{e})$ with the evaluated utility vector $\bm{\lambda}^{k}_{e}$ by function $h_{e}$ and the correlation matrix $\bm{\Psi}_{e}^{k}$. Finally, the total computational complexity for deriving the correlated sensitivity $\Delta\lambda^{k}_{e,gc}$ is $\text{O}(f_{e}^{2})$ with the utility vector $\bm{\lambda}^{k}_{e}$ and the correlation matrix $\bm{\Psi}_{e}^{k}$.

The detailed algorithm to generate redundant pre-fetching video requests is presented in Alg. 2. It can be proved that Alg. 2 guarantees a $\sum_{i\in\mathcal{A}_{e}^{k}}\epsilon_{e,i}$-DP for the $k$-th pre-fetching decision at ED $e$, where $\sum_{i\in\mathcal{A}^{k}_{e}}\epsilon_{e,i}$ denotes the total privacy budget assigned by Alg. 1. The proof can be directly deduced by considering the properties of the EM and the Composition Theorem [30]. The EM facilitates the selection of one video from the candidate set for pre-fetching while ensuring $\epsilon_{e}^{k}$-DP compliance. Based on the Composition Theorem [30], Alg. 1 makes a maximum $f_{e}$ times of selections, adhering to $f_{e}\cdot\epsilon_{e}^{k}$-DP, which is equivalent to $\sum_{i\in\mathcal{A}^{k}_{e}}\epsilon_{e,i}$-DP.

The core of a point process lies in its intensity function, denoting the occurrence probability of an event within a tiny time window $[t,t+\rm{d}t)$ [34]. By abusing notations a little bit, an intensity function can be defined by $h(\iota,t)\text{d}t=P\{\Omega\,|\,\mathcal{V}(t)\}=\text{E}(\text{d}N(\iota,t)|\mathcal{V})$, where $N(\iota,t)$ is the count function and $\text{E}(\text{d}N(\iota,t)\,|\,\mathcal{V})$ represents the expected count of occurrences of event $\Omega$ with type $\iota$ in the time window $[t,t+\text{d}t)$ based on the historical event set $\mathcal{V}$ [34].

In PPVF, the historical event set $\mathcal{V}$ corresponds to the historical record set of viewing requests. We can create an intensity function for a particular video $i$ (i.e., event type $\iota$) indicating the expected request rate from users for that video, which is regarded as the utility of video $i$ for caching. Recall that the set $\mathcal{T}_{e,i}^{0,t^{k}}$ represents the timestamps corresponding to requests of video $i$ in local viewing records $\mathcal{V}_{e}^{k}$ at ED $e$ within the time interval $[0,t^{k})$. We can create the intensity function for video $i$ and time $t^{k}$ at ED $e$ as:

where $\bm{\omega}=[\omega_{i,j}]^{\text{I}\times\text{I}},\omega_{i,j}\in\mathbb{R}^{+}$ denotes the influencing parameter matrix among all videos, while $\bm{\beta}=[\beta_{i}]^{\text{I}},\beta_{i}\in\mathbb{R}^{+}$ is the bias parameter vector of the intensity functions. Specifically, $\phi(\cdot)$ is defined as $\phi(t)=\exp(-\delta\cdot t)$, where exponential decreasing kernel functions are adopted to gauge the influence of historical events for point process models [34, 32, 31]. Here, $\delta>0$ serves as a hyper-parameter of the influence attenuation coefficient.

To make our presentation concise, $h_{e}(i,t^{k})$ is used to represent $h_{e}(i,t^{k}\,|\,\mathcal{V}_{e}^{k},\bm{\beta},\bm{\omega})$ hereafter if the meaning is clear. The parameter space of $\omega_{i,j}$ in Eq. (9) is $\text{O}(\text{I}^{2})$ which is prohibitive for solving directly. The parameter space can be reduced by Singular Value Decomposition (SVD) [33]. Given that $\omega_{i,j}$ represents how much video $j$ influences video $i$, it can be decomposed as the product of $\omega_{i,j}=\bm{p}_{i}\cdot\bm{q}_{j}^{\intercal}$. Here, $\bm{p}_{i}$ and $\bm{q}_{j}$ are latent vectors with dimension $\text{D}\ll\text{I}$. Hence, we can significantly shrink the dimension space of $\bm{\omega}$ to avoid overfitting. Specifically, the parameter dimensions can be condensed from $\text{I}\times\text{I}$ to $2\times\text{I}\times\text{D}$, where $\text{D}\ll\text{I}$. Consequently, the utility $\lambda_{e,i}^{k},\forall e,i,k$ can be obtained by the revised form in Eq. (10).

Next, we can use the maximum likelihood estimation (MLE) [22] to optimize all parameters denoted by $\bm{\theta}\stackrel{{\scriptstyle\mathrm{def}}}{{=}}\{\bm{\beta},\bm{p},\bm{q}\}$ in Eq. (10). With local timestamp set $\mathcal{T}_{e,i}$ for video $i$ in time $[0,T)$ at ED $e$, the local log-likelihood function is derived as:

Here, $\mathcal{V}_{e}$ represents the whole private dataset at ED $e$ to generate the time timestamp $\mathcal{T}_{e,i}$ for any $i\in\mathcal{I}$. The detailed derivation can be found in Appendix B. To preserve privacy, each ED $e$ should locally maximize Eq. (11). However, the estimation accuracy will be inferior because request records owned by each ED can be very scarce. Moreover, given the dynamic nature of video popularity, parameter estimation cannot be solved by one-time training. Continuous online learning is necessary to closely track the changes in video request patterns. To address these challenges, we propose an FL-based online parameter estimation algorithm, and the CP can coordinate the training process by collecting, aggregating, and distributing model parameters.

Given the large scale of Tencent Video Datasets, we randomly sample a small subset of $10,000$ users drawn from the upper echelon of active users (i.e., the set of $20\%$ users with the largest interactive viewing records) in the origin public dataset [22]. The new dataset consists of $933,541$ video viewing requests for $10,373$ unique videos, all within a specific city over 30 days. Following [33], we evenly group these users into $25$ fixed groups to replicate a real online video system aided by $25$ EDs during the whole 30 days. It is important to note that this number set is simulation-based, and this setting can be tuned by the customized strategy that is adaptable to various scenarios and meets different user privacy requirements. The experimental results also demonstrate the robustness of our framework at different levels of EDs. As such, each request record in the dataset is collated by the metadata $(e,u,i,\tau)$.

Similar to [22], the time interval in our experiments is quantized at $1$ hour for all requests, i.e., the requests arrived at the same hour have the same timestamp $\tau$. It is important to emphasize that the pre-fetching video’s timing is not tied to a specific time slot. If a request is not met at the edge, EDs must promptly retrieve the video from CP using the pre-fetching algorithm. Additionally, we split the dataset into two date-based subsets. The initial subset, containing requests with time $0\leq\tau<240$ hours, is used to initialize the system. The subsequent subset with requests over the next $20$ days (i.e., $240\leq\tau<720$ hours) functions as the test period.

Other experimental setups are described according to different tasks: (1) Point process and FL: Following [33], the decay parameter and the dimension of the latent vector are designated as $\delta=0.01$ and $D=10$, respectively. In alignment with [22], all model parameters (i.e., $\bm{\beta}$, $\bm{p}$, and $\bm{q}$) are initialized at $1.0$. For online FL-based parameter estimation, the maximum iteration count is $20$ and the truncated threshold is set to $\phi_{th}=e^{-0.48}$. Therefore, the interval $t_{\theta}$ to update $\bm{\beta}$, $\bm{p}$, and $\bm{q}$ is $2$ days ($48$ hours), which is the same as that setting in [22]. Some detailed experiments are conducted to study the influence of the online updated interval of the FL framework. (2) Edge pre-fetching and caching: For experimental consistency, the privacy cost ($\epsilon_{e,i},\forall e,\,i$) is uniformly set to $1$ for each video’s pre-fetching requests [35]. Additionally, we standardize the allocation of the privacy budget, pre-fetching capacity, and caching capacity across all EDs with values set at $\xi_{e}=15$, $f_{e}=4$, and $c_{e}=1\%$, respectively. In specific experiments, one of these parameters might be varied to assess its impact, with the other two being constant.

We compare PPVF with three types of baselines. The first type includes privacy-preserving video fetching algorithms, while the second and third types are video caching algorithms that do not consider privacy leakage. Privacy-preserving caching algorithms include: (1) SAGE [36], which pre-fetches videos with randomly assigned privacy budgets until the privacy budgets reach the maximum constraints; (2) BESTFIT, which allocates the privacy budget to pre-fetch videos with the highest utility until the privacy budgets reach the maximum constraints. Note that these two baselines are only designed for privacy allocation without designing a video utility predictor. For a fair comparison, we implement our video utility predictor in SAGE and BESTFIT for caching.

To further demonstrate the superiority of our utility predictor, we replicate two advanced caching utility prediction methods at the edge for comparison. These algorithms are introduced as follows: (3) MAV [37], which caches the videos at the edge nodes considering the strength of user requests in the future round within the dynamic Stackberg game. The caching utility is calculated by the moving average value (MAV) method, and the weight of MAV is set as $0.9$ based on [37]; (4) HRS [22], which serves as a video popularity prediction model designed for the edge server, employing a fusion of three distinct point process models. All parameter configurations within this baseline align with the defaults specified in [22]. It is worth mentioning that these two baselines are mainly designed to improve edge caching efficiency with utility (e.g., popularity) prediction. Both of them overlook the privacy of users exposed by pre-fetching requests. Therefore, we only replace our utility predictor module with MAV and HRS and keep the other system components unchanged.

We also compare PPVF with the following two eviction caching algorithms, in which EDs only fetch videos watched by users when the cache is missed. These algorithms include: (5) LRU (Least Recently Used), which replaces the video that has not received any request for the longest time with a newly requested video; (6) LFU (Least Frequently Used), which replaces the video that has been requested in the least number of times with a newly requested video. These two conventional caching algorithms are extensively employed both in industry and academia, making them suitable benchmarks for comparing caching performance.

To evaluate PPVF, we employ three metrics to evaluate both privacy protection and system efficiency. More specifically, we adopt the following metrics in our experiments:

1. 1.

   JS (Jaccard Similarity) measures the averaged similarity between users’ real profiles and profiles exposed by their ED for video fetching. Each profile is represented by a vector of dimension I, where each element indicates whether a video has been requested by a user or ED during the entire testing period. A lower similarity is more desirable, implying stronger privacy protection.

2. 2.

   RHR (Recommendation Hit Rate) Degradation, which calculates the averaged degradation of RHR among all users when using a recommendation algorithm to recommend videos for users based on their original profiles and noisy profiles exposed by EDs. A larger degradation of RHR implies stronger privacy protection. A popular collaborative filtering recommendation algorithm [26], NCF, is implemented with the same settings in [26] as the adversary in our experiments.

3. 3.

   CHR (Cache Hit Ratio), which is defined as the number of video hits at all EDs divided by the total number of original video requests from users over the entire test period. CHR is employed to evaluate the caching system efficiency.

We first evaluate the performance of privacy protection using two metrics, i.e., the average JS and the degradation of RHR. We then further investigate the final status of the remaining privacy budget of all content.