A resource allocation and data selection method for high-performance federated edge learning

Abstract

The present application relates to a kind of resource allocation and data selection methods for high-performance federal edge learning, belong to machine learning and wireless communication technical field.The method includes: S1: construct the FEEL network that exists data sample label error and partial device is unavailable;S2: construct the FEEL algorithm suitable for FEEL network, under the constraint condition that available device successfully uploads local gradient is met, the optimization problem of joint communication resource allocation and data sample selection is established;S3: the original optimization problem is equivalently converted into optimization problem that can be solved in server side;S4: the problem after conversion is equivalently decomposed into resource allocation subproblem and data selection subproblem and is solved;S5: using low-complexity algorithm, obtains the joint resource allocation and data selection method in the FEEL scene that exists data label error and partial device is unavailable, while minimizing system training cost.

Description

Technical Field

[0001] This invention belongs to the field of machine learning and wireless communication technology, and relates to a resource allocation and data selection method for high-performance federated edge learning. Background Technology

[0002] Currently, a large number of connected devices inevitably generate massive amounts of data at the network edge. This data can be used to expand the applications of machine learning (ML), such as for consumer product design and promotion, and scientific research. Traditional ML algorithms require the raw data to be publicly disclosed to third-party entities for model training, which may compromise data privacy. To address this issue, a distributed machine learning framework called Federated Edge Learning (FEEL), located at the edge of a wireless network, has been proposed and has received widespread attention from academia and industry. During FEEL training, edge devices (also known as clients) need to send local training results, such as model parameters or local gradients, via wireless channels, instead of the raw data, thus protecting their data privacy while participating in training. Since the wireless resources available at the network edge (such as bandwidth and time) are limited, appropriate wireless resources need to be allocated to each device during model training. Furthermore, in practice, the data possessed by the devices may be mislabeled; for example, a handwritten digit "1" may be labeled as "0," and an image of a "t-shirt" may be labeled as "trouser." Training ML models with such mislabeled data will severely degrade the performance of FEEL; therefore, it is necessary to reasonably select appropriate data samples during model training.

[0003] Numerous studies have explored resource allocation in FEEL systems, including designing efficient joint device scheduling and wireless resource allocation schemes to minimize total energy consumption or accelerate model training convergence; and jointly optimizing computational and communication resource allocation to minimize the weighted sum of training time and energy costs. A key concern in FEEL system research is that excessive energy consumption can hinder device participation in model training, thereby reducing FEEL performance. Therefore, some studies have proposed incentivizing device participation by providing appropriate rewards to compensate for energy consumption. For example, rewards could be based on the number of CPU cycles or available training data samples contributed by all devices, with higher rewards for greater contributions.

[0004] None of the aforementioned studies considered the data selection design within the FEEL system, so the corresponding training algorithms may not be suitable for situations with mislabeled local data. However, existing research has demonstrated that the quality of client-side data samples directly impacts the performance of machine learning model training. Currently, very few studies combine FEEL and data sample selection, and existing research either ignores resource allocation issues, fails to analyze model training convergence, or does not consider the impact of device availability on model training. Therefore, there is an urgent need for a FEEL system training algorithm that can simultaneously consider device availability, data sample selection, and wireless resource allocation. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a resource allocation and data selection method for high-performance federated edge learning, solve the resource allocation and data selection problems of practical FEEL systems, and provide a design idea for the practice of FEEL systems.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A resource allocation and data selection method for high-performance federated edge learning includes the following steps:

[0008] S1: Construct a FEEL network with data sample labeling errors and some devices being unavailable, where FEEL stands for Federated Edge Learning;

[0009] S2: Construct the FEEL algorithm suitable for the FEEL network constructed in step S1. Under the constraints of successful local gradient upload by available devices, establish an optimization problem P1 that combines communication resource allocation and data sample selection.

[0010] S3: Transform the original optimization problem that cannot be solved on the server into an equivalent optimization problem P2 that can be solved on the server.

[0011] S4: The transformed problem P2 is equivalently decomposed into a resource allocation subproblem P3 and a data selection subproblem P4. The resource allocation subproblem P3 and the data selection subproblem P4 are solved respectively based on matching theory, convex and concave processes and gradient projection.

[0012] S5: Employs a low-complexity algorithm to obtain a joint resource allocation and data selection method for FEEL scenarios with data sample labeling errors and some devices being unavailable.

[0013] Furthermore, in step S1, the constructed FEEL network includes an edge server attached to the BS and K single-antenna edge devices, all of which are represented by a set. This indicates that for a set of edge devices... Any device k in the dataset has a local dataset. in, This represents the j-th d-dimensional data sample. Represents data sample x j The tag; additionally, define the collection. This represents the total dataset stored across all edge devices.

[0014] Furthermore, in step S2, the mathematical model for the optimization problem P1 of joint communication resource allocation and data sample selection is as follows:

[0015]

[0016]

[0017] In the NOMA communication system, considering the resource allocation protocol and the availability characteristics of edge devices, C1 to C4 represent the constraints of resource block allocation, C5 to C6 represent the constraints of transmission power allocation, and C7 to C8 represent the constraints of edge device data sample selection. The data sample set selected by each edge device must be a subset of its local data set, and in order to ensure the participation of the device, the data sample subset selected by each edge device cannot be an empty set; λ∈[0,1] represents a weight coefficient used to balance the training performance and training cost of the FEEL system. This represents the net cost of all edge devices. This represents the optimization terms related to the selection of data samples. This indicates the design of data sample selection. This indicates that during the i-th round of training, edge device k starts from... The selected data sample set; and These represent the design parameters for resource block allocation and transmission power allocation, respectively. N represents the number of resource blocks in the network, and Q represents the maximum number of edge devices that can occupy each resource block at the same time, where Q≥1. This represents the maximum transmission power of device k; α represents the data transmission rate of edge device k during the i-th round of training; k ∈{0,1} represents the availability of edge device k, where α k =1 indicates that edge device k can upload local gradients; L and T represent local gradients respectively. The size and the time for uploading gradients.

[0018] Furthermore, in step S2, the net cost of all edge devices is expressed as:

[0019]

[0020] Among them, Ccom (ρ (i) ,p (i) The communication cost of successfully uploading the local gradient to the edge server is represented as . Where c k This represents the training cost per unit of energy consumed by device k;

[0021] C cmp The cumulative net cost of all edge devices performing local computation is expressed as: Where c k This represents the cost per unit of energy consumed by edge device k; The energy consumed by edge device k in calculating the gradient of all local data samples is denoted as: Where κ is an energy consumption parameter related to the computing chip's capability, and F k Indicates calculation Number of CPU cycles required, f k Indicates the CPU frequency of device k;

[0022] Represents a set The total reward that all edge devices can obtain is expressed as Where q k This represents the reward for each data sample from edge device k.

[0023] Furthermore, step S3 specifically includes introducing a new optimization variable δ. (i) The constraints related to data sample selection in optimization problem P1 can be equivalently transformed into the following constraints:

[0024]

[0025]

[0026] This leads to the following optimization problem:

[0027]

[0028] in, Δ(δ (i) )and The specific expressions are as follows:

[0029]

[0030]

[0031] in, Let q represent the probability that user device k can upload local gradients. k This represents the reward for each data sample from edge device k.

[0032] Furthermore, step S4 specifically includes: based on the structural characteristics and mathematical properties of optimization problem P2, P2 is equivalently decomposed into two subproblems: resource allocation subproblem P3 and data selection subproblem P4, to obtain a low-complexity suboptimal solution to P2; firstly, based on matching theory and convex-concave processes, the resource allocation subproblem P3 is solved to obtain the resource allocation strategy (ρ *(i) p *(i) Then, based on the resource allocation strategy of optimization problem P3, the gradient projection method is used to obtain the relaxed form of the low-complexity suboptimal solution of the data selection subproblem P4. Finally, the relaxed solution is projected onto the feasible region δ of the optimization problem P4. *(i) In the end, a low-complexity suboptimal solution (δ) to the optimization problem P2 is obtained. *(i) , ρ *(i) p *(i) ).

[0033] Furthermore, step S5 specifically includes: first, the edge server broadcasts the global model to the edge server; the edge server calculates the squared norm of the gradient of the local data sample and uploads the calculation result; then, the edge server selects appropriate data samples and allocates communication resources reasonably using the method proposed in this invention; next, the edge device calculates the local gradient according to the joint resource allocation and data selection strategy and uploads the local gradient; finally, the edge server aggregates the local gradient and updates the global model; the above process iterates until the FEEL network training model converges.

[0034] The beneficial effects of this invention are as follows: This invention takes into account that edge devices participating in FEEL may not be able to participate in local gradient uploading and / or that the local data samples of edge devices may have label errors that affect the performance of FEEL, making it more practical; in addition, the low-complexity suboptimal algorithm proposed in this invention significantly outperforms other representative baseline schemes under various network settings.

[0035] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0036] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0037] Figure 1 The FEEL network system model diagram provided by this invention takes into account device availability and data labeling errors;

[0038] Figure 2 This is a flowchart of the optimization problem solved in this invention;

[0039] Figure 3 This is a graph showing the relationship between the test accuracy of the FEEL network system based on the MNIST dataset in this invention and the number of training rounds under different schemes;

[0040] Figure 4 This is a graph showing the relationship between the cumulative net cost of the FEEL network system based on the MNIST dataset in this invention and the number of training rounds under different schemes;

[0041] Figure 5 This is a graph showing the relationship between the test accuracy of the FEEL network system based on the Fashion-MNIST dataset in this invention and the number of training rounds under different schemes;

[0042] Figure 6 This is a graph showing the relationship between the cumulative net cost of the FEEL network system based on the Fashion-MNIST dataset in this invention and the number of training rounds under different schemes;

[0043] Figure 7 The graph showing the relationship between the test accuracy of the FEEL network system based on the MNIST dataset and the proportion of different data error labels in this invention;

[0044] Figure 8 The graph showing the relationship between the cumulative net cost of the FEEL network system based on the MNIST dataset and the proportion of different data error labels in this invention;

[0045] Figure 9 The graph in this invention shows the relationship between the test accuracy of the FEEL network system and the proportion of different data error labels based on the Fashion-MNIST dataset.

[0046] Figure 10 The graph in this invention shows the relationship between the cumulative net cost and the proportion of different data error labels in the FEEL network system based on the Fashion-MNIST dataset.

[0047] Figure 11 The graph in this invention shows the relationship between the test accuracy of the FEEL network system based on the MNIST dataset and the availability ratio of different devices.

[0048] Figure 12 The graph in this invention shows the relationship between the cumulative net cost of the FEEL network system and the availability ratio of different devices based on the MNIST dataset.

[0049] Figure 13The graph in this invention shows the relationship between the test accuracy of the FEEL network system and the availability ratio of different devices based on the Fashion-MNIST dataset.

[0050] Figure 14 The graph in this invention shows the relationship between the cumulative net cost of the FEEL network system based on the Fashion-MNIST dataset and the availability ratio of different devices. Detailed Implementation

[0051] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0052] Please see Figures 1 to 14 This invention provides a resource allocation and data selection method for high-performance federated edge learning, specifically including the following steps:

[0053] S1: Establish a federated edge learning (FEEL) network with data sample labeling errors and some devices being unavailable.

[0054] like Figure 1 As shown, this embodiment of the invention provides a FEEL network that considers device availability and data tag errors. This model includes an edge server attached to the BS and K single-antenna edge devices. All edge devices use... This indicates that for any device k in the set, there exists a local dataset. in This represents the j-th d-dimensional data sample. This represents the label of the data sample. Additionally, we define a set. This represents the total dataset stored across all edge device vendors.

[0055] S2: Construct a FEEL algorithm suitable for the FEEL network considered in this invention. Under the constraints of successful local gradient upload by available devices, establish a mathematical model P1 for the joint optimization problem of communication resource allocation and data sample selection. Its specific content includes the following steps:

[0056] S21: Construct a FEEL algorithm suitable for the network considered in this invention.

[0057] Perform the following procedure at global iteration i:

[0058] Broadcasting global model and RF power: The edge server simultaneously broadcasts the global model w to all edge devices. (i -1) Each edge device initializes its local model as

[0059] Calculate local gradients for each edge device. Based on its local dataset and global model w (i-1) The output of the stochastic gradient descent algorithm is the local gradient.

[0060] Upload local gradients: Each available device k will upload updated local gradients. Upload to the edge server for global model aggregation and updates.

[0061] Update the global model: After receiving local gradients uploaded by available devices, the edge server aggregates the gradients into a global gradient. And update the global model

[0062] S22: In a real-world FEEL network system, the set Some data in the dataset is incorrectly labeled; for example, a handwritten digit "1" might be labeled as "0," and the label for an image of a "t-shirt" might be incorrectly assigned as "trouser." To address these issues, this invention proposes a data sample selection strategy that selects only data from a set... A portion of the data samples in the dataset is used to calculate the local gradient:

[0063]

[0064] in, This indicates that during the i-th round of training, all edge devices k are... The selected data sample set.

[0065] Assume that the edge server will give each edge device a certain reward, let q k Let the set be the reward for each data sample from edge device k. The total reward that all edge devices can obtain can be expressed as:

[0066]

[0067] in, This indicates the design of the data sample selection.

[0068] Performing gradient calculations consumes a certain amount of energy from each edge device. Specifically, F is defined as follows:k Indicates calculation Number of CPU cycles required, f k Let $\mathbf{k}$ represent the CPU frequency of device k. Then, the time taken for edge device k to compute the gradient of all local data samples is $\mathbf{k}$. The corresponding energy consumed is Where κ is an energy consumption parameter related to the computing chip's capabilities. Define c k This represents the cost per unit of energy consumed by edge device k. The cumulative net cost of all edge devices performing local computation is:

[0069]

[0070] S23: Edge devices use NOMA for local gradient uploads. Some devices may be unable to upload local gradients due to connection loss or making phone calls, defining α. k ∈{0,1} represents the availability of edge device k, where α k =1 indicates that edge device k can upload local gradients. Assuming there are N resource blocks in the system, and each resource block can be occupied by a maximum of Q (Q≥1) edge devices simultaneously, the following constraints should be satisfied when allocating resource blocks:

[0071]

[0072]

[0073]

[0074]

[0075] When an edge device is unable to upload local gradients, no transmission power is allocated to it, resulting in:

[0076]

[0077] The data transmission rate of edge devices is modeled as follows:

[0078]

[0079] Where B represents the bandwidth of each resource block. Let L and T represent the indicator function. The size and upload time of the gradients are considered to ensure successful upload of local gradients to the edge server.

[0080]

[0081] The corresponding communication cost is:

[0082]

[0083] in, and These represent the design parameters for resource block allocation and transmission power allocation, respectively. Finally, based on the rewards and costs of edge devices, the net cost of all edge devices can be expressed as:

[0084]

[0085] S24: Edge servers aggregate local gradients and update the global model.

[0086]

[0087] Obtain the global gradient Then, the edge server updates the global federated learning model according to the model update formula: Where, η (i) Let represent the learning rate in the i-th round.

[0088] The upper bound of convergence for one round of training of the FEEL network system is:

[0089]

[0090] The optimization terms related to data sample selection are specifically represented as follows:

[0091]

[0092] in, Represents the gradient of the loss function for data samples The norm squared value. Data sample selection directly affects the convergence speed of the training algorithm, and the convergence expression... The smaller the value, the faster the training algorithm converges.

[0093] S25: To minimize the net cost of edge devices while accelerating the convergence of the FEEL network training model, an optimization problem is established that jointly optimizes resource allocation and data selection.

[0094] The mathematical model for the chosen optimization problem P1 is:

[0095]

[0096] Specifically, regarding the resource allocation protocol and the availability characteristics of edge devices in the NOMA communication system, C1-C4 provide constraints on resource block allocation, C5-C6 are constraints on transmission power allocation, and C7-C8 represent constraints on edge device data sample selection. The set of data samples selected by each edge device must be a subset of its local data set, and in order to ensure the participation of the devices, the subset of data samples selected by each edge device cannot be an empty set.

[0097] S3: Transform the original optimization problem that cannot be solved on the server into an equivalent mathematical model of optimization problem P2 that can be solved on the server.

[0098] First, the data selection optimization variables are equivalently converted into discrete optimization variables δ. (i) The following constraints can be obtained:

[0099]

[0100]

[0101] This leads to the following optimization problem:

[0102]

[0103] S4: The transformed problem P2 is equivalently decomposed into a resource allocation subproblem P3 and a data selection subproblem P4. The resource allocation subproblem and the data selection subproblem are solved respectively based on matching theory, convex and concave processes and gradient projection.

[0104] The solution steps are as follows: Figure 2 As shown, the specific steps are as follows:

[0105] Based on the structural characteristics and mathematical properties of optimization problem P2, P2 is equivalently decomposed into two subproblems: resource allocation subproblem P3 and data selection subproblem P4, thus obtaining a low-complexity suboptimal solution to P2. First, the resource allocation subproblem P3 is solved based on matching theory and convex-concave processes, yielding the resource allocation strategy (ρ). *(i) p *(i) Then, based on the resource allocation strategy of optimization problem P3, the gradient projection method is used to obtain the relaxed form of the low-complexity suboptimal solution of the data selection subproblem P4. Finally, the relaxed solution is projected onto the feasible region δ of the optimization problem P4. *(i) Finally, a low-complexity suboptimal solution (δ) to the optimization problem P2 is obtained. *(i) , ρ *(i) p *(i) ).

[0106] S5: Design a low-complexity algorithm to obtain a joint resource allocation and data selection method for FEEL scenarios with data labeling errors and some devices being unavailable. The specific content includes:

[0107] First, the edge server broadcasts the global model to other edge servers. Each edge server calculates the squared norm of the gradient of its local data samples and uploads the result. Then, using the method proposed in this invention, the edge server selects appropriate data samples and allocates communication resources accordingly. Next, the edge devices calculate their local gradients based on the joint resource allocation and data selection strategy and upload their local gradients. Finally, the edge server aggregates the local gradients and updates the global model. This process iterates until the FEEL-trained model converges.

[0108] Comparative experiment:

[0109] like Figures 3-6 As shown, this experiment presents the relationship between the test accuracy and cumulative net cost of edge devices for FEEL network systems trained using the MNIST and Fashion-MNIST datasets, and the number of training epochs under different schemes. Baseline scheme 1 involves the edge device randomly selecting half of its local data samples for training and uploading its local gradient through the resource block with the minimum channel power gain. In baseline scheme 2, the edge device randomly selects half of its local data samples for training and uploads its local gradient through the resource block with the maximum channel power gain. For baseline scheme 3, edge device k uses all its local data samples to calculate... And select the resource block with the lowest channel power gain for uploading. In baseline scheme 4, the edge device calculates its local gradient using all local data samples and uploads it through the resource block with the largest channel power gain. It should be noted that the baseline schemes for all experimental groups in this invention are the same as those in baseline schemes 1-4. As shown in the figure, the test accuracy fluctuates and increases with the number of training rounds. The low-complexity suboptimal algorithm proposed in this invention outperforms all baseline schemes in both test accuracy and cumulative net cost of the device. The test accuracy of the other baseline schemes is relatively close. Simulation results show that, because the scheme proposed in this invention can effectively select appropriate data samples and rationally allocate communication resources while considering device availability, the training performance of the FEEL system based on the scheme proposed in this invention and the net training cost of the device are significantly improved.

[0110] Figures 7-10The test accuracy and cumulative net cost of different schemes under different data sample mislabeling ratios are shown in the figure. As can be seen from the figure, the test accuracy of the FEEL network system decreases with increasing mislabeling ratio, but the test accuracy of the proposed scheme is higher than other representative baseline schemes under different mislabeling ratios. Furthermore, the cumulative net cost of edge devices is independent of the data sample mislabeling ratio, but the cumulative net cost of the proposed scheme is lower than other baseline schemes regardless of the mislabeling ratio. Simulation results demonstrate that the proposed scheme can reduce the negative impact of data mislabeling through reasonable data sample selection, and that the proposed scheme has stronger robustness.

[0111] Figures 11-14 The test accuracy and cumulative net cost of different schemes under varying device availability ratios are presented. As can be seen from the figures, the test accuracy of the FEEL network system increases with the device availability ratio, and the proposed scheme consistently outperforms other baseline schemes under all device availability ratios. Furthermore, the cumulative net cost of edge devices is lower than other baseline schemes, except when no devices can upload gradients (because other baseline schemes contribute more samples and thus receive more incentives). Simulation results demonstrate that the proposed scheme can improve FFEL training performance while reducing the net training cost of devices through reasonable data sample selection and resource allocation.

[0112] This invention proposes a resource allocation and data selection method for high-performance federated edge learning. Considering that edge devices participating in FEEL may not be able to participate in local gradient uploading and / or that the local data samples of edge devices may have label errors that affect the performance of FEEL, this method is more practical. In addition, the low-complexity suboptimal algorithm proposed in this invention significantly outperforms other representative baseline schemes under various network settings.

[0113] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A resource allocation and data selection method for high-performance federated edge learning, characterized in that, The method specifically includes the following steps: S1: Construct a FEEL network with data sample labeling errors and some devices being unavailable, where FEEL stands for Federated Edge Learning; S2: Construct the FEEL algorithm suitable for the FEEL network constructed in step S1. Under the condition that the available devices can successfully upload local gradients, establish an optimization problem P1 that combines communication resource allocation and data sample selection. S3: Transform the optimization problem P1, which cannot be solved on the server side, into an equivalent optimization problem P2 that can be solved on the server side; S4: The transformed problem P2 is equivalently decomposed into a resource allocation subproblem P3 and a data selection subproblem P4. The resource allocation subproblem P3 and the data selection subproblem P4 are solved based on matching theory, convex-concave process and gradient projection method respectively. S5: Employs a low-complexity algorithm to obtain a joint resource allocation and data selection method for FEEL scenarios with data sample labeling errors and some devices being unavailable.

2. The resource allocation and data selection method according to claim 1, characterized in that, In step S1, the constructed FEEL network includes an edge server attached to the BS and Each single-antenna edge device, all edge devices are aggregated Indicates; for the set of edge devices Any device in Having a local dataset ,in, Indicates the first indivual Dimensional data samples, Represents data samples The tag; additionally, define the collection. This represents the total dataset stored across all edge devices.

3. The resource allocation and data selection method according to claim 2, characterized in that, In step S2, the mathematical model for the optimization problem P1 of joint communication resource allocation and data sample selection is as follows: Specifically, regarding the resource allocation protocol and the availability characteristics of edge devices in the NOMA communication system, C1~C4 represent the constraints of resource block allocation, C5~C6 represent the constraints of transmission power allocation, and C7~C8 represent the constraints of edge device data sample selection. The set of data samples selected by each edge device must be a subset of its local data set, and the subset of data samples selected by each edge device cannot be an empty set. This represents a weighting coefficient used to balance the training performance and training cost of the FEEL system; This represents the net cost of all edge devices. This represents the optimization terms related to the selection of data samples. This indicates the design of data sample selection. Indicates the first Edge devices during round training from The selected data sample set; and These represent the design parameters for resource block allocation and transmission power allocation, respectively. N This indicates the number of resource blocks in the network. This indicates that each resource block can be at most [number] times. Multiple edge devices occupy the space simultaneously. ; Indicates equipment Maximum transmission power; Indicates the first Edge devices during round training Data transmission rate; Indicates edge device Availability, of which Indicates edge device Local gradients can be uploaded; and These represent the local gradients respectively. The size and the time for uploading gradients.

4. The resource allocation and data selection method according to claim 3, characterized in that, In step S2, the net cost of all edge devices is expressed as: in, The communication cost of successfully uploading the local gradient to the edge server is denoted as . ,in Indicates equipment The training cost per unit of energy consumed; The cumulative net cost of all edge devices performing local computation is expressed as: ,in Indicates edge device The energy consumed in calculating the gradient of all local data samples is expressed as: ,in These are energy consumption parameters related to the computing chip's capabilities. Indicates calculation Number of CPU cycles required Indicates equipment CPU frequency; Represents a set The total reward received by all edge devices is represented as ,in Indicates edge device Each data sample is rewarded.

5. The resource allocation and data selection method according to claim 4, characterized in that, Step S3 specifically includes introducing new optimization variables. The constraints related to data sample selection in optimization problem P1 can be equivalently transformed into the following constraints: This leads to the following optimization problem: in, , and The specific expressions are as follows: ； in, , indicating user equipment It is possible to upload the probability of local gradients. Indicates edge device Each data sample is rewarded.

6. The resource allocation and data selection method according to claim 5, characterized in that, Step S4 specifically includes: based on the structural characteristics and mathematical properties of optimization problem P2, P2 is equivalently decomposed into two subproblems: resource allocation subproblem P3 and data selection subproblem P4, to obtain a low-complexity suboptimal solution to P2; firstly, the resource allocation subproblem P3 is solved based on matching theory and convex-concave processes to obtain the resource allocation strategy. Then, based on the resource allocation strategy of optimization problem P3, the gradient projection method is used to obtain a relaxed form of the low-complexity suboptimal solution to the data selection subproblem P4. Finally, the relaxed solution is projected onto the feasible region of optimization problem P4. Finally, a low-complexity suboptimal solution to the optimization problem P2 is obtained. .

7. The resource allocation and data selection method according to claim 6, characterized in that, Step S5 specifically includes: First, the edge server broadcasts the global model to the edge server. The edge server calculates the squared norm of the gradient of the local data sample and uploads the calculation result. Then, the edge server selects appropriate data samples and allocates communication resources reasonably. Next, the edge device calculates the local gradient according to the joint resource allocation and data selection strategy and uploads the local gradient. Finally, the edge server aggregates the local gradient and updates the global model. The above process is iterated until the FEEL network training model converges.

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