A privacy-preserving personalized federated learning method based on model hierarchical optimization

By adopting model hierarchical optimization and differential privacy technologies in federated learning, the problem of reducing heterogeneity impact and communication efficiency while protecting user privacy is solved, and efficient model training and communication is achieved.

CN119646885BActive Publication Date: 2025-05-06QILU UNIVERSITY OF TECHNOLOGY (SHANDONG ACADEMY OF SCIENCES) +1
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Patent Information

Application Number
CN202510173637.9
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-02-18
Publication Date
2025-05-06
Estimated Expiration
2045-02-18

AI Technical Summary

Technical Problem

In federated learning, it is difficult for the prior art to reduce the model performance impact and communication efficiency caused by heterogeneity while ensuring user privacy.

Method used

A personalized federated learning method for privacy protection based on model hierarchical optimization is adopted. By hierarchical optimization before the local model is uploaded, some parameters of the model are selected for uploading, and differential privacy noise is introduced into the uploaded parameters.

Benefits of technology

It reduces communication costs, significantly reduces traffic, enhances the robustness of the global model, improves the overall performance of the system and the accuracy of the global model, and guarantees user privacy.

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Abstract

The present invention belongs to the technical field of federated learning, and more specifically, relates to a privacy-preserving personalized federated learning method based on model hierarchical optimization. The method includes each client obtaining a global model from a server, updating a local model using a training data set from the client, and then hierarchically optimizing the local model to determine the partial model parameters to be uploaded by each client; trimming the partial model parameters to be uploaded by each client, introducing differential privacy noise, and then sending them to the server; the server assigns weights to each client according to the amount of data of each client, and then aggregates the model parameters uploaded by each client to obtain a new global model and sends it to each client; repeat S1 to S3 until the set training rounds or convergence are reached. The present invention solves the problem of improving the model performance impact and communication efficiency caused by heterogeneity in federated learning while protecting user privacy.
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Description

Technical Field

[0001] The present invention belongs to the technical field of federated learning, and more specifically, relates to a privacy-preserving personalized federated learning method based on model hierarchical optimization. Background Art

[0002] In modern society, data is often stored in users' devices or in different institutions. It is not realistic to directly transfer large amounts of data to a central server. In addition, with the increase in privacy regulations (such as GDPR) and data security requirements, traditional centralized machine learning methods face the risk of data privacy leakage. To address this challenge, federated learning (FL) was introduced to solve the problem of data privacy protection while promoting multi-party collaboration to improve the performance of machine learning models. In a typical FL setting, the parameter server is responsible for training the global model by aggregating local model parameters from the client. Federated learning breaks data silos, promotes multi-party collaboration, and enables different organizations or devices to jointly train high-performance models without sharing original data. It has important research value and practical application significance.

[0003] Chinese invention patent CN118350038A discloses a hierarchical privacy-preserving federated learning method based on core data sets. First, the end user divides the original data into core and non-core data sets according to the data coreness. Secondly, Gaussian noise with different privacy budgets is added to the core and non-core data sets respectively. Then, the core and non-core data sets with noise are merged for local model training. Finally, the central server aggregates the local model updates to obtain the global model, and sends the global model to the end user, iterating the above steps until the global model converges.

[0004] However, in practical applications, the parameters of the entire model need to be frequently uploaded and downloaded, and each participant needs to upload the complete parameters or gradients of the model to the server. This means that in each round of training, all participants will transmit the parameters of the entire model, which consumes huge bandwidth. In addition, the data between clients is often not independent and identically distributed. Existing technologies for protecting user privacy and security usually rely on three basic technologies: differential privacy DP, secure multi-party computing SMC, and homomorphic encryption HE. Differential privacy is a privacy protection technology commonly used in federated learning. Its purpose is to protect the client's local data from being leaked while ensuring the effectiveness of the global model. By adding noise to the data or gradients / weights, differential privacy can provide a strict privacy protection guarantee. Therefore, in such an environment, how to reduce the impact of model performance and communication efficiency caused by heterogeneity in federated learning while protecting user privacy has become an urgent problem to be solved in federated learning. Summary of the invention

[0005] The present invention aims to overcome at least one defect of the above-mentioned prior art and provide a privacy-preserving personalized federated learning method based on model hierarchical optimization to solve the problem of reducing the impact of model performance and communication efficiency caused by heterogeneity in federated learning while protecting user privacy.

[0006] The detailed technical scheme of the present invention is as follows:

[0007] A privacy-preserving personalized federated learning method based on model hierarchical optimization, the method comprising:

[0008] S1: Each client obtains the global model from the server, updates the local model using its own training data set, and then performs hierarchical optimization on the local model to determine the partial model parameters to be uploaded by each client;

[0009] S2: Crop some model parameters to be uploaded by each client, introduce differential privacy noise, and then send them to the server;

[0010] S3: The server assigns weights to each client according to the amount of data from each client, then aggregates the model parameters uploaded by each client to obtain a new global model and sends it to each client;

[0011] S4: Repeat S1 to S3 until the set training rounds or convergence are reached to obtain the federated learning model.

[0012] Furthermore, the S1 specifically includes:

[0013] S11, client i downloads the global model from the server , t is the tth round of training, in the first round of training, that is At the beginning, the server initializes the global model as ;

[0014] S12, client i uses its own training data set locally Train and use stochastic gradient descent to train the global model Update to client i's local model ;

[0015] S13. In the tth round, the parameters of the updated local model are layered to obtain , , which means the i-th client in the local model in the t-th round l Layer parameters, where L represents the total number of layers in the local model;

[0016] For the model l Layer Calculation lThe updated L2 norm of the layer is calculated, and the size of the L2 norm of the layer is saved for use in the next round. l The difference between the L2 norm of the layer update and the L2 norm of the t-1 round , the formula is as follows:

[0017] (1);

[0018] In formula (1), represents the L2 norm of the layer update in round t, represents the L2 norm of the layer update in round t-1;

[0019] S14, calculate the contribution of each layer, and then rank the contribution of each layer, take the top K layers for uploading, and the client i in the tth round l Contribution of layer The calculation process is as follows:

[0020] (2);

[0021] S15. In the tth iteration, client i calculates the , determine the top K layers uploaded, that is, a client will upload K layers, and according to the ranking of each layer, a one-dimensional array array of size L is obtained, where array[ l ]=1 means that the layer needs to be uploaded, array[ l ]=0 means no uploading is required;

[0022] S16. Finally, according to the array array corresponding to each layer, the partial model parameters to be uploaded by each client are obtained. :

[0023] (3);

[0024] In formula (3), Indicates l The parameters uploaded by the client are combined into the parameters uploaded by the client. .

[0025] Furthermore, the S2 specifically includes:

[0026] S21. Upload parameters To crop:

[0027] (4);

[0028] In formula (4), C is the clipping threshold, which indicates the maximum range of allowed update values;

[0029] S22, add noise , get the updated parameters after noise addition for each client :

[0030] (5);

[0031] In formula (5), given the noise variance In the case of represents Gaussian distributed noise, m represents the number of participating local clients;

[0032] S23. Finally, the updated parameters after adding noise to each client are sent to the server.

[0033] Furthermore, the S3 specifically includes:

[0034] S31. Assign weights to each client according to the amount of data on each client:

[0035] (6);

[0036] In formula (6), represents the sample weight of the i-th client in round t, Indicates the data size of the i-th client;

[0037] S32. Use sample weights Take a weighted average of the weights of each client;

[0038] (7);

[0039] In formula (7), Represents the global parameters after aggregation, Indicates the update parameters of the i-th client received by the server.

[0040] Furthermore, the parameters of the local model are layered according to the number of neural network layers of the local model, or layered according to a fixed amount of data per layer.

[0041] In another aspect of the present invention, a device for a privacy-preserving personalized federated learning method based on model hierarchical optimization is provided, the device comprising:

[0042] at least one processor; and

[0043] A memory storing instructions, which, when executed by the at least one processor, enables the at least one processor to execute the privacy-preserving personalized federated learning method based on model hierarchical optimization as described above.

[0044] In another aspect of the present invention, a computer-readable storage medium is provided, which stores executable instructions, and when the instructions are executed, the machine performs the privacy-preserving personalized federated learning method based on model hierarchical optimization as described above.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] The present invention provides a privacy-preserving personalized federated learning method based on model hierarchical optimization, and proposes a method for hierarchical and partially uploading a local model to a federated learning method. Before uploading the local model, some parameters of the model are selected, and partial uploading of the local model is achieved through hierarchical optimization. On the one hand, the communication cost is reduced, which can significantly reduce the communication volume. On the other hand, the robustness of the global model is enhanced, and the interference of irrelevant parameters on the global model is reduced, thereby improving the overall performance of the system and the accuracy of the global model. At the same time, by trimming some of the uploaded model parameters and introducing differential privacy noise for further protection, the model performance impact and communication efficiency caused by heterogeneity in federated learning are improved while protecting user privacy. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a flow chart of a privacy-preserving personalized federated learning method based on model hierarchical optimization described in the present invention.

[0048] Figure 2 3 is a schematic diagram comparing the privacy protection accuracy of the present invention in Example 1 of the present invention. DETAILED DESCRIPTION

[0049] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0050] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0051] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0052] In the absence of conflict, the embodiments of the present invention and the features of the embodiments may be combined with each other.

[0053] Example 1

[0054] Ginseng Figure 1 This embodiment provides a privacy-preserving personalized federated learning method based on model hierarchical optimization, the method comprising:

[0055] S1: The client obtains the global model and performs hierarchical optimization;

[0056] Each client obtains the global model on the server side, uses its own training data set to update the local model, and then optimizes the local model in layers to determine the partial model parameters to be uploaded by each client; specifically, the global model on the server side obtained for the first time is the initial global model.

[0057] Federated learning involves multiple local client devices that train models on local data and send them to the server, which aggregates these local models to update the global model without transmitting the original data; any client , including the training data set ,in, ;

[0058] In federated learning, the local client model is a model trained independently on each client device (such as a mobile phone, IoT device, or other computing node) participating in federated learning. The model architecture of all clients and the architecture of the server-side global model must be consistent, and are usually defined based on a shared model architecture.

[0059] The S1 specifically includes the following steps:

[0060] S11, client i downloads the global model from the server , t is the tth round of training, in the first round of training, that is At the beginning, the server initializes the global model as .

[0061] S12, client i uses its own training data set locally Train and use stochastic gradient descent to train the global model Update to client i's local model .

[0062] S13. In the tth round, the parameters of the updated local model are layered to obtain , , represents the number of the local model of the i-th client in the t-th round l Layer parameters, where L represents the total number of layers in the local model;

[0063] For the model lThe layer calculates the updated L2 norm of the layer, and saves the size of the L2 norm of the layer to be used in the next round. The difference between the updated L2 norm of the layer in round t and the L2 norm of round t-1 is calculated. The formula is as follows:

[0064] (1);

[0065] in, represents the L2 norm of the layer update in round t, Represents the L2 norm of the layer update in round t-1.

[0066] Preferably, the stratification is performed according to the neural network layer of the local model. For example, if the local model includes three convolutional layers and three fully connected layers, it is divided into six layers, namely three convolutional layers and three fully connected layers. Secondly, the stratification can also be performed by fixing the amount of data in each layer.

[0067] S14, calculate the contribution of each layer, and then rank the contribution of each layer, take the first K layers for uploading, and the contribution of each layer The calculation process is as follows:

[0068] (2);

[0069] S15. In the tth iteration, client i calculates the , determine the top K layers uploaded, that is, a client will upload K layers, and according to the ranking of each layer, a one-dimensional array array of size L is obtained, where array[ l ]=1 means that the layer needs to be uploaded, array[ l ]=0 means no uploading is required.

[0070] S16. Finally, according to the array array corresponding to each layer, get the parameters uploaded by each client ;

[0071] (3);

[0072] in, Indicates l The parameters uploaded by the client are combined into the parameters uploaded by the client. .

[0073] Through hierarchical optimization, partial uploading of the local model is achieved, which reduces the communication cost on the one hand. In federated learning, communication cost is a key bottleneck, especially when the model scale is large or the number of clients is large, uploading complete model parameters will consume a lot of bandwidth. By uploading partial parameters of the model, the communication volume can be significantly reduced, and on the other hand, the robustness of the global model is enhanced. In federated learning, the data of different clients may be non-independent and identically distributed (Non-IID), which makes the global model vulnerable to abnormal updates of a single client. By uploading only partial parameters, the parameters that contribute the most to the global model can be selected; therefore, the interference of irrelevant parameters on the global model is reduced, thereby improving the robustness of the model. This improves the overall performance of the system and the accuracy of the global model.

[0074] S2: Crop the model parameters to be uploaded by each client, introduce differential privacy noise, and then send the model to the server;

[0075] The S2 specifically includes the following processes:

[0076] S21, parameters uploaded after selection To crop:

[0077] (4);

[0078] C represents the clipping threshold, which indicates the maximum range of allowed update values.

[0079] S22, add noise , get the updated parameters after noise addition for each client

[0080] (5);

[0081] Given the noise variance In the case of Represents Gaussian distribution noise, and m represents the number of participating local clients. It is adjusted according to the number of participants m, so that the noise added to a large-scale data set is relatively small, which helps to improve the accuracy. That is, when the noise is constant, the noise is averaged to each client.

[0082] S23. Finally, the updated parameters after adding noise to each client are sent to the server.

[0083] S3: The server assigns weights to each client and aggregates them;

[0084] The server assigns weights to each client according to the amount of data from each client, then aggregates the uploaded models of each client to obtain a new global model and sends it to each client;

[0085] Furthermore, after receiving the parameters sent by each client, the server performs an aggregation operation to obtain a trained global model and sends it to each client. S3 specifically includes:

[0086] S31. Assign weights to each client according to the amount of data on each client:

[0087] (6);

[0088] in, represents the sample weight of the i-th client in round t, Indicates the data size of the i-th client.

[0089] S32. Use sample weights Take a weighted average of the weights of each client.

[0090] (7);

[0091] in, Represents the global parameters after aggregation, Indicates the update parameters of the i-th client received by the server.

[0092] Clients with large sample sizes have a greater impact on the global weight. This is because federated learning assumes that the data distribution of each client may be different, and larger datasets usually reflect the performance of the model more accurately.

[0093] Aggregate the local models of each client to obtain a trained global model and send it to each client for the next round of local client training. Each client obtains the trained global model , completing one iteration.

[0094] S4: Repeat the above steps S1 to S3 until the set training rounds or convergence are reached, and then end the process to obtain the federated learning model.

[0095] Preferably, this embodiment evaluates the performance of the proposed method and the comparative method under the same conditions by conducting experiments on the CIFAR-10 dataset. Specifically, for the CIFAR-10 dataset, the α parameter is set equal to 1 to simulate a non-IID distribution, and the accuracy is evaluated accordingly. This experimental setting reflects the actual situation and ensures a comprehensive evaluation of the robustness and adaptability of the method.

[0096] CIFAR-10 is a widely used image classification dataset, which consists of 60,000 32×32 pixel color images, divided into 10 categories, each category has 6,000 images, and the dataset is divided into 50,000 training images and 10,000 test images. For CIFAR-10, a deeper model is used, which has 3 convolutional layers and 3 fully connected layers.

[0097] The comparison method is as follows:

[0098] The performance of the proposed method is compared with several state-of-the-art methods in federated learning supporting differential privacy, including DP-FedAvg and FedDPA.

[0099] The implementation details are as follows:

[0100] For the CIFAR-10 dataset, the learning rate is set to 1e-3, the clipping threshold C is set to 1.0, the number of clients N is 10, and the Rényi Differential Privacy (RDP) algorithm provided by Opacus is used as a privacy accountant. For CIFAR-10, the global iteration number is set to 40, the local iteration number is set to 4, the batch size is set to 64, the dataset is divided into 10 subsets through Dirichlet distribution, and a fixed noise multiplier is used to ensure differential privacy.

[0101] like Figure 2 As shown in Figure 3, this is the average accuracy of the clients after 40 rounds of system iterations. The average accuracy of local clients represents the prediction accuracy of the model trained on local data of each client. It provides feedback for the training process of the global model and helps evaluate whether the model is effectively learning on data from multiple clients.

[0102] Benchmark 1 is DPFedAvg, an algorithm that combines differential privacy and federated learning. It aims to protect data privacy while achieving effective model training. It prevents the leakage of each participant's private data during the training process by adding differential privacy technology to the federated learning process; Benchmark 2 is a federated learning method based on dynamic Fisher personalization and adaptive constraints.

[0103] like Figure 2 As shown, the ordinate represents the average accuracy of the client. The higher the average accuracy of the client, the higher the personalization level of the local client. After 40 iterations, the solutions of the present invention, benchmark 1 and benchmark 2 all tend to be stable, where the average accuracy of the client of the solution of the present invention is 49.6, benchmark 1 is 43.8, and benchmark 2 is 45.2. It can be seen that the present invention greatly improves the prediction accuracy and personalization level of the model trained on the local data of the client.

[0104] Example 2

[0105] This embodiment provides a device for implementing a privacy-preserving personalized federated learning method based on model hierarchical optimization, the device comprising:

[0106] at least one processor; and

[0107] A memory storing instructions, which, when executed by the at least one processor, enables the at least one processor to execute the privacy-preserving personalized federated learning method based on model hierarchical optimization as described above.

[0108] In this embodiment, electronic devices include but are not limited to: personal computers, server computers, workstations, desktop computers, laptop computers, notebook computers, mobile computing devices, smart phones, tablet computers, cellular phones, personal digital assistants (PDAs), handheld devices, messaging devices, wearable computing devices, consumer electronic devices, etc.

[0109] Example 3

[0110] This embodiment also provides a computer-readable storage medium storing executable instructions, which, when executed, enable the machine to perform the privacy-preserving personalized federated learning method based on model hierarchical optimization as described above.

[0111] Specifically, a system or device equipped with a readable storage medium can be provided, on which software program codes that implement the functions of any of the above-mentioned embodiments are stored, and a computer or processor of the system or device can read and execute instructions stored in the readable storage medium.

[0112] In this case, the program code itself read from the computer-readable medium can realize the function of any one of the above embodiments, and thus the computer-readable code and the computer-readable storage medium storing the computer-readable code constitute part of this specification.

[0113] Examples of readable storage media include floppy disks, hard disks, magneto-optical disks, optical disks (such as CD-ROM, CD-R, CD-RW, DVD-ROM, DVD-RAM, DVD-RW, DVD-RW), magnetic tapes, non-volatile memory cards, and ROMs. Optionally, the program code may be downloaded from a server computer or a cloud via a communication network.

[0114] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0115] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0116] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0117] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0118] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the technical solution of the present invention, and are not intended to limit the specific implementation methods of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the claims of the present invention shall be included in the protection scope of the claims of the present invention.

Claims

1. A privacy-preserving personalized federated learning method based on model hierarchical optimization, characterized in that: The method comprises: S1: Each client obtains the global model from the server, updates the local model using its own training data set, and then performs hierarchical optimization on the local model to determine the partial model parameters to be uploaded by each client; S2: Crop some model parameters to be uploaded by each client, introduce differential privacy noise, and then send them to the server; S3: The server assigns weights to each client according to the amount of data from each client, then aggregates the model parameters uploaded by each client to obtain a new global model and sends it to each client; S4: Repeat S1 to S3 until the set training rounds or convergence are reached to obtain the federated learning model; The S1 specifically includes: S11, client i downloads the global model from the server , t is the tth round of training, in the first round of training, that is At the beginning, the server initializes the global model as ; S12, client i uses its own training data set locally Train and use stochastic gradient descent to train the global model Update to client i's local model ; S13. In the tth round, the parameters of the updated local model are layered to obtain , , which means the i-th client in the local model in the t-th round l Layer parameters, where L represents the total number of layers in the local model; For the model l The layer calculates the updated L2 norm of the layer and saves the size of the L2 norm of the layer to be used in the next round. Calculate the tth round l The difference between the L2 norm of the layer update and the L2 norm of the t-1 round , the formula is as follows: (1); In formula (1), represents the L2 norm of the layer update in round t, Indicates the t-1th round l L2 norm of layer updates; S14. Calculate the contribution of each layer, and then rank the contribution of each layer, take the first K layers for uploading, and the i-th client is the first in the t-th round. l Contribution of layer The calculation process is as follows: (2); S15. In the tth iteration, client i calculates the , determine the top K layers uploaded, that is, a client will upload K layers, and according to the ranking of each layer, a one-dimensional array array of size L is obtained, where array[ l ]=1 means that the layer needs to be uploaded, array[ l ]=0 means no uploading is required; S16. Finally, according to the array array corresponding to each layer, the partial model parameters to be uploaded by each client are obtained. : (3); In formula (3), Indicates l The parameters uploaded by the client are combined into the parameters uploaded by the client. .

2. According to claim 1, a privacy-preserving personalized federated learning method based on model hierarchical optimization is characterized in that: The S2 specifically includes: S21. Upload parameters To crop: (4); In formula (4), C is the clipping threshold, which indicates the maximum range of allowed update values; S22, add noise , get the updated parameters after noise addition for each client : (5); In formula (5), given the noise variance In the case of represents Gaussian distributed noise, m represents the number of participating local clients; S23. Finally, the updated parameters of each client after adding noise are sent to the server.

3. According to claim 2, a privacy-preserving personalized federated learning method based on model hierarchical optimization is characterized in that: The S3 specifically includes: S31. Assign weights to each client according to the amount of data on each client: (6); In formula (6), represents the sample weight of the i-th client in round t, Indicates the data size of the i-th client; S32. Use sample weights Take a weighted average of the weights of each client; (7); In formula (7), Represents the global parameters after aggregation, Indicates the update parameters of the i-th client received by the server.

4. According to claim 2, a privacy-preserving personalized federated learning method based on model hierarchical optimization is characterized in that: The parameters of the updated local model are layered according to the number of neural network layers of the local model.

5. A device for a privacy-preserving personalized federated learning method based on model hierarchical optimization, characterized in that: The device comprises: processor; a memory having stored thereon a computer program executable on the processor; Wherein, when the computer program is executed by the processor, the steps of a privacy-preserving personalized federated learning method based on model hierarchical optimization are implemented as described in any one of claims 1 to 4.

6. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 4 are implemented.

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