Personalized federal learning method and learning system

By introducing global information and collaborative training features into federated learning, and adjusting client weights in combination with the exponential tilt mechanism, the problem of personalization and fairness balance in the existing technology is solved, and higher accuracy and global fairness of the personalized model are achieved.

CN119670850APending Publication Date: 2025-03-21INNER MONGOLIA UNIVERSITY
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Patent Information

Application Number
CN202411721630.8
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-11-28
Publication Date
2025-03-21

AI Technical Summary

Technical Problem

The existing federated learning methods have challenges in balancing personalization and fairness. Overemphasizing personalized model optimization may ignore fairness across the global scope, resulting in widening performance gaps between clients and weakening the generalization performance of global models.

Method used

By introducing global information into local training, global features and personalized features are trained in collaboratively, and the client weight is dynamically adjusted in combination with the exponential tilt mechanism to ensure that the personalized model is not dominated by the characteristics of some clients during the optimization process, thereby achieving a balance of personalization and fairness.

Benefits of technology

Improve the accuracy of personalized models, ensure that all clients can benefit equally, reduce model differences between clients, and promote fairness on a global scale.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention provides a personalized federal learning method and system, and the method comprises the following steps: a client carries out the local training of a received global model, then uploads model parameters, and a central server carries out the dynamic weighting optimization updating according to all received model parameters; wherein the step of local training comprises the steps of learning global information under the guidance of local category embedding, and guiding learning of a personalized model through cooperative training of global and personalized features. The global information is introduced into the local training, and the global features and the personalized features are cooperatively trained, so that the accuracy of the personalized model is improved. Index tilt is used to flexibly adjust personal loss to introduce consideration of fairness, and it is ensured that in the model optimization process, features of individual clients do not dominate a global model.
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Description

Technical Field

[0001] The present invention relates to the field of federated learning, and in particular to a personalized federated learning method and a learning system. Background Art

[0002] Federated learning has emerged as a new distributed learning method that trains algorithms across multiple decentralized clients or servers without exchanging local data samples. In this era of big data, large-scale data is becoming increasingly popular, but it also faces the risk of data leakage. Federated learning aims to solve this problem by allowing clients to collaboratively train a global model without sharing original data. However, since each client's local data presents a different distribution, the single global model obtained by simple averaging in traditional federated learning methods may not fully understand the data distribution of clients with less data, thereby reducing the accuracy of model training. Clients update the global model on their own local datasets, causing local models to be misaligned, resulting in weight bias and even very poor performance. To solve this problem, personalized federated learning is introduced. Personalized federated learning emphasizes customizing a dedicated model for each client to make the model more suitable for local data. Significant differences in data characteristics between different clients may cause personalized models for some clients to perform well, while personalized models for other clients may perform poorly. This personalization can improve local performance, but may exacerbate overall performance differences between clients, leading to fairness issues.

[0003] Most existing federated learning works aim to solve specific problems, either focusing on personalization to meet the personalized needs of all clients for the model, or focusing on fairness to solve the problem of unfair performance among all clients.

[0004] For example, some methods only use personalized information to train models to achieve personalization goals, or introduce batch normalization layers into the model to achieve personalized training of neural networks, or interpolate between global models and local models, or improve aggregation strategies to build personalized models. Some methods use (local training) regularized loss functions (loss functions generated after training based on global models and local data) to reduce the differences between client data to train powerful global models. Knowledge distillation extracts knowledge from the global model of federated learning into the local training model to maintain the model effect of the local client.

[0005] However, although the above existing methods effectively solve the problem of data heterogeneity, they often only focus on training powerful global models or personalized models. Over-emphasizing the optimization of personalized models and ignoring the optimization of fairness on a global scale may lead to a widening performance gap between clients, weakening the generalization performance of the global model on other clients, and ultimately causing damage to the personalized performance of other clients, affecting overall fairness. Over-emphasizing the optimization of the global model may ignore clients with poor performance when the data differences between clients are large. They cannot get more personalized support and their fairness is limited.

[0006] Therefore, it can be seen that it is difficult for existing federated learning frameworks to effectively balance personalization and fairness. This is because there are many challenges in the conflict between model global optimization and personalization requirements, the difficulty of heterogeneous data processing, the imbalance of resources and communication capabilities, the privacy protection mechanism that limits the effectiveness of personalization, and the complexity and convergence of personalized model training.

[0007] In view of this, the present invention is proposed. Summary of the invention

[0008] In view of this, the present invention proposes a personalized federated learning method and learning system, which introduces global information into local training, and collaboratively trains global features and personalized features to improve the accuracy of the personalized model. By using exponential tilt to flexibly adjust personal losses to introduce fairness considerations, it is ensured that during the model optimization process, the characteristics of individual clients will not dominate the global model, so that all clients can benefit equally. Through the personalized federated learning method based on collaborative learning and dynamic weighted optimization of the present invention, an effective balance is achieved between personalization and fairness.

[0009] Specifically, the present invention is achieved through the following technical solutions:

[0010] The present invention provides a personalized federated learning method, comprising the following steps:

[0011] The client performs local training on the received global model and then uploads the model parameters. The central server performs dynamic weighted optimization updates based on all received model parameters.

[0012] The local training step includes: learning global information under the guidance of local category embedding, and guiding the learning of personalized models by co-training global and personalized features.

[0013] In addition to providing a personalized federated learning method, the present invention also provides a personalized federated learning system, including:

[0014] Local training module: used for the client to perform local training on the received global model and then upload the model parameters, wherein the local training steps include: learning global information under the guidance of local category embedding, and guiding the learning of personalized models by co-training global and personalized features;

[0015] Update module: used by the central server to perform dynamic weighted optimization updates based on all received model parameters.

[0016] In summary, the solution of the present invention has the following beneficial effects:

[0017] 1) This paper designs a personalized fairness-aware federated learning method that considers both personalization and fairness goals. This method guides the learning of global features by introducing local category embedding, and then co-trains global and personalized features, integrating global feature information into local training to guide the learning of personalized models.

[0018] 1) This method introduces the tilted empirical risk minimization (TERM) fairness mechanism into the global model optimization process, aiming to reduce the model differences between customers and promote fairness among customers by dynamically weighted optimization of global model parameters.

[0019] 3) The local category embedding matrix is ​​only updated locally on the client and optimized with the feedback of global features to ensure that the global model can adapt to the specific data distribution of each client while protecting the client's privacy data. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Various other advantages and benefits will become apparent to those skilled in the art by reading the following detailed description of the preferred embodiments. The accompanying drawings are only for the purpose of illustrating the preferred embodiments and are not to be considered as limiting the present invention. The same reference symbols are used throughout the accompanying drawings to represent the same components. In the accompanying drawings:

[0021] Figure 1 is a flow chart of the personalized federated learning method of the present invention;

[0022] Figure 2 A framework diagram of the personalized federated learning method of the present invention;

[0023] Figure 3 A data flow diagram of the client module of the present invention;

[0024] Figure 4 A flowchart of a computer device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0025] Exemplary embodiments will be described in detail herein, examples of which are shown in the accompanying drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present disclosure. Instead, they are only examples of devices and methods consistent with some aspects of the present disclosure as detailed in the appended claims.

[0026] The terms used in the present disclosure are only for the purpose of describing specific embodiments and are not intended to limit the present disclosure. The singular forms "a", "said" and "the" used in the present disclosure and the appended claims are also intended to include plural forms, unless the context clearly indicates otherwise. It should also be understood that the term "and / or" used herein refers to and includes any or all possible combinations of one or more of the associated listed items.

[0027] It should be understood that although the terms first, second, third, etc. may be used in the present disclosure to describe various information, such information should not be limited to these terms. These terms are only used to distinguish the same type of information from each other. For example, without departing from the scope of the present disclosure, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Depending on the context, the word "if" used herein may be interpreted as "at the time" or "when" or "in response to determining",

[0028] Example

[0029] like Figure 1-2 As shown, the present invention provides a personalized federated learning method, comprising the following steps:

[0030] The client performs local training on the received global model and then uploads the model parameters. The central server performs dynamic weighted optimization updates based on all received model parameters.

[0031] The local training step includes: learning global information under the guidance of local category embedding, and guiding the learning of personalized models by co-training global and personalized features.

[0032] The personalized federated learning method based on collaborative learning and dynamic weighted optimization proposed in this paper is integrated with the local-global embedding learning algorithm (LGER) and the tilted empirical risk minimization (TERM) to balance the weights of the global and personalized models, and achieve good generalization in the global scope while meeting the personalized needs of each client, thereby enhancing fairness. The specific implementation steps are as follows:

[0033] S1: The client downloads the latest global model from the central server and receives the global model parameters of the current round for local update;

[0034] S2: The client performs local training on the client model of the current training round based on the local training data. The training is divided into two stages. The first stage introduces a local category embedding layer to learn global information under the guidance of local category embedding. The second stage guides the learning of personalized models by co-training global and personalized features.

[0035] S3: After all clients complete training, they upload model parameters, but do not upload embedding layer parameters to the server. Instead, they keep these parameters locally for optimization.

[0036] S4: The central server dynamically weights and optimizes the parameters of each client through tilted empirical risk minimization (TERM) based on the model parameters received from all clients;

[0037] S5: The central server performs global aggregation using the previously determined weights to obtain the next round of model training parameters, and returns to step S1 to complete a training cycle until the global model of the central server converges.

[0038] Furthermore, in the step S2, the first stage extracts the embedding vector of each category based on the global features through the search operation in the embedding layer, generates a local category embedding matrix, and guides the learning of global features, which includes the following two steps:

[0039] Step S21: extract feature information from the feature vector of the client and convert the original features into global features and personalized features;

[0040] Step S22: Extract the embedding vector of each category based on the global features and generate a local category embedding matrix to guide the learning of global information.

[0041] Furthermore, in step S21, in order to obtain a global model and a personalized model, representation learning is used to divide the deep learning model into a feature extractor and a head component. The head component is designated as the last fully connected layer, which represents the personalized characteristics of the client, and the remaining layers are set as feature extractors, which represent the common characteristics of all clients. First, the input data is passed through the feature extractor to extract the feature vector, and the data sample is mapped to a lower space of dimension k through φ, which is represented as Get the original feature vector V i ,formal, Then, the original feature vector V is transformed into i Convert to global eigenvector and personalized feature vector Global feature extraction and personalized feature extraction are performed separately. Specifically, firstly, a low-dimensional feature vector V is extracted from the input data sample through the feature extractor φi , expressed as:

[0042]

[0043] For each client with heterogeneous data, they include both global feature information and personalized feature information. In order to utilize these two types of feature information respectively and extract feature information from feature vectors, affine mapping transformation is used to adjust the scaling and offset of the original features respectively to meet the global and personalized learning needs. i Converted into global eigenvectors V i G and personalized feature vector

[0044]

[0045]

[0046] Where 1 and V i have the same shape, all values ​​are equal to 1. σ is the ReLU activation function. ⊙ is the Hadamard product. First V i Each element of is scaled by a factor of ε or ε i After scaling, V i Each element of i , and finally apply the ReLU activation function to increase the nonlinear characteristics. Through this process, the original feature V i are adjusted to global features and personalized features This enables them to adapt to different learning tasks. The key parameters ε, ε in the affine mapping i , η, η i It is generated by conditional variables. Specifically, the conditional variables pass through a fully connected layer (FC layer), a ReLU activation layer, and a layer normalization layer to generate a scaling factor or an offset factor. i The conditional variable used to guide the feature extractor to learn personalized feature information in the personalized task, g i Contains local data distribution information and is used to provide conditional variables for global information reference in global guidance.

[0047] Furthermore, in the step S22, the conditional variables are used to generate scaling coefficients and offset coefficients in the affine mapping according to the global information and personalized information of the client. i Convert to Global Features and personalized features First, the generation of global conditional input is used to provide global information reference in global guidance, and any trainable category embedding u is obtained by using the embedding technology to find the operation: u = E(u; C i ), where u is the category ID. Based on the global features, the embedding vector of each category is extracted to generate the local category embedding matrix to guide the learning of global features.

[0048] g i =E(u;C i )

[0049] Where E(u;C i ) is the client's local category embedding model, which is used to store the embedding vector of the local category and use the global feature through the lookup operation. The extracted category IDs u are used to look up the corresponding embedding vectors in the embedding layer using these indices. i , first we need to get the data distribution of client i.

[0050]

[0051] Where U is the number of all categories, is the indicator function. These embedding vectors combine global features Generate a local category embedding matrix.

[0052] Furthermore, in the step S2, the global information is introduced into the local training in the second stage (that is, the local category embedding matrix obtained in the first stage above) to guide the learning of the local personalized model. The client can not only learn the features of the global information, but also optimize the personalized model according to the distribution of personalized information, specifically including:

[0053] The overall architecture assumes that there are K clients and one central server. Each client i is given a training dataset distributed by There are different labels / tasks in the dataset, and the personalized goal on client i is represented as:

[0054]

[0055] Among them l i is the personalized loss function, w i are all module parameters on client i. For all clients, the optimization goal of this method is:

[0056]

[0057] in is the number of training samples on client i.

[0058] Furthermore, in the S3 step, global and personalized features are collaboratively learned and jointly participate in model optimization. Through collaborative learning, the model can share knowledge on different clients while retaining the unique data characteristics of each client. In each iteration, the client adds the base layer parameter w f , and the learnable parameters D for affine mapping between the feature extractor and the local category embedding to generate global feature information and personalized feature information are uploaded to the server for global aggregation. The client does not upload the embedding layer parameters (local category embedding matrix) to the server, but keeps these parameters locally for optimization. We upload the training parameters to the central server, and the parameters are expressed as W = {w f ,D}. After the parameters are aggregated, a new global model is formed and sent to all clients. During the local training process, all clients share the global parameter W. We represent the trainable parameters as The client uses the global features generated by the global model parameters sent down, combines these features to update the embedding layer, and optimizes through contrast loss to ensure that the local features can be consistent with the global features. Formally, our local loss function is:

[0059]

[0060] Where l is the cross entropy loss function, μ is a hyperparameter, and the contrast loss is used to calculate the global loss function, which is used to calculate the relationship between the embedding vector and the global feature, so as to ensure that the local category embedding can effectively capture the global model information. The local model parameters are optimized and updated according to the local loss function. Through the combination of global features and personalized features, the model can adapt to the global data distribution while maintaining personalized adaptation to local data. Global features Through contrastive learning and local category embedding matrix E(u; C i ) Collaborative optimization to ensure a balance between global and personalized features.

[0061] Further, in the step S4, in federated learning, the concept of fairness does not only focus on non-discrimination of certain features of the data, but also emphasizes unified model performance across devices. Each client has its own unique data distribution, which may cause inconsistent execution of the global model on different clients. The dominant data features of some clients will cause performance differences. The fairness of federated learning needs to ensure that all clients can benefit equally from the learning process and will not cause poor learning performance of some clients. Through collaborative learning, each client can not only learn the features of the global model, but also optimize the personalized model according to the local data distribution to improve personalized performance. At the same time, the fairness optimization mechanism ensures that the performance of the global model on each client is more balanced by dynamically adjusting the client weights, thereby achieving higher consistency and fairness among clients. The tilted adjustment of the loss function is adopted by tilted empirical risk minimization, and the weight of each client is dynamically adjusted based on the performance of the client, and the clients with poor performance (i.e., clients with larger losses) are optimized first to improve the performance of the model on these clients. The central server receives the model parameters and corresponding losses uploaded by each client, and calculates based on the losses of each client. This tilted loss increases the weight of the client with larger losses. Compute the logarithmic mean of the sum of the weighted exponentials of each client's loss function, a step known as computing the tilted objective:

[0062]

[0063] Where f(x i ,W) represents the loss difference between the local model of client i and the global model, is the number of participating clients in round t, and τ is the temperature parameter used to control the degree of weighting. Based on the historical estimate of the previous round, update the current empirical tilt estimate:

[0064]

[0065] Where λ is a smoothing coefficient used to balance the historical estimate and the new estimate of the current round. Finally, the updated experience tilt is used To calculate the new weight of client i

[0066]

[0067] These steps are critical to ensure that the model training process takes into account the distribution and loss characteristics of different customers. When the value of τ is small, the model is more inclined to average the loss, and when τ is large, the model tends to favor customers with larger losses, making abnormal customers have a greater impact on the model, thereby making the model more fair. However, setting a too large value of τ may cause the model to focus only on the clients with the largest losses, resulting in an unstable model training process.

[0068] Based on this, the overall optimization objective of this method is updated as:

[0069]

[0070] in

[0071] Furthermore, in step S5, the server aggregates model updates from multiple clients to generate a new set of model parameters. The data flow diagram of the specific client is as follows: Figure 3 Specifically, the update is performed according to the following formula:

[0072]

[0073] Where λ represents the learning rate of server aggregation, represents the client set selected in round t. A set of new model parameters generated is sent to the training clients in a new round, and the cycle continues until the global model of the central server converges.

[0074] In addition, in addition to providing a personalized federated learning method, the present invention also provides a personalized federated learning system, which specifically includes:

[0075] Local training module: used for the client to perform local training on the received global model and then upload the model parameters, wherein the local training steps include: learning global information under the guidance of local category embedding, and guiding the learning of personalized models by co-training global and personalized features;

[0076] Update module: used by the central server to perform dynamic weighted optimization updates based on all received model parameters.

[0077] In specific implementation, the above modules can be implemented as independent entities, or can be arbitrarily combined and implemented as the same or several entities. The specific implementation of the above units can refer to the previous method embodiments, which will not be repeated here.

[0078] Figure 4 This is a schematic diagram of the structure of a computer device disclosed in the present invention. Figure 4 As shown, the computer device 400 includes at least a memory 402 and a processor 401; the memory 402 is connected to the processor via a communication bus 403, and is used to store computer instructions executable by the processor 401, and the processor 401 is used to read computer instructions from the memory 402 to implement the steps of the method described in any of the above embodiments.

[0079] For the above-mentioned device embodiments, since they basically correspond to the method embodiments, the relevant parts can refer to the partial description of the method embodiments. The device embodiments described above are only schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the disclosed solution. A person of ordinary skill in the art can understand and implement it without paying any creative work.

[0080] Computer readable media suitable for storing computer program instructions and data include all forms of non-volatile memory, media and memory devices, including, for example, semiconductor memory devices (e.g., EPROM, EEPROM and flash memory devices), magnetic disks (e.g., internal disks or removable disks), magneto-optical disks, and CD ROM and DVD-ROM disks. The processor and memory may be supplemented by, or incorporated in, special purpose logic circuits.

[0081] Finally, it should be noted that although this specification contains many specific implementation details, these should not be interpreted as limiting the scope of any invention or the scope of protection claimed, but are mainly used to describe the features of specific embodiments of specific inventions. Certain features described in multiple embodiments within this specification may also be implemented in combination in a single embodiment. On the other hand, the various features described in a single embodiment may also be implemented separately in multiple embodiments or in any suitable sub-combination. In addition, although features may work in certain combinations as described above and even initially claimed as such, one or more features from the claimed combination may be removed from the combination in some cases, and the claimed combination may point to a sub-combination or a variation of a sub-combination.

[0082] Similarly, although operations are depicted in a particular order in the accompanying drawings, this should not be understood as requiring that these operations be performed in the particular order shown or performed sequentially, or requiring that all illustrated operations be performed to achieve the desired results. In some cases, multitasking and parallel processing may be advantageous. In addition, the separation of various system modules and components in the above-described embodiments should not be understood as requiring such separation in all embodiments, and it should be understood that the described program components and systems can generally be integrated together in a single software product, or packaged into multiple software products.

[0083] Thus, specific embodiments of the subject matter have been described. Other embodiments are within the scope of the appended claims. In some cases, the actions recited in the claims can be performed in a different order and still achieve the desired results. In addition, the processes depicted in the drawings do not necessarily require the particular order or sequential order shown to achieve the desired results. In some implementations, multitasking and parallel processing may be advantageous.

[0084] The above description is only a preferred embodiment of the present disclosure and is not intended to limit the present disclosure. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present disclosure shall be included in the scope of protection of the present disclosure.

Claims

1. A personalized federated learning method, characterized in that: The steps include: The client performs local training on the received global model and then uploads the model parameters. The central server performs dynamic weighted optimization updates based on all received model parameters. The local training method includes: learning global information under the guidance of local category embedding, and guiding the learning of personalized models by collaboratively training global and personalized features.

2. The personalized federated learning method according to claim 1, characterized in that: After performing the weighted optimization update, the central server uses the previously determined weights to perform a global aggregate update to obtain the next round of model training parameters, and returns to the initial step to perform local training until the global model of the central server converges. The global aggregate update is based on the following formula: Where λ represents the learning rate of server aggregation, Represents the set of clients selected in round t.

3. The personalized federated learning method according to claim 1, characterized in that: The steps of learning global information under the guidance of local category embedding include: Extract feature information from the client's feature vector and convert the original features into global features and personalized features; The embedding vector of each category is extracted based on the global features, and a local category embedding matrix is ​​generated to guide the learning of global information.

4. The personalized federated learning method according to claim 3, characterized in that: Methods for converting original features into global features and personalized features include: Mapping the data samples to a lower space of dimension k through φ is represented as Get the original feature vector V i , V i =φ(x i ;w f ); The original feature vector V is transformed into i Convert to global eigenvector and personalized feature vector Perform global feature extraction and personalized feature extraction respectively: Where 1 and V i Have the same shape, all values ​​are equal to 1, σ is the ReLU activation function, ⊙ is the Hadamard product, first V i Each element of is scaled by a factor of ε or ε i After scaling, V i Each element of i , and finally the ReLU activation function is applied.

5. The personalized federated learning method according to claim 4, characterized in that: The calculation formula for generating the local category embedding matrix is ​​as follows: g i =E(u;C i ) Where E(u;C i ) is the client's local category embedding model, which is used to store the embedding vector of the local category and use the global feature through the lookup operation. Extract the category ID u, use these indices to look up in the embedding layer and return the corresponding embedding vectors, for the personalized condition input p i , get the data distribution of client i: Where U is the number of all categories, As the indicator function, these embedding vectors are combined with the global features Generate a local category embedding matrix.

6. The personalized federated learning method according to claim 1, characterized in that: The training method of collaboratively training global and personalized features to guide learning of personalized models includes: Clients train their personalized models w1,…,w K , K clients are given a training data set distributed by There are different labels / tasks in the generated dataset, and the personalized target on client i is expressed as: in is the personalized loss function, w i are all module parameters on client i, and for all clients, the optimization objective is: in is the number of training samples on client i.

7. The personalized federated learning method according to claim 6, characterized in that: When uploading model parameters, embedding layer parameters are not uploaded to keep them optimized locally. The optimization methods include: All clients share the global parameter W = {w f ,D}, and the trainable parameters are expressed as The client uses the global features generated by the global model parameters sent down to optimize through contrast loss. The local loss function of contrast loss is: Where l is the cross entropy loss function and μ is a hyperparameter.

8. The personalized federated learning method according to claim 6, characterized in that: The method for dynamic weighted optimization and updating comprises: The central server receives the model parameters and corresponding losses uploaded by each client, and calculates the logarithmic mean of the weighted sum of the exponentials of each client's loss function: Where f(x i ,W) represents the loss difference between the local model of client i and the global model, is the number of participating clients in round t, τ is the temperature parameter used to control the degree of weighting, and the current empirical tilt estimate is updated based on the historical estimate of the previous round: Where λ is the smoothing coefficient, which is used to balance the historical estimate and the new estimate of the current round, and finally use the updated experience tilt To calculate the new weight of client i The overall optimization objective is updated as: in 9. A learning system using the personalized federated learning method according to any one of claims 1 to 8, characterized in that: include: Local training module: used for the client to perform local training on the received global model and then upload the model parameters, wherein the local training steps include: learning global information under the guidance of local category embedding, and guiding the learning of personalized models by co-training global and personalized features; Update module: used by the central server to perform dynamic weighted optimization updates based on all received model parameters.

10. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps of the personalized federated learning method as described in any one of claims 1 to 8 are implemented.