A group personalized federated learning method based on Moreau envelope

Abstract

The present invention relates to a group personalized federated learning method based on Morrow envelope, which belongs to the field of wireless communications. The method mainly includes: constructing a wireless edge network system consisting of several user nodes, their corresponding sub-servers and an edge server, wherein the user nodes connected to the same sub-server are called a group; establishing a mutually decoupled two-layer parallel federated learning optimization problem, wherein the first layer is an edge group personalized optimization problem improved based on Morrow envelope, and the second layer is a federated optimization problem within the group; promoting the group and the associated sub-server to collaborate in training a personalized model, and updating the corresponding group model according to the personalized model obtained by iteration. The group personalized federated learning method based on Morrow envelope proposed in the present invention can effectively improve the performance of the federated wireless edge network model under the Non-IID data setting at the group level.

Description

Technical Field

[0001] The present invention belongs to the field of wireless communications and relates to a group personalized federated learning method based on Morrow envelope. Background Art

[0002] Federated learning (FL), an emerging distributed machine learning paradigm, has attracted widespread attention from both industry and academia due to its ability to train a suitable global model for all participating user devices while preserving user data privacy. However, traditional FL faces numerous challenges. For example, its performance degrades significantly when faced with large amounts of heterogeneous device data. This problem is particularly pronounced when applied to the edge of mobile networks, resulting in the trained global model failing to generalize well to every user device.

[0003] Data heterogeneity stems from differences in user device attributes, preferences, and data collection patterns. To address the challenges posed by data heterogeneity to federated learning, personalized federated learning (PFL) has been proposed. Its core is to develop a personalized solution for each participating user device. Compared to traditional FL, PFL pays more attention to data differences between different user devices, thereby maximizing model performance. Currently, various PFLs have been proposed that effectively address the challenges of data heterogeneity, but most designs remain at the individual level. Proposed group personalized federated learning (GPFL) methods, such as synchronous group personalized federated learning with attention message passing (AMP-GPFL), require less computing power from user devices and have a limited scope of application. Summary of the Invention

[0004] In view of this, the object of the present invention is to provide a group personalized federated learning method based on Morrow envelope.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] A group personalized federated learning method based on Moreau envelope, the method comprising the following steps:

[0007] S1: Establish an edge network system consisting of several user nodes, several sub-servers and an edge server, where a sub-server and the user nodes connected to it constitute an edge group;

[0008] S2: Establish a personalized federated learning model with decoupled two-layer parallel optimization, including optimization problems between edge groups based on the improved Moreau envelope, and FL optimization problems within an edge group;

[0009] S3: The user group and the associated sub-server collaborate to train and update the personalized model, and then use the obtained personalized model to update the corresponding personalized group model;

[0010] S4: The edge server collects personalized group models from the sub-servers, updates the global model in an aggregated manner, and then returns it to the corresponding sub-server;

[0011] S5: Repeat S3 and S4. After several iterations, the convergence condition will be reached.

[0012] Furthermore, the S1 specifically includes the following contents:

[0013] Establish an edge network system consisting of N user nodes, M sub-servers and an edge server; Represents a collection of sub-servers, Represents a collection of user nodes; the sub-server is connected to the edge server through a wired backhaul link, and each sub-server serves a group of user nodes that do not interfere with each other; each sub-server The set of user nodes it serves Constitute an edge group m, where The sub-server and the user node communicate through a wireless channel. During the communication process, the user device may lose connection with the sub-server due to insufficient power or unstable network connection. The user device is not always available to participate in model training. m,n ∈{0,1} represents the availability status of user device n in group m, X m,n =1 means user device n can participate in model training, X m,n =0 means that user device n cannot participate in model training; define the devices in group m The probability of participating in model training is User devices in group m The dataset used is represented as The total data set of group m is then expressed as And the dataset of each user device in group m The distribution between them is non-IID.

[0014] Furthermore, the step S2 specifically includes the following steps:

[0015] Establish the FL optimization problem P1 for edge groups:

[0016] P1:

[0017] Among them, w is defined as the global model, w *represents the optimal solution of the optimization problem P1; F m (w) is related to the Morrow envelope and is defined as the following optimization problem P2:

[0018] P2:

[0019] Among them, u m is defined as the personalized model for group m; λ is a regularization parameter used to control u m The difference between w; f m (u m ) represents the training loss of all users in group m The sum of f n (u m ) represents the personalized model u m On user equipment Local dataset The loss function on the θ; in the two-layer parallel optimization process represented by P1 and P2, problem P1 is to solve the outer optimization problem of the global model w, and problem P2 is to solve the personalized model u m The inner optimization problem of the two optimization problems is decoupled from each other; define the personalized model u m The optimal solution is The local optimal solution of problem P1 is in Furthermore, the local optimal solution Calculated by the following formula:

[0020]

[0021] The above solution is the local optimal solution The calculation process adopts the gradient descent method, where α is the gradient descent step size.

[0022] Furthermore, the step S3 specifically includes the following steps:

[0023] S31: The sub-server sends the latest group model to all corresponding user nodes. The content is as follows:

[0024] use represents the global iteration index, where is the index set of T global iterations; use e∈E to represent the index of group iteration, where is the index set of E group iterations; the group model of group m after the e-th group iteration in the t-th global iteration is expressed as

[0025] Before each global iteration starts the group iteration, the group model Initialized to w t-1 ;

[0026] Sub-server m will update the latest group model Broadcast to all participants in group m User node;

[0027] S32: The user group and the associated sub-server collaborate to train a personalized model, as follows:

[0028] User device n in group m calculates the local user model by performing K steps of stochastic gradient descent (user device n is based on the local dataset The model obtained by updating the following formula)

[0029]

[0030] in, η t represents the step size, f n (·) represents the loss function of the user device;

[0031] S33: The sub-server aggregates the models uploaded by the available devices, updates the obtained personalized model, and updates the group model. The content is as follows:

[0032] 1) Sub-server m aggregates all models of user devices in group m that can participate in training To generate a personalized model:

[0033]

[0034] 2) According to the above local optimal solution The calculation process of , the update process of the group model in the e-th group iteration is as follows:

[0035]

[0036] 3) After E group iterations, the group model update task is completed and a personalized model is obtained and group models

[0037] Furthermore, the S4 specifically includes the following steps:

[0038] S41: Edge server collects group model, the content is as follows:

[0039] At the tth iteration of the model, the edge server receives data from all child servers. Get the group model

[0040] S42: The edge server aggregates the collected group models and updates the global model, which is as follows:

[0041] The edge server aggregates the group model and updates the global model using the following formula:

[0042]

[0043] Among them, the constant β>0 is used to control the aggregation of group models on the global model w t degree of impact.

[0044] Furthermore, the S5 specifically includes the following steps:

[0045] Repeat S3 and S4. Each time a global iteration is performed, the global iteration index t is updated to t+1 until the specified number of global iterations T is reached. The iteration is stopped and the solution w of problem P1 is obtained. T and the solution to problem P2

[0046] The beneficial effects of the present invention are:

[0047] (1) This invention breaks the inherent situation of personalized federated learning methods that are only oriented to individuals and proposes a group personalized federated learning method based on the Morrow envelope. The user device nodes connected to the same edge sub-server are grouped together. The personalized group model is trained between the groups through a two-layer parallel optimization mechanism, which includes an inner optimization problem based on the Morrow envelope and an optimization problem based on the federated averaging mechanism. The group model is trained within the group through the federated averaging mechanism.

[0048] (2) The present invention promotes the collaborative training of personalized group models between edge sub-servers and their connected user device nodes through a two-layer parallel optimization mechanism between groups, thereby improving the generalization ability of the model. At the same time, the final model convergence effect of the present invention is better when facing user devices with higher computing power.

[0049] (3) The present invention trains the group model through the intra-group federated averaging mechanism, which can reduce the impact of changes in device availability on training.

[0050] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following description or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below with reference to the accompanying drawings, in which:

[0052] Figure 1A flowchart of a group personalized federated learning method based on Moreau envelope;

[0053] Figure 2 This is a system architecture diagram of a group personalized federated learning method based on Moreau envelope;

[0054] Figure 3 The average test accuracy of the proposed method and the comparative method under different device availability when the number of devices is fixed, the device group division is fixed, and the device data is non-independent and identically distributed (non-IID). DETAILED DESCRIPTION

[0055] The following describes the embodiments of the present invention by means of specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways 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 illustrations of the basic concept of the present invention, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0056] Among them, the accompanying drawings are only for illustrative purposes and represent only schematic diagrams rather than actual pictures, and should not be understood as limiting the present invention. In order to better illustrate the embodiments of the present invention, some parts of the accompanying drawings may be omitted, enlarged or reduced, and do not represent the dimensions of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions may be omitted in the accompanying drawings.

[0057] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", "front", "back", etc. indicating directions or positional relationships, they are based on the directions or positional relationships shown in the drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operate in a specific direction. Therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0058] The present invention provides a group personalized federated learning method based on Morrow envelope, which is applicable to group non-IID data sets in high equipment computing power scenarios; the process of the method is as follows Figure 1 As shown, the following steps are included:

[0059] S1, establish Figure 2The wireless edge network system model and edge device availability model shown are as follows:

[0060] Establish an edge network system consisting of N user nodes, M sub-servers and an edge server. Represents a collection of sub-servers, Represents a collection of user nodes. In the system model proposed by this invention, the sub-server and the edge server are connected through a wired backhaul link, and each sub-server serves a group of user nodes that do not interfere with each other. Each sub-server The set of user nodes it serves Constitute an edge group m, where The sub-server and the user node communicate through a wireless channel. During the communication process, the user device may lose connection with the sub-server due to insufficient power, unstable network connection, etc. Therefore, the user device is not always available to participate in model training. m,n ∈{0,1} represents the availability status of user device n in group m. Specifically, X m,n =1 means user device n can participate in model training, X m,n =0 means that user device n cannot participate in model training; define the devices in group m The probability of participating in model training is User devices in group m The dataset used is represented as Thus the total data set of group m can be expressed as And the dataset of each user device in group m The distribution between them is non-IID;

[0061] S2, establishes a personalized federated learning optimization problem with two-layer parallel optimization, including the optimization problem between edge groups based on the improvement of Morrow envelope, and the FL optimization problem within an edge group. The specific contents are as follows:

[0062] 1) Establish the FL optimization problem P1 for edge groups:

[0063] P1:

[0064] Among them, w is defined as the global model, w * represents the optimal solution to the optimization problem P1;

[0065] 2)F m (w) is related to the Morrow envelope and can be defined as the following optimization problem P2:

[0066] P2:

[0067] Among them, u m is defined as the personalized model for group m; λ is a regularization parameter used to control u m The difference between w; f m (u m ) represents the training loss of all users in group m The sum of f n (u m ) represents the personalized model u m On user equipment Local dataset The loss function on the θ; in the two-layer parallel optimization process represented by P1 and P2, problem P1 is to solve the outer optimization problem of the global model w, and problem P2 is to solve the personalized model u m The inner optimization problem of the two optimization problems is decoupled from each other; define the personalized model u m The optimal solution is The local optimal solution of problem P1 is in Furthermore, the local optimal solution It can be calculated by the following formula:

[0068]

[0069] The above solution is the local optimal solution The calculation process adopts the gradient descent method, where α is the gradient descent step size.

[0070] S3 includes the following sub-steps:

[0071] In sub-S31, the sub-server collects and sends the latest group model to the user node and defines the model update parameters. The specific contents are as follows:

[0072] use represents the global iteration index, where is the index set of T global iterations; use e∈E to represent the index of group iteration, where is the index set of E group iterations; the group model of group m after the e-th group iteration in the t-th global iteration is expressed as

[0073] Before each global iteration starts the group iteration, the group model Initialized to w t-1 ;

[0074] Sub-server m will update the latest group model Broadcast to all participants in group m User node;

[0075] In sub-S32, the user device and the associated sub-server collaborate to train a personalized model. The specific contents are as follows:

[0076] User device n in group m calculates the local user model by performing K steps of stochastic gradient descent (user device n is based on the local dataset The model obtained by updating the following formula)

[0077]

[0078] in, η t represents the step size, f n (·) represents the loss function of the user device;

[0079] In sub-S33, the sub-server aggregates the personalized models uploaded by the user devices and updates the group model. The specific contents are as follows:

[0080] S33: The sub-server aggregates the models uploaded by the available devices, updates the obtained personalized model, and updates the group model. The content is as follows:

[0081] Sub-server m aggregates all models of user devices in group m that can participate in training To generate a personalized model:

[0082]

[0083] According to the above local optimal solution The calculation process of , the update process of the group model in the e-th group iteration is as follows:

[0084]

[0085] After E group iterations, the group model update task is completed and a personalized model is obtained. and group models

[0086] S4, specifically includes the following sub-steps:

[0087] In sub-S41, the edge server collects the group model from the sub-servers, the specific content is as follows:

[0088] At the tth iteration of the model, the edge server receives data from all child servers. Get the group model

[0089] In sub-S42, the edge server aggregates the group model and updates the global model. The specific contents are as follows:

[0090] The edge server aggregates the group model and updates the global model using the following formula:

[0091]

[0092] Among them, the constant β>0 is used to control the aggregation of group models on the global model w t degree of impact.

[0093] S5 can be regarded as judging whether the model has reached the convergence condition. The specific contents are as follows:

[0094] Repeat S3 and S4. Each time a global iteration is performed, the global iteration index t is updated to t+1 until the specified number of global iterations T is reached. The iteration is stopped and the solution w of problem P1 is obtained. T and the solution to problem P2

[0095] Furthermore, the present invention conducts simulation experiments in the constructed wireless edge network system model through the proposed solution, and the specific results are as follows: Figure 3 As shown;

[0096] Furthermore, if Figure 3 As shown in the figure, the present invention uses the CIFAR-10 dataset to show the relationship between the average test accuracy of the federated learning system and the number of model iterations under different training schemes and different user availability probabilities. Among them, the individual personalized federated learning scheme is a scheme based on the Morrow envelope that targets individual-level data heterogeneity, the comparative group personalized federated learning scheme is a scheme based on the attention message transmission mechanism that targets group-level data heterogeneity, and the traditional federated averaging scheme is a scheme based on traditional federated averaging that targets individual-level data heterogeneity.

[0097] Figure 3 The paper shows that when the number of devices is fixed, the user device groups are divided, the group data is non-independent and identically distributed (non-IID), and the device computing power is high, the group personalized federated learning scheme proposed in this invention is compared with comparison schemes 1, 2, and 3 under different device availability probabilities. Among them, comparison scheme 1 is a group personalized federated learning scheme based on the attention message passing mechanism, comparison scheme 2 is an individual personalized federated learning scheme based on the Morrow envelope, and comparison scheme 3 is traditional federated learning. Specifically, from Figure 3 The following content can be obtained:

[0098] 1) The performance of the individual personalized federated learning scheme is significantly better than that of traditional federated learning, proving its effectiveness when the data is non-IID distributed and can alleviate the shortcomings of traditional federated learning.

[0099] 2) Compared with the individual-level personalized federated learning solution, the group-level personalized federated learning solution performs better when the group data distribution is non-IID, demonstrating the superiority of the group-level personalized federated learning solution.

[0100] 3) The performance of the group-personalized federated learning solution based on the Morrow envelope proposed in this paper is further superior to the group-personalized federated learning solution based on the attention message passing mechanism, demonstrating that the advantages of the proposed solution are more obvious in scenarios with higher device computing power requirements;

[0101] 4) For individual personalized federated learning schemes, the device availability probability ρ m,n When the performance is greatly reduced, the performance is greatly reduced, but the solution proposed in this invention is almost not affected by ρ m,n The impact of the changes proves the robustness of the proposed scheme when some devices are unavailable;

[0102] comprehensive Figure 3 Analysis shows that the solution proposed in this invention can effectively improve model performance in realistic wireless edge network scenarios where the data distribution at the group level is non-IID and the device computing power requirements are high.

[0103] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, which should all be included in the scope of the claims of the present invention.

Claims

1. A group personalized federated learning method based on Moreau envelope, characterized by: The method comprises the following steps: S1: Establish an edge network system consisting of several user nodes, several sub-servers, and an edge server, wherein a sub-server and the user nodes connected to it constitute an edge group; specifically, the following are included: Establish an edge network system consisting of N user nodes, M sub-servers and an edge server; Represents a collection of sub-servers, Represents a collection of user nodes; the sub-server is connected to the edge server through a wired backhaul link, and each sub-server serves a group of user nodes that do not interfere with each other; each sub-server The set of user nodes it serves Constitute an edge group m, where The sub-server and the user node communicate through a wireless channel. During the communication process, the user device may lose connection with the sub-server due to insufficient power or unstable network connection. The user device is not always available to participate in model training. m,n ∈{0,1} represents the availability status of user device n in group m, X m,n =1 means user device n can participate in model training, X m,n =0 means that user device n cannot participate in model training; define the devices in group m The probability of participating in model training is User devices in group m The dataset used is represented as The total data set of group m is then expressed as And the dataset of each user device in group m The distribution between them is non-IID; S2: Establish a personalized federated learning model with decoupled two-layer parallel optimization, including optimization problems between edge groups based on the improved Moreau envelope, and federated learning optimization problems within an edge group. The specific steps include: Establish the FL optimization problem P1 for edge groups: Among them, w is defined as the global model, w * represents the optimal solution of the optimization problem P1; F m (w) is related to the Morrow envelope and is defined as the following optimization problem P2: Among them, u m is defined as a personalized model for group m; λ is a regularization parameter used to control u m The difference between w; f m (u m ) represents the training loss of all users in group m The sum of f n (u m ) represents the personalized model u m On user equipment Local dataset The loss function on the θ; in the two-layer parallel optimization process represented by P1 and P2, problem P1 is to solve the outer optimization problem of the global model w, and problem P2 is to solve the personalized model u m The inner optimization problem of the two optimization problems is decoupled from each other; define the personalized model u m The optimal solution is The local optimal solution of problem P1 is in Furthermore, the local optimal solution Calculated by the following formula: The above solution is the local optimal solution The calculation process adopts the gradient descent method, where α is the gradient descent step size; S3: The user group and the associated sub-server collaborate to train and update the personalized model, and then use the obtained personalized model to update the corresponding personalized group model; S4: The edge server collects personalized group models from the sub-servers, updates the global model in an aggregated manner, and then returns it to the corresponding sub-server; S5: Repeat S3 and S4. After several iterations, the convergence condition will be reached.

2. The group personalized federated learning method based on Morrow envelope according to claim 1, characterized in that: The S3 specifically includes the following steps: S31: The sub-server sends the latest group model to all corresponding user nodes. The content is as follows: use represents the global iteration index, where is the index set of T global iterations; use e∈E to represent the index of group iteration, where is the index set of E group iterations; the group model of group m after the e-th group iteration in the t-th global iteration is expressed as Before each global iteration starts the group iteration, the group model Initialized to w t-1 ; Sub-server m will update the latest group model Broadcast to all user nodes in group m that can participate in training; S32: The user group and the associated sub-server collaborate to train a personalized model, as follows: User device n in group m computes the local user model by performing K steps of stochastic gradient descent in, η t represents the step size, f n (·) represents the loss function of the user device; S33: The sub-server aggregates the models uploaded by the available devices, updates the obtained personalized model, and updates the group model. The content is as follows: 1) Sub-server m aggregates all models of user devices in group m that can participate in training To generate a personalized model: 2) According to the above local optimal solution The calculation process of , the update process of the group model in the e-th group iteration is as follows: 3) After E group iterations, the group model update task is completed and a personalized model is obtained and group models 3. The group personalized federated learning method based on Morrow envelope according to claim 1, characterized in that: The S4 specifically includes the following steps: S41: Edge server collects group model, the content is as follows: At the tth iteration of the model, the edge server receives data from all child servers. Get the group model S42: The edge server aggregates the collected group models and updates the global model, which is as follows: The edge server aggregates the group model and updates the global model using the following formula: Among them, the constant β>0 is used to control the aggregation of group models on the global model w t degree of impact.

4. The group personalized federated learning method based on Morrow envelope according to claim 3 is characterized by: The S5 specifically includes the following steps: Repeat S3 and S4. Each time a global iteration is performed, the global iteration index t is updated to t+1 until the specified number of global iterations T is reached. The iteration is stopped and the solution w of problem P1 is obtained. T and the solution to problem P2

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