A wireless federated learning framework and resource optimization method

Abstract

The application discloses a wireless federated learning framework and a resource optimization method, solves the problem that federated learning is not applicable to many hardware limited Internet of Things devices with small amount of computing resources, in the framework, a user with sufficient computing resources uploads a locally trained model parameter to a base station, and a user with limited computing resources only needs to send training data to the base station, and then obtains a global model through data training and model aggregation at the base station end, thereby meeting the demand of the user with limited computing resources and the user with sufficient computing resources for cooperative training of the global model. In addition, in order to improve the data transmission rate and reduce the aggregation error of federated learning, the application constructs a non-convex optimization problem to jointly design the sending power of the user and the receiving strategy of the base station, and uses a continuous convex approximation method to solve the problem.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of wireless resource management and computer technology, and in particular to a wireless federated learning framework and resource optimization method. BACKGROUND

[0002] By deploying a large number of Internet of Things devices such as low-end sensors, high-definition cameras and advanced robots at the edge of the network, the next generation network will be able to support a variety of emerging applications such as smart factories, autonomous driving, interactive games and metaverse, and the successful implementation of these applications is based on the full use of huge amounts of data.

[0003] Traditional centralized learning requires the collection of data samples from edge users, however, a large amount of data is distributed on terminals isolated from each other in geographical locations, which brings huge communication overhead to centralized learning, and considerable transmission delay will affect the real-time performance of the application. In addition, direct transmission of raw data will bring the risk of privacy leakage to individual users.

[0004] In order to solve the main challenges faced by centralized learning, federated learning allows users to perform model updates locally, thereby avoiding the transmission of raw data. Compared with centralized learning, the core idea of federated learning is to replace data upload with model sharing, which not only plays an important role in protecting user privacy, but also greatly reduces the communication burden.

[0005] The success of federated learning depends on the rich computing resources on Internet of Things terminals, however, this is impractical for many hardware-limited Internet of Things devices. For example, low-end sensors with limited computing resources. Therefore, it is extremely challenging to directly implement existing (centralized or federated) machine learning frameworks in heterogeneous Internet of Things devices with different computing capabilities.

[0006] In order to solve these challenges, it is necessary to explore new machine learning frameworks to relax the computing requirements of these resource-limited Internet of Things devices. In addition, in order to improve the rate of data transmission and reduce the aggregation error of federated learning, it is very important to propose new learning and optimization methods to fully utilize the distributed data and computing resources of the federated learning server and all clients. SUMMARY

[0007] The present application is directed to the deficiencies of the prior art, and proposes a wireless federated learning framework and resource optimization method.

[0008] In order to achieve the above purpose, the present application provides the following technical solutions:

[0009] The application provides a wireless federated learning framework, comprising:

[0010] N computing resource-limited centralized training users, which send training data to a base station for centralized training to participate in federated learning;

[0011] K computing resource-sufficient federated learning users, which obtain local models by training local data, and then upload local model parameters to the base station as aggregated models;

[0012] The base station is used as a federated learning server to calculate a global model; the base station performs centralized training on the training data accumulated by the centralized training users, obtains a centralized training model, and obtains the global model by weighted summation of the centralized training model and the received aggregated model according to data volume.

[0013] Further, it is assumed that there are T federated learning cycles, denoted as At the tth federated learning cycle, the local model update formula of the kth federated learning user is:

[0014]

[0015] The centralized update formula at the base station end is:

[0016]

[0017] The global model aggregation formula is:

[0018]

[0019] Wherein, η is the learning rate of the stochastic gradient descent method, is the training data set accumulated at the base station end in t cycles, F k (·) and are the local loss function and gradient of the kth federated learning user, respectively, F(·) and are the loss function and gradient when the base station end is centrally trained, respectively, is the global model aggregated at the base station end.

[0020] The application also provides a resource optimization method of the wireless federated learning framework, comprising the following steps:

[0021] S1, the base station initializes a training task and a global model, and sends the global model to all users;

[0022] S2, after receiving the global model, the federated learning user calculates a local loss function and a gradient value based on local data, and updates the local model;

[0023] S3, federated learning users and centralized training users upload local models and send data at the same time using the same frequency band. The base station uses imperfect continuous interference cancellation to detect the received signal and separate the training data and the aggregated model.

[0024] S4. Obtain the data transmission rate of all centralized training users and the aggregated model mean square error of federated learning users, and use imperfect continuous interference cancellation to detect the signals of all centralized training users in the order of 1, 2, ..., N.

[0025] S5. Construct a non-convex optimization problem based on data transmission rate and the mean square error of the aggregation model;

[0026] S6. Use the continuous convex approximation method to transform and solve the non-convex optimization problem in S5, and output the user's transmit power and receive strategy.

[0027] Furthermore, in step S2, the local loss function is either the mean squared error loss function or the cross-entropy loss function.

[0028] Furthermore, the specific process of step S3 is as follows:

[0029] Before users upload their local models or send data, the user's local training dataset will be centrally trained. and local models of federated learning users {w k} are normalized to the communication symbol set {s} n} and computation symbol set {s k The superimposed signal received by the base station is as follows:

[0030]

[0031] Among them, h n (h k ) is the channel parameter from the nth (kth) user to the base station, p n (p k ) is the transmission power of the nth (kth) user and its value must be in the interval [0, P]. max ]Inside, It is additive noise in the channel;

[0032] By adjusting the user's transmit power, the SIC limit for different users is satisfied:

[0033]

[0034] After receiving the superimposed signal y, the base station sequentially detects the uploaded signals {s} of the 1st, 2nd, ..., Nth centralized training users. n After detecting the signals from all centralized training users, the remaining signals are as follows:

[0035]

[0036] in, It is the interference coefficient of the residual signal. and These correspond to the cases of perfect SIC and no SIC, respectively.

[0037] To obtain the average federated learning model, the base station uses a reception factor 'a' from the aforementioned residual signals. To obtain the estimated value of the aggregation model. After inverse normalization post-processing, from signal {s n}and The dataset and aggregated model of all centralized training users are decoded.

[0038] Furthermore, in step S4, the formula for the data transmission rate of the nth centralized training user is:

[0039]

[0040] in, It is the interference coefficient of the residual signal. and Corresponding to the cases of perfect SIC and no SIC respectively, the sum of all user data transmission rates is:

[0041] Furthermore, in step S4, the formula for the mean squared error of the aggregation model is:

[0042]

[0043] in, It is interference with the signals of centralized training users.

[0044] Furthermore, in step S5, the nonconvex optimization problem is constructed as follows:

[0045]

[0046]

[0047]

[0048] MSE≤∈0,

[0049]

[0050] Where p = [p1, p2, ..., p N ,p N+1 ,…,p N+K ] is the transmission power, R minis the minimum data transmission rate required by centralized training users, P max is the maximum transmission power of all users, ∈0is the maximum aggregated model error that the federated learning users can tolerate, λ is a constant used to balance between and the rate R sum and the mean square error MSE.

[0051] Further, the transformed convex optimization problem in step S6 is as follows:

[0052]

[0053]

[0054]

[0055] MSE≤∈0,

[0056]

[0057]

[0058]

[0059] where γ = [γ1, γ2, …, γ N ] and b = [b1, b2, …, b N ,b N+1 ,b N+2 ,…, b N+K ] are auxiliary vectors introduced, τ in and τ jn are CUB coefficients.

[0060] Further, the solving steps of the convex optimization problem in step S6 are as follows:

[0061] S6.1 initialize p (0) , a (0) , γ (0) , b (0) , the maximum number of iterations L, the threshold ε, set the iteration index l = 0;

[0062] S6.2 calculate the objective function value

[0063] S6.3 given p (l) , a (l) , γ (l) , b (l) , update and and and

[0064] S6.4 Given and , solve the above convex optimization problem using the mathematical tool CVX to obtain p (l+1) , a (l+1) , γ (l+1) , b (l+1) ;

[0065] S6.5 Calculate the objective function value

[0066] S6.6 Update l = l + 1, and calculate Δ U = |U (l) -U (l-1) |;

[0067] S6.7 Repeat steps S6.3-S6.6 until Δ U ≤ ε or l ≥ L Output the user transmit power p (l-1) and the receiving factor a (l-1) .

[0068] Compared with the prior art, the beneficial effects of the present application are:

[0069] 1) The wireless federated learning framework proposed in the present application can support both users with limited computing resources and users with sufficient computing resources to participate in federated learning, and fully utilize the data on heterogeneous users to improve the performance of machine learning models.

[0070] 2) All users in the present application upload models or send data on the same frequency band at the same time, which can effectively save spectrum resources and reduce communication delay. The base station uses non-perfect SIC to detect signals, which is more in line with the actual situation.

[0071] 3) The resource optimization method proposed in the present application constructs a non-convex optimization problem based on the user data transmission rate and model aggregation MSE, jointly designs the user transmission power and base station receiving strategy, and uses the SCA method to solve it, which can effectively realize the maximization of the rate and the minimization of the MSE. BRIEF DESCRIPTION OF DRAWINGS

[0072] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments described in the present application, and other drawings can also be obtained by those skilled in the art based on these drawings.

[0073] Figure 1 The wireless federated learning framework and the transceiver structure diagram provided by the embodiments of the present application.

[0074] Figure 2 An algorithm flowchart of the resource optimization method of the wireless federated learning framework provided for the embodiments of the present application. DETAILED DESCRIPTION

[0075] The success of federated learning relies on rich computing resources on local users. However, this is impractical for many hardware-limited Internet of Things devices, such as low-end sensors with a small amount of computing resources. To solve the above problem, the present application proposes a wireless federated learning framework to meet the needs of collaborative training of global models by users with limited computing resources and users with sufficient computing resources. In this framework, users with sufficient computing resources upload the locally trained model parameters to the base station, while users with limited computing resources only need to send training data to the base station, and then obtain the global model through data training and model aggregation at the base station end. In addition, in order to improve the rate of data transmission and reduce the aggregation error of federated learning, the present application constructs a non-convex optimization problem to jointly design the transmission power of the user and the reception strategy of the base station, and uses the continuous convex approximation method to solve the problem.

[0076] In order to better understand the technical solution, the method of the present application will be described in detail below in conjunction with the drawings.

[0077] Please refer to Figure 1 , the embodiment includes the following steps:

[0078] S1, a wireless federated learning framework is proposed, which meets the needs of collaborative training of global models by users with limited computing resources and users with sufficient computing resources. In the framework, users with sufficient computing resources upload the trained model parameters to the base station, while users with limited computing resources only need to send training data to the base station;

[0079] As Figure 1 shown, in the architecture, considering N users with limited computing resources and K users with sufficient computing resources, the base station serves as a federated learning server for computing the global model. The users with limited computing resources cannot meet the requirements of local data training due to limited computing power, and can only send training data to the base station for centralized training to participate in federated learning, also known as centralized learning users (Centralized Learning user, abbreviated as CL user), represented by the set ; while the users with sufficient computing resources can train local models on local data, and then upload the local model parameters to the base station, without sending training data, also known as federated learning users (Federated Learning user, abbreviated as FL user), represented by the set .

[0080] S2, the base station centrally trains the accumulated data, obtains a centralized training model, and sums the model and the received aggregated model by data weight to obtain a global model; assuming that there are T federal learning cycles, the set is represented as At the tth cycle, the training data of the nth CL user and the local model of the kth FL user are represented as and The random gradient descent method is used for training, at this time, the user local model update, the base station centralized update, and the global model aggregation expression are represented as follows:

[0081] Local model update:

[0082] Base station centralized update:

[0083] Global model aggregation:

[0084] Where η is the learning rate of the random gradient descent method, is the training data set accumulated at the base station end for t cycles, F k (·) and are the local loss function and gradient of the kth FL user, F(·) and are the loss function and gradient during centralized training at the base station end, is the global model aggregated at the base station end.

[0085] S3, the base station initializes the training task and the global model, and sends the global model to all users;

[0086] S4, the user with sufficient computing resources updates the local model according to the training data; after receiving the global model, the user with sufficient computing resources, i.e., the FL user, calculates the local loss function and the gradient value based on the local data, which can be a mean square error loss function or a cross-entropy loss function, depending on the specific learning task, and then the FL user updates the local model using the local model update expression in step S2.

[0087] S5, the user with sufficient computing resources and the user with limited resources upload the local model and send the data respectively at the same time using the same frequency band, and the base station uses the non-perfect successive interference cancellation (SIC) to detect the received signal and separate the training data and the aggregated model.

[0088] Considering the conflict between limited bandwidth and a massive number of users in practical IoT applications, in order to save communication bandwidth and reduce latency, this invention uses the same time slot and frequency band for all users to upload local models or send data; before users upload their local models or send data, the local training dataset of CL users is... and the local model of FL users {w k} are normalized to the communication symbol set {s} n} and computation symbol set {s k The superimposed signal received by the base station is as follows:

[0089]

[0090] Among them, h n (h k ) is the channel parameter from the nth (kth) user to the base station, p n (p k ) is the transmission power of the nth (kth) user and its value must be in the interval [0, P]. max ]Inside, This refers to additive noise in the channel. After receiving the superimposed signal, the base station uses imperfect SIC detection due to decoding errors to separate the training data and the aggregation model. By adjusting the user's transmit power, the SIC constraints for different users are satisfied.

[0091]

[0092] After receiving the superimposed signal y, the base station sequentially detects the uploaded signals {s} of the 1st, 2nd, ..., Nth CL users. n After detecting signals from all CL users, the remaining signals are as follows:

[0093]

[0094] in, It is the interference coefficient of the residual signal. and These correspond to the cases of perfect SIC and no SIC, respectively. To obtain the average federated learning model, the base station uses a reception factor 'a' from the aforementioned residual signals. To obtain the estimated value of the aggregation model. After further post-processing such as inverse normalization, the signal {s} n}and The dataset and aggregation model of all CL users are decoded.

[0095] S6, obtain the aggregate model mean square error (MSE) of all computing resource-limited user data transmission rates and computing resource-sufficient users; based on the superposition signal expression received by the base station in step S5, all CL user signals are detected in the order of 1, 2, …, N using non-perfect SIC, and the data transmission rate of the nth CL user is:

[0096]

[0097] wherein, is the interference coefficient of the residual signal, and correspond to perfect SIC and no SIC, respectively, and the sum of all user data transmission rates (sum rate) is

[0098] Assuming that the aggregate model obtained by the base station under ideal conditions is and the actual aggregate model obtained in step 5 is The mean square error (MSE) is used to measure the aggregation error, and the MSE expression is as follows:

[0099]

[0100] wherein, is the interference of the CL user signal.

[0101] S7, construct a non-convex optimization problem based on the data transmission rate and the aggregate model MSE; the communication-centric CL user hopes that the data transmission rate can be maximized, and the computing-centric FL user hopes that the aggregate model error MSE can be minimized, in order to simultaneously meet the above requirements of the two types of users, the present application jointly designs the user transmission power and the base station reception strategy, and the optimization problem is constructed as follows:

[0102]

[0103]

[0104]

[0105] MSE≤∈0,

[0106]

[0107] wherein, p = [p1, p2, …, p N , N+1 …, p N+K ] is the transmission power, R min is the minimum data transmission rate required by the CL user, and Pmax is the maximum transmit power of all users, ∈0is the maximum aggregate model error that FL users can tolerate, λ is a constant here, and the purpose is to balance between the sum rate and the MSE. Since the optimization variables p, a are coupled with each other in the objective function and the constraint condition, the above optimization problem is a non-convex optimization problem, and it is difficult to obtain the optimal solution.

[0108] S8, using a successive convex approximation (SCA) method to transform and solve the non-convex optimization problem in S7; in the present application, in order to solve the non-convex optimization problem constructed in step S7, auxiliary variables and are introduced, and then the data transmission rate R n can be rewritten as R n = log2 (1 + γ n ), and the MSE can be rewritten as

[0109]

[0110] Therefore, the non-convex optimization problem in step S7 is transformed into the following optimization problem:

[0111]

[0112]

[0113]

[0114]

[0115]

[0116] MSE≤ ∈0,

[0117]

[0118] where γ = [γ1, γ2, …, γ N ] and b = [b1, b2, …, b N , b N+1 , b N+2 , …, b N+K ] are auxiliary vectors introduced, and here a, {b is the interference received by the nth CL user. At this time, R n is a concave function with respect to {γ n}, and the MSE is a convex function with respect to a and {b i}, so the objective function of the above optimization problem is with respect to a, {b i} and {γ n} is a concave function. It can be seen that, in the above optimization problem, all the constraints are convex except and To transform the two non-convex constraints into convex constraints, the CUB and SCA methods are used.

[0119] To solve the non-convex constraints It can be equivalently transformed into the following expression:

[0120]

[0121] It can be observed that the product terms p i γ n and p j γ n are non-convex. To solve them, the present invention sets f(p i ,γ n ) = p i γ n and the CUB of f(p i ,γ n ) is where τ in is a CUB coefficient. It can be easily proved that f(p in ,γ n ) ≤ g(p i ,γ i ,τ n ) can take equality when τ i = γ n / p in . Similarly, set f(p j ,γ n ) = p j γ n and the CUB of f(p j ,γ n ) is

[0122] After the CUBs of p i γ n and p j γ n are replaced, the original non-convex constraints are transformed into the following convex constraints:

[0123]

[0124] In the above convex constraints, the update of the CUB coefficient τ in is where and are the solutions of the optimization problem at the lth iteration. Similarly, the update of the CUB coefficient τjn The update for

[0125] To address the non-convex constraint At p i ≠ 0, rewrite it as

[0126]

[0127] The non-convexity of the above expression comes from the a 2 term on the left side of the inequality. The present invention uses the first order Taylor expansion of a 2 at the point a l to make the substitution, so the non-convex constraint is transformed into the following convex constraint:

[0128]

[0129] Based on the above approximation, the non-convex optimization problem in step S7 can be transformed into the following convex optimization problem:

[0130]

[0131]

[0132]

[0133] MSE≤∈0,

[0134]

[0135]

[0136]

[0137] The above convex optimization problem can be solved for the optimal solution using the mathematical toolbox CVX.

[0138] As shown in Figure 2 , the steps to solve the non-convex optimization problem in step S7 are as follows:

[0139] S8.1 initialize p (0) , a (0) , γ (0) , b (0) , the maximum number of iterations L, the threshold ε, set the iteration index l = 0;

[0140] S8.2 calculate the objective function value

[0141] S8.3 given p (l) , a (l) , γ(l) , b (l) , a and update and

[0142] S8.4 Solve the above convex optimization problem using the mathematical tool CVX given and , obtain p (l+1) , a (l+1) , γ (l+1) , b (l+1) ;

[0143] S8.5 Calculate the objective function value

[0144] S8.6 Update l = l + 1, and calculate Δ U = |U (l) - U (l-1) |;

[0145] S8.7 Repeat steps S8.3-S8.6 until Δ U ≤ ε or l ≥ L Output the user transmit power p (l-1) and the receiving factor a (l-1) ;

[0146] Here, the user's transmit power has an upper bound and the value of MSE is non-negative, so the objective function of the optimization problem has an upper bound, and the convergence of the above iterative algorithm can be guaranteed.

[0147] S9, The user uses the transmit power solved in S8 to transmit local models or data in the same time using the same frequency band, the base station uses non-perfect SIC to detect user data and uses the receiving strategy solved in S8 to decode the aggregated model.

[0148] S10, The base station obtains a centralized training model based on the accumulated data, and obtains a global model by weighted sum of the centralized training model and the received aggregated model according to the data amount.

[0149] S11, The base station broadcasts the global model to all users, and repeats S3-S10 until the total cycle number requirement is reached.

[0150] In summary, the wireless federated learning framework proposed in the present application can support users with limited computing resources and users with sufficient computing resources to participate in federated learning together, and fully utilize the data on heterogeneous users to improve the performance of machine learning models. All users in the present application upload models or send data using the same frequency band at the same time, which can effectively save spectrum resources and reduce communication delay. The base station uses non-perfect SIC to detect signals, which is more in line with the actual situation. In addition, the present application constructs a non-convex optimization problem based on the user data transmission rate and model aggregation MSE, jointly designs the user transmission power and base station receiving strategy, and uses the SCA method to solve it, which can effectively realize the maximization of rate and the minimization of MSE.

[0151] The above examples are only used to illustrate the technical solutions of the present application, but not to limit it; although the present application has been described in detail with reference to the foregoing examples, those skilled in the art should understand that the technical solutions recorded in the foregoing examples can be modified, or some technical features can be replaced by equivalents, but these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A resource optimization method of a wireless federated learning system, characterized in that, The wireless federated learning system comprises: N computing resource-limited centralized training users, which send training data to the base station for centralized training to participate in federated learning; K computing resource-sufficient federated learning users, which train local models based on local data and then upload local model parameters to the base station as aggregated models; The base station, as a federated learning server, is used for calculating a global model; the base station performs centralized training on the training data accumulated by the centralized training users, obtains a centralized training model, and obtains the global model by weighted summation of the centralized training model and the received aggregated model according to data volume; The wireless federated learning system has T federated learning cycles, denoted as T = {1, 2,..., T}, and the local model update formula of the kth federated learning user at the tth federated learning cycle is: The centralized update formula at the base station end is: The global model aggregation formula is: where η is the learning rate of the stochastic gradient descent method, is the training data set accumulated by the base station end in t periods, F k (·) and are the local loss function and gradient of the kth federal learning user, respectively, F (·) and is the global model aggregated by the base station end; The resource optimization method comprises the following steps: S1, the base station initializes a training task and a global model, and sends the global model to all users; S2, after receiving the global model, the federated learning user calculates a local loss function and a gradient value based on local data, and updates the local model; S3, the federated learning user and the centralized training user use the same frequency band to upload the local model and send data at the same time, respectively, and the base station uses non-perfect successive interference cancellation detection to receive signals and separate training data and aggregated models; the specific process of step S3 is: Before the user uploads the local model or sends the data, the centralized training user's local training dataset {D n} and the local model {w k} of the federal learning user are normalized into the communication symbol set {s n} and the calculation symbol set {s k}, respectively. The superimposed signal received at the base station end is as follows: where h n is the channel parameter of the nth user to the base station, h k is the channel parameter of the kth user to the base station, p n is the transmission power of the nth user and takes values in the interval [0, P max ], p k is the transmission power of the kth user and takes values in the interval [0, P max ], n0~CN(0, σ 2 ) is the additive noise in the channel; By adjusting the user sending power, the SIC limit of different users satisfies: After receiving the superimposed signal y, the base station sequentially detects the uplink signals of the 1st, 2nd,..., Nth centralized training users {s n} respectively; after detecting the signals of all the centralized training users, the remaining signal is as follows: wherein is the interference coefficient of the residual signal, and corresponds to perfect SIC and no SIC, respectively; To obtain an averaged federated learning model, the base station uses a receive factor a to obtain an estimate of the aggregated model from the above remaining signals After further post-processing by de-normalization, all centralized training users' datasets and the aggregated model are decoded from signals {s n} and ​​ S4, the data sending rate of all centralized training users and the aggregated model mean square error of the federated learning user are obtained, and non-perfect successive interference cancellation is used to detect all centralized training user signals in the order of 1, 2,..., N; S5, a non-convex optimization problem is constructed based on the data sending rate and the aggregated model mean square error; S6, a continuous convex approximation method is used to transform and solve the non-convex optimization problem in S5, and the user sending power and receiving strategy are output.

2. The method of Claim 1, wherein, In step S2, the local loss function adopts a mean square error loss function or a cross-entropy loss function.

3. The method of Claim 1, wherein, In step S4, the formula of the data sending rate of the nth centralized training user is: where is the interference coefficient of the residual signal, and correspond to perfect SIC and no SIC, respectively, and the sum of all user data transmission rates is σ 2 is the additive noise power in the channel.

4. The resource optimization method of the wireless federated learning system according to claim 3, wherein, In step S4, the formula of the aggregated model mean square error is: wherein is the interference of the centralized trained user signal.

5. The method of Claim 1, wherein, In step S5, the non-convex optimization problem is constructed as follows: MSE≤∈0 Where p = [p1, p2, ..., p N ,p N+1 ,…,p N+K ] is the transmission power, R min It is the minimum data transmission rate required by centralized training users, P max is the maximum transmit power of all users, ∈ 0 is the maximum aggregation model error that federated learning users can tolerate, and λ is a constant used in the sum and rate R sum A balance is achieved between the mean squared error (MSE) and the mean squared error (MSE).

6. The method of Claim 1, wherein, In step S6, the transformed convex optimization problem is as follows: MSE≤∈0 where γ = [γ1, γ2,..., γ N ] and b = [b1, b2,..., b N , b N+1 , b N+2 , ..., b N+K ] are auxiliary vectors introduced, τ in and τ jn are CUB coefficients.

7. The resource optimization method of the wireless federated learning system according to claim 6, wherein, In step S6, the solving steps of the convex optimization problem are as follows: S6.1 initialize p (0) , a (0) , γ (0) , b (0) , maximum number of iterations L, threshold ε, set iteration index l = 0; S6.2 Calculate objective function value S6.3 At given p (l) , a (l) , γ (l) , b (l) , use ) and update and S6.4 At given and the above convex optimization problem is solved using the mathematical tool CVX to obtain p (l+1) , a (l +1) , γ (l+1) , b (l+1) ; S6.5 Compute objective function value S6.6 Update / = / + 1, and compute Δ U = |U (l) -U (l-1) |; S6.7 Repeat steps S6.3-S6.6 until Δ U ≤ ε or l ≥ L output user transmit power p (l-1) and receive factor a (l-1) .

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