Federal learning local data dynamic updating method based on information age incentive

Abstract

The invention provides a federal learning local data dynamic updating method based on information age incentive. The method comprises the following steps: calculating age expected dynamic change of local data information of a client; establishing a central server utility function and a client utility function; determining a target optimization problem corresponding to a central server utility function and a client utility function based on a two-stage Stackelberg game; the target optimization problem is solved, and the optimal updating probability of local data of each client and the optimal reward corresponding to the optimal updating probability are obtained; and the client dynamically updates the local data based on each round. According to the method, the local data updating strategy of the client is dynamically adjusted, so that the adaptive capacity of the model to the rapid change of the data is remarkably improved; according to the two-stage Stackelberg game model, interaction between the central server and the client is effectively processed, and the timeliness and accuracy of the model are improved; by introducing the average field estimator and the time average estimator, the calculation efficiency is remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of federated learning, and in particular to a method for dynamically updating local data of federated learning based on information age incentive. Background Art

[0002] The amount of data generated by edge devices is increasing significantly. Against the backdrop of increasing concerns about data privacy and security, federated learning (FL) has attracted widespread attention as an effective solution for processing sensitive data. Federated learning provides a distributed machine learning framework that allows data scattered across different devices or servers to be processed locally, thereby inherently enhancing data privacy and security. In particular, in areas such as healthcare, finance, and the Internet of Things where personal sensitive data needs to be handled with caution, federated learning has become a key technology.

[0003] Although federated learning has made significant progress in key areas such as communication efficiency, privacy protection, and model aggregation, existing research has obvious shortcomings in considering data freshness. Current technology mainly uses a variety of incentive mechanisms to encourage clients to participate in model training based on local data, but generally ignores the importance of data freshness. Moreover, existing incentive mechanisms focus on data reliability and compensation for privacy costs, but fail to fully consider how the timeliness of data affects the accuracy and applicability of the model. If the data uploaded by the client fails to reflect changes in the current environment and user behavior in a timely manner, the information eventually integrated into the global model may become outdated, thereby reducing the model's predictive ability and practicality. Therefore, the design of the incentive mechanism needs to ensure that clients are encouraged to provide reliable data, and also incentivize them to use the latest data for training, thereby improving the overall performance and adaptability of the federated learning model in a dynamic environment. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention provides a method for dynamically updating local data in federated learning based on information age incentive. The present invention addresses the problem of data freshness in the federated learning process and considers the age of information (AoI) as an indicator to measure the freshness of local data.

[0005] The technical solution of the present invention is: a method for dynamically updating local data in federated learning based on information age incentive, comprising the following steps:

[0006] S1), based on the local data update probability of each client, obtain the dynamic change of the client's local data information age expectation;

[0007] S2), establishing a central server utility function and a client utility function according to the client's local data update probability and information age expectation;

[0008] S3), establishing a two-stage Stackelberg game between the central server and the client, and determining the target optimization problem corresponding to the utility function of the central server and the utility function of the client based on the two-stage Stackelberg game;

[0009] S4) Solve the target optimization problem to obtain the optimal update probability of each client's local data and the optimal reward corresponding to the optimal update probability;

[0010] S5) Based on the client that dynamically updates local data in each round, a federated learning framework is constructed for training until the aggregation model converges to obtain the target model.

[0011] Preferably, in step S1), the dynamic change of the client local data information age is expressed as:

[0012]

[0013] In the formula, A i (t+1) represents the information age of the i-th client at the t+1th iteration; A0 represents the initial value of the local data information age; A i (t) The information age of the i-th client at the t-th iteration; k i (t) represents the update of local data of the i-th client in the t-th iteration, where k i (t) = 1, indicating that client i has updated the local data; k i (t)=0 Client i does not update local data.

[0014] As a preferred embodiment, in step S1), the client i has an expected local data information age in the t+1th round of iteration. The dynamic change process is as follows:

[0015]

[0016] In the formula, p i (t) represents the probability that client i updates local data in the tth iteration.

[0017] Preferably, in step S2), establishing a central server utility function and a client utility function specifically includes the following steps:

[0018] S21), based on the local data update probability and information age of each client, a convergence error function and a reward for motivating client updates are obtained, and a utility function of the central server is calculated;

[0019] S22), sending rewards to each client terminal;

[0020] S23), based on the expected local data update probability and information age of each client, the cost function of the client and its allocated reward are obtained, and the utility function of the client terminal is calculated.

[0021] Preferably, in step S3), in the two-stage Stackelberg game, in stage I, the central server determines the optimal reward to minimize its cost;

[0022] In the two-stage Stackelberg game, in stage II, based on the reward, each client maximizes its utility by determining the optimal data update strategy.

[0023] Preferably, in step S3), the two-stage Stackelberg game is expressed as:

[0024]

[0025] Where, Stage I and Stage II represent the I and II stages of the two-stage Stackelberg game respectively; R represents the reward of the central server; U T and U i They represent the utility function of the central server and the utility function of the client respectively; p represents the local data update probability vector of all clients; p -i represents the local data update probability vector except for the i-th client; p i Represents the local data update probability vector of the i-th client.

[0026] Preferably, in step S4), the expected mean of the information age is estimated by citing the mean field estimator φ(t); and the time average estimator δ is designed i Approximately quantify the reduction in the dynamic information age; solve the mean field estimator φ(t) and the time average estimator δ by using an iterative algorithm with linear complexity i Substitute it into the optimization problem and transform it into a discrete-time linear quadratic optimal control problem with dynamic constraints. Using the inverse solution method and dynamic programming method, the analytical solution p of the optimal local data update probability is obtained. * , and design a heuristic algorithm with low computational complexity to solve the optimal reward R of the central server * .

[0027] Preferably, in step S5), starting from the 0th iteration round, each round determines whether to update local data in the current iteration round based on the probability of updating local data in the current iteration round of the client, and training is performed based on the updated or unupdated local data. Each client performs small batch stochastic gradient descent training in parallel to update its local model parameters.

[0028] Preferably, in step S5), after all clients have updated their local model parameters, the central server performs weighted averaging of the local models from all clients to update the global model. After the global model is aggregated, the central server distributes the updated global parameters to all clients for the next iteration of training.

[0029] Preferably, in step S5), the optimization goal of federated learning is to find the optimal global parameters to minimize the global loss function. When the global model achieves stable performance and minimized error, the global model converges, and the target model is obtained.

[0030] The beneficial effects of the present invention are:

[0031] 1. The present invention significantly improves the model's ability to adapt to rapid data changes by dynamically adjusting the client's local data update strategy; since the client tends to update its data to obtain more rewards, the global model can be trained with fresher data, which not only improves the accuracy and convergence speed of the model, but also provides an effective solution for data-sensitive applications;

[0032] 2. The present invention encourages clients to update local data through an incentive mechanism in an AoI-based federated learning system, which helps the global model to capture and adapt to data changes in a timely manner, thereby improving the timeliness and accuracy of the model;

[0033] 3. The present invention allows the model to be dynamically adjusted according to real-time data. This flexibility is lacking in existing federated learning systems. It ensures that the global model can maintain high adaptability and accuracy even in an environment where data changes rapidly.

[0034] 4. The two-stage Stackelberg game model of the present invention effectively handles the interaction between the central server and the client, and obtains the optimal reward and optimal update strategy through theoretical solution. This optimal strategy combination constitutes the Stackelberg Nash equilibrium, ensuring that all game participants can reach a stable state in a non-cooperative environment, thereby improving the long-term operating efficiency and stability of the system;

[0035] 5. The mean field estimator and the time average estimator introduced in the present invention provide an efficient approximate method for solving the model, and the present invention also proposes an iterative algorithm with linear complexity to determine them, which significantly improves the computational efficiency;

[0036] 6. The present invention improves the timeliness of the system in processing data by optimizing the objective function and solving dynamic programming problems, ensures that the model can quickly adapt to data changes, and achieves higher accuracy and better convergence effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a flow chart of the method of the present invention;

[0038] Figure 2 It is a schematic diagram of the process of the present invention;

[0039] Figure 3 A schematic diagram of a flow chart for establishing a central server utility function and a client utility function according to the present invention;

[0040] Figure 4 An accuracy curve diagram of the impact of data update on data distribution on different data sets according to an embodiment of the present invention;

[0041] Figure 5 This is an accuracy curve diagram of the impact of data update on data quantity on different data sets according to an embodiment of the present invention. DETAILED DESCRIPTION

[0042] The specific implementation of the present invention will be further described below in conjunction with the accompanying drawings:

[0043] like Figure 1 This embodiment provides a method for dynamically updating local data in federated learning based on information age incentives. In this embodiment, multiple client terminals communicate with a central server through a network to perform data processing and model training. The client performs computing tasks locally and sends the results back to the central server for model aggregation. This embodiment models the interaction between the central server and the client into a two-stage Stackelberg game. In stage I, the central server determines the optimal reward to minimize its cost. In stage II, based on the reward, each client maximizes its utility by determining the optimal data update strategy. The update process of information age is represented by a simplified diagram, where Figure 1 The timeline on the right shows the impact of data updates on data freshness in different iteration rounds (t-2, t-1, t, t+1), which is quantified by AoI; the blue block represents the status of the information, and the darker the color, the older the data. In addition, the system can monitor and adjust the data update frequency of each device to ensure the timeliness and accuracy of the data, and ultimately optimize the performance and response speed of the entire network through centralized aggregation.

[0044] like Figure 2 As shown, the method of this embodiment specifically includes the following steps:

[0045] S1), based on the local data update probability of each client, obtain the dynamic change of the client's local data information age expectation;

[0046] This example analyzes the design of the information age incentive mechanism based on discrete time through probability and expectation, and defines k i(t) indicates whether the i-th client (i∈{1, 2, ..., N}) updates its local data in the t-th iteration (t∈{0, 1, ..., T}). In the t-th iteration, if the client i updates its local data, it is recorded as k i (t) = 1, and the probability that the i-th client updates its local data in the t-th iteration is p i (t) means, that is, P(k i (t) = 1) = p i (t); otherwise, k i (t)=0.

[0047] In the t+1 round of iteration, if client i updates the local data, k i (t) = 1, then the information age A of the client at the t+1th iteration i (t+1) restores the initial value A0 of the local data information age, where A0 represents the expected transmission delay of data update; otherwise, client i does not update the local data, i.e., k i (t) = 0, then the information age A of the client at the t+1th iteration i (t+1) is based on the information age of the previous round plus one, that is, A i (t+1)=A i (t)+1. Therefore, starting from the 0th iteration, the dynamic change of the client's local data information age is as follows:

[0048]

[0049] In the formula, A i (t+1) represents the information age of the i-th client at the t+1th iteration; A0 represents the initial value of the local data information age; A i (t) The information age of the i-th client at the t-th iteration; k i (t) represents the update of local data of the i-th client in the t-th iteration, where k i (t) = 1, indicating that client i has updated the local data; k i (t)=0 Client i does not update local data.

[0050] According to the dynamic change process of the local data update probability and information age of each client terminal at the tth iteration (t∈{0, 1, ..., T}), the expected information age of the local data of client i at the t+1th iteration can be calculated: The dynamic change process is as follows:

[0051]

[0052] In the formula, p i(t) represents the probability that client i updates local data in the tth iteration.

[0053] S2), establish the central server utility function and the client utility function according to the client's local data update probability and information age expectation; such as Figure 3 As shown, the specific steps include:

[0054] S21), based on the local data update probability and information age of each client, a convergence error function and a reward for motivating client updates are obtained, and a utility function of the central server is calculated;

[0055] By jointly analyzing the update rules of the local model and the aggregation rules of the global model, the upper bound of the convergence error of the federated learning global model can be obtained. The items related to the client decision variables are taken as the convergence error function of the central server. The remaining variables are independent of the client decision and can be regarded as fixed variables.

[0056] Therefore, the convergence error function can be calculated based on the local data update probability of each client, that is:

[0057]

[0058] In the formula, θ i represents the proportion of the local data volume of the i-th client to the local data volume of all clients; T is the number of iteration rounds; N is the number of clients; p i (t) represents the probability that the i-th client updates its local data in the t-th iteration;

[0059] The central server provides a reward R∈(0, +∞) to each client in each iteration. For the client's expected information age, the larger the proportion of the client's expected information age, the smaller the reward allocated. Therefore, the utility function U of the central server is T (p, R) can be established based on the convergence error function and the reward that encourages the client to update as follows:

[0060]

[0061] Where p represents the local data update probability vector of all client terminals, p = {p i , i∈{1, 2, ..., N}}, p i ={p i(t), t∈{0, 1, ..., T}}; ρ∈(0, 1) represents the discount coefficient, that is, the reward for incentivizing client updates will decay over time; α∈(0, 1) balances the trade-off between the convergence error function and the reward allocated to the client terminal, avoiding the trade-off between the convergence error function and the numerical disparity of the reward for incentivizing client updates; R is the reward of the central server; is the penalty item; then the reward allocated to the client is A i (t) The information age of the i-th client at the t-th iteration; A j (t) The information age of the jth client at the tth iteration; It represents the expected age of information of the i-th client at the t-th iteration.

[0062] S22), sending rewards to each client terminal;

[0063] The central server sends a reward R and global model parameters to the client, so that the client can train and update the global model based on the global model. In federated learning, rewards are the key to ensuring that clients actively participate and contribute fresh data. It maintains the accuracy and timeliness of the global model by incentivizing clients to update the model with the latest data, while promoting the fairness and efficiency of the entire learning process.

[0064] S23), based on the expected local data update probability and information age of each client, the cost function of the client and its allocated reward are obtained, and the utility function of the client terminal is calculated.

[0065] The cost function for client participation in training and data update adopts quadratic cost function Among them, the cost coefficient a>0; the goal of the i-th client is to dynamically adjust the local data update probability p of each iteration according to the reward R of the central server i (t) to maximize the client’s utility function U i ; Therefore, the utility function U of the i-th client is i Expressed as the difference between the allocated reward and the cost function, the client's utility function U i Can be established as follows:

[0066]

[0067] Where p represents the local data update probability vector of all client terminals, p = {p i , i∈{1, 2, ..., N}}, p i ={p i (t),t∈{0,1,...,T}},p -irepresents the local data update probability vector except for the i-th client; p -i ={p1(t), ..., p i-1 (t), p i+1 (t), ..., P N (t)}, t∈{0, 1, ..., T}; γ∈(0, 1) is the discount factor, which indicates the preference of the i-th client for immediate cost and future cost; is the cost function; It represents the expected age of information of the i-th client at the t-th iteration.

[0068] S3), establishing a two-stage Stackelberg game between the central server and the client, and determining the target optimization problem corresponding to the utility function of the central server and the utility function of the client based on the two-stage Stackelberg game;

[0069] The reward R assigned to the client will affect the probability p of the client updating local data i (t) design, thus affecting the utility of the central server. In addition, the utility of each client will be affected by the data update strategy of other clients in the formula; therefore, the two-stage Stackelberg game is expressed as:

[0070]

[0071] Where, Stage I and Stage II represent the I and II stages of the two-stage Stackelberg game respectively; R represents the reward of the central server; U T and U i They represent the utility function of the central server and the utility function of the client respectively; p represents the local data update probability vector of all clients; p -i represents the local data update probability vector except for the i-th client; p i Represents the local data update probability vector of the i-th client.

[0072] In the two-stage Stackelberg game described above, in stage I, the central server determines the optimal reward to minimize its cost;

[0073] In the two-stage Stackelberg game, in stage II, based on the reward, each client maximizes its utility by determining the optimal data update strategy.

[0074] In the federated learning method, the utility function of the central server is composed of the convergence error function and the reward that encourages the client to update, with the goal of minimizing the total loss of participating in federated learning. The utility function of the client terminal is composed of the allocated reward minus its cost, representing its net benefit from participating in federated learning. The client's goal is to maximize this utility income. The reward allocated to the client will affect the local data update probability p designed by it. i (t), which will not only change the client's expectation of the local data information age, but also further affect the utility function of the central server. At the same time, the data update strategy of each client will also affect each other, which together constitutes a system optimization problem.

[0075] S4) Solve the target optimization problem to obtain the optimal update probability of each client's local data and the optimal reward corresponding to the optimal update probability;

[0076] According to the client's utility function U i , we can find that its local data update probability p i (t) The determination is significantly affected by the age expectations of other clients’ information impact.

[0077] However, there is a lack of information exchange between clients during local training, so clients cannot directly obtain information about the expected information age of other clients, which brings challenges to solving multi-client joint dynamic data update strategies that change over time. In addition, due to the expected information age of local data Constrained by the dynamic change process, when the optimization problem is substituted for solution, the solution scale will grow exponentially with the increase of iteration rounds, thus causing the dimensionality disaster. Therefore, this embodiment uses the mean field estimator φ(t) to estimate the expected mean of the information age, that is:

[0078]

[0079] At the same time, in order to solve the existence of nonlinear constraints, this embodiment designs the time average estimator δ i The reduction in the age of dynamic information can be approximately quantified as:

[0080]

[0081] This embodiment uses an iterative algorithm with linear complexity to solve the mean field estimator φ(t) and the time average estimator δ i Substitute it into the optimization problem and transform it into a discrete-time linear quadratic optimal control problem with dynamic constraints. Using the inverse solution method and dynamic programming method, the analytical solution p of the optimal local data update probability is obtained. *, and design a heuristic algorithm with low computational complexity to solve the optimal reward R of the central server * .

[0082] S5) Based on the client that dynamically updates local data in each round, a federated learning framework is constructed for training until the aggregated model converges to obtain the target model;

[0083] Starting from the 0th iteration, each round determines whether to update the local data in the current iteration based on the probability of updating the local data of the client in the current iteration, and performs training based on the updated or unupdated local data. Each client performs small batch stochastic gradient descent training in parallel to update its local model parameters, namely:

[0084]

[0085] Where η represents the learning rate of local model training, represents the local gradient of the client at the tth iteration, w(t) represents the global model parameters transmitted by the central server at the tth iteration; ξ i (t) is the correction coefficient of client i in the tth iteration; w i (t+1) represents the local model parameters of client i in the t+1th iteration; F i represents the loss function of the local model of client i;

[0086] Among them, the correction coefficient ξ i (t) is expressed as:

[0087]

[0088] Among them, k i (t) indicates whether the i-th client (i∈{1, 2, ..., N}) updates the local data in the t-th iteration (t∈{0, 1, ..., T}).

[0089] Correction coefficient ξ i (t) is related to the update probability of client i and whether it is actually updated. It can dynamically adjust the data update probability p i (t) to obtain better model performance.

[0090] When all clients have updated their local model parameters, the central server performs a weighted average of the local models from all clients to update the global model. After the global model is aggregated, the central server distributes the updated global parameters to all clients for the next iteration of training, namely:

[0091] w(t+1)=θ i w i (t+1)

[0092] Where w(t+1) represents the global model parameters of the central server in round t+1; w i (t+1) represents the local model parameters of client i in the t+1th iteration; θ i Indicates the proportion of the local data volume of the i-th client to the local data volume of all clients.

[0093] The optimization goal of federated learning is to find the optimal global parameters to minimize the global loss function. When the global model achieves stable performance and minimizes the error, the global model converges, and the target model is obtained. The loss function is expressed as:

[0094]

[0095] In the formula, w * represents the optimal global model parameters, F(w) represents the loss function of the global model; F i (w) represents the loss function of the local model of client i; θ i Indicates the proportion of the local data volume of the i-th client to the local data volume of all clients.

[0096] In addition, this embodiment performs a performance test on the method of the present invention based on a real data set, and the results are as follows: Figure 4 and Figure 5 As shown. Figure 4 and Figure 5 The accuracy curves shown show that under different data sets (from top to bottom, the data sets are: MNIST, Fashion-MNIST, CIFAR-10 and CIFAR-100), compared with the classic baseline algorithms (FedAvg, FedProx, FedBABU, FedGH), the method of this embodiment (FedAdd) speeds up the convergence of the FL system. The larger increase in the accuracy curve in the initial iteration highlights the ability of the method of this embodiment to accelerate the learning process, enabling the model to achieve higher accuracy compared to the baseline method. In addition, the continued high accuracy shows the effectiveness of the method of the present invention.

[0097] This embodiment models the interaction between the central server and the client as a two-stage Stackelberg game, in which the central server optimizes the cost function and the client optimizes the utility to jointly motivate the client to actively update local data. This method not only improves the timeliness of the data and ensures that the model can respond to data changes in a timely manner, but also enhances the client's motivation to participate by fairly compensating the client's resource losses, thereby improving the overall performance of the system. Through this method that combines information age and incentive mechanisms, the present invention ensures that the global model is synchronized with the latest data, providing an effective federated learning solution for sensitive fields that need to respond quickly to data changes.

[0098] At the same time, this embodiment introduces the mean field estimator and the time average estimator to solve the problem of information incompleteness caused by the lack of information exchange between clients and nonlinear constraints in federated learning.

[0099] By dynamically adjusting the client's local data update strategy, the timeliness of training data is significantly improved, allowing the model to quickly adapt to data changes, thereby achieving better performance in data-sensitive applications.

[0100] The above embodiments and descriptions are only for illustrating the principles and best embodiments of the present invention. Without departing from the spirit and scope of the present invention, the present invention may be subject to various changes and improvements, all of which fall within the scope of the present invention to be protected.

Claims

1. A method for dynamically updating local data in federated learning based on information age incentive, characterized in that: The steps include: S1), based on the local data update probability of each client, obtain the dynamic change of the client's local data information age expectation; S2), establishing a central server utility function and a client utility function according to the client's local data update probability and information age expectation; S3), establishing a two-stage Stackelberg game between the central server and the client, and determining the target optimization problem corresponding to the utility function of the central server and the utility function of the client based on the two-stage Stackelberg game; S4) Solve the target optimization problem to obtain the optimal update probability of each client's local data and the optimal reward corresponding to the optimal update probability; S5) Based on the client that dynamically updates local data in each round, a federated learning framework is constructed for training until the aggregation model converges to obtain the target model.

2. According to claim 1, a method for dynamically updating local data in federated learning based on information age incentive is characterized in that: In step S1), the dynamic change of the client local data information age is expressed as: In the formula, A i (t+1) represents the information age of the i-th client at the t+1th iteration; A0 represents the initial value of the local data information age; A i (t) The information age of the i-th client at the t-th iteration; k i (t) represents the update of local data of the i-th client in the t-th iteration, where k i (t) = 1, indicating that client i has updated the local data; k i (t)=0 Client i does not update local data.

3. According to claim 2, a method for dynamically updating local data in federated learning based on information age incentive is characterized in that: In step S1), the client i expects the local data information age in the t+1th round of iteration The dynamic change process is as follows: In the formula, p i (t) represents the probability that client i updates local data in the tth iteration.

4. According to claim 3, a method for dynamically updating local data in federated learning based on information age incentive is characterized in that: In step S2), a central server utility function and a client utility function are established, which specifically includes the following steps: S21), based on the local data update probability and information age of each client, a convergence error function and a reward for motivating client updates are obtained, and a utility function of the central server is calculated; S22), sending rewards to each client terminal; S23), based on the expected local data update probability and information age of each client, the cost function of the client and its allocated reward are obtained, and the utility function of the client terminal is calculated.

5. According to claim 4, a method for dynamically updating local data in federated learning based on information age incentive is characterized in that: In step S21), the utility function U of the central server is T (p,R) is built based on the convergence error function and the reward that motivates the client to update: Where p represents the local data update probability vector of all client terminals, p = {p i ,i∈ {1,2,…,N}}, p i ={p i (t), t∈{0,1,…,T}}; ρ∈(0,1) represents the discount coefficient, that is, the reward for incentivizing client updates will decay over time; α∈(0,1) balances the trade-off between the convergence error function and the reward allocated to the client terminal, avoiding the trade-off between the convergence error function and the numerical disparity of the reward for incentivizing client updates; R is the reward of the central server; is the penalty item; then the reward allocated to the client is A i (t) The information age of the i-th client at the t-th iteration; A j (t) The information age of the jth client at the tth iteration; represents the expected age of information of the i-th client at the t-th iteration.

6. According to claim 5, a method for dynamically updating local data in federated learning based on information age incentive is characterized in that: In step S23), the utility function U of the i-th client i Expressed as the difference between the allocated reward and the cost function, the client's utility function U i It is expressed as: Where p represents the local data update probability vector of all client terminals, p = {p i ,i∈{1,2,…,N}},p i ={p i (t),t∈{0,1,…,T}},p -i represents the local data update probability vector except for the i-th client; p -i ={p1(t),…,p i-1 (t),p i+1 (t),…,p N (t)}, t∈{0,1,…,T}; γ∈(0,1) is the discount coefficient, which indicates the preference of the i-th client for immediate cost and future cost; is the cost function; represents the expected age of information of the i-th client at the t-th iteration.

7. The method for dynamically updating local data in federated learning based on information age incentive according to claim 6 is characterized in that: The two-stage Stackelberg game is expressed as: Where, Stage I and Stage II represent the I and II stages of the two-stage Stackelberg game respectively; R represents the reward of the central server; U T and U i They represent the utility function of the central server and the utility function of the client respectively; p represents the local data update probability vector of all clients; p -i represents the local data update probability vector except for the i-th client; p i Represents the local data update probability vector of the i-th client.

8. The method for dynamically updating local data in federated learning based on information age incentive according to claim 7 is characterized in that: In step S3), in the two-stage Stackelberg game, in stage I, the central server determines the optimal reward to minimize its cost; In Phase II, based on the optimal reward, each client maximizes its utility by determining the optimal data update strategy.

9. The method for dynamically updating local data in federated learning based on information age incentive according to claim 8 is characterized in that: In step S4), the expected mean of the information age is estimated by citing the mean field estimator φ(t); and the time average estimator δ is designed i Approximately quantify the reduction in the age of dynamic information; The mean field estimator φ(t) and the time average estimator δ are solved by using an iterative algorithm with linear complexity. i Substitute it into the optimization problem and transform it into a discrete-time linear quadratic optimal control problem with dynamic constraints. Using the inverse solution method and dynamic programming method, the analytical solution p of the optimal local data update probability is obtained. * , and design a heuristic algorithm with low computational complexity to solve the optimal reward R of the central server * .

10. The method for dynamically updating local data in federated learning based on information age incentive according to claim 1, characterized in that: In step S5), starting from the 0th iteration round, each round determines whether to update the local data in the current iteration round based on the probability of updating the local data of the client in the current iteration round, and performs training based on the updated or unupdated local data. Each client performs small batch stochastic gradient descent training in parallel to update its local model parameters; When all clients have updated their local model parameters, the central server performs a weighted average of the local models from all clients to update the global model. After the global model is aggregated, the central server distributes the updated global parameters to all clients for the next iteration of training. The optimization goal of federated learning is to find the optimal global parameters to minimize the global loss function. When the global model achieves stable performance and minimizes the error, the global model converges and the target model is obtained.

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