A method for dynamic updating of local data in federated learning based on information age incentive

Abstract

The present invention provides a method for dynamically updating local data in federated learning based on information age incentives, including calculating the dynamic changes in the expected information age of client local data; establishing a central server utility function and a client utility function; determining the target optimization problem corresponding to the central server utility function and the client utility function based on a two-stage Stackelberg game; solving 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; and dynamically updating the local data based on the client in each round. The present invention significantly improves the model's adaptability to rapid data changes by dynamically adjusting the client's local data update strategy; the two-stage Stackelberg game model of the present invention effectively handles the interaction between the central server and the client, improving the timeliness and accuracy of the model; and significantly improves computational efficiency by introducing mean field estimators and time average estimators.

Description

Technical Field

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

[0002] The amount of data generated by edge devices is increasing significantly. Against the backdrop of growing 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 distributed across different devices or servers to be processed locally, inherently enhancing data privacy and security. It has become a key technology, particularly in sectors such as healthcare, finance, and the Internet of Things, where the careful handling of personal and sensitive data is crucial.

[0003] While federated learning has made significant progress in key areas such as communication efficiency, privacy protection, and model aggregation, existing research has significant shortcomings in considering data freshness. Current technologies primarily use various incentive mechanisms to encourage clients to participate in model training based on local data, but the importance of data freshness is generally overlooked. Furthermore, existing incentive mechanisms focus on data reliability and compensation for privacy costs, but fail to fully consider how data timeliness affects model accuracy and applicability. If the data uploaded by the client fails to promptly reflect changes in the current environment and user behavior, the information ultimately integrated into the global model may become outdated, thereby reducing the model's predictive power and practicality. Therefore, the design of the incentive mechanism must ensure that clients are encouraged to provide reliable data while also incentivizing them to use the latest data for training, thereby improving the overall effectiveness and adaptability of federated learning models in dynamic environments. Summary of the Invention

[0004] In response to the shortcomings of the existing technology, the present invention provides a method for dynamically updating local data in federated learning based on information age incentives. 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, the expected dynamic change of the client's local data information age is obtained;

[0007] S2) Establishing a central server utility function and a client utility function based on 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 central server utility function and the client utility function 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] Where 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 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] Where p i (t) represents the probability that client i updates its local data in the tth iteration.

[0017] Preferably, in step S2), establishing the central server utility function and the 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 probability vector of local data update except for the i-th client; p i Represents the local data update probability vector of the i-th client.

[0026] As a preference, 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 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 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 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 on 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 minimizes the error, the global model converges, and the target model is obtained.

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

[0031] 1. This invention significantly improves the model's adaptability to rapidly changing data by dynamically adjusting the client's local data update strategy. Since clients tend to update their data to obtain more rewards, the global model can be trained with fresher data. This not only improves the model's accuracy and convergence speed, but also provides an effective solution for data-sensitive applications.

[0032] 2. This invention uses an incentive mechanism in an AoI-based federated learning system to encourage clients to update their local data, 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. This invention allows the model to dynamically adjust based on real-time data. This flexibility is lacking in existing federated learning systems. It ensures that the global model remains highly adaptable and accurate even in environments with rapidly changing data.

[0034] 4. The two-stage Stackelberg game model of the present invention effectively handles the interaction between the central server and the client. Through theoretical solution, the optimal reward and optimal update strategy are obtained. 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 time average estimator introduced in the present invention provide an efficient approximation 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. By optimizing the objective function and solving dynamic programming problems, the present invention improves the timeliness of the system in processing data, 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 Schematic diagram of the process of the present invention;

[0039] Figure 3 A schematic diagram of the process of establishing the central server utility function and the client utility function of the present invention;

[0040] Figure 4 This is a graph showing the accuracy of data distribution as a result of data updates on different data sets according to an embodiment of the present invention;

[0041] Figure 5 This is a graph showing the accuracy of how data updates affect data quantity on different data sets according to an embodiment of the present invention. DETAILED DESCRIPTION

[0042] The specific embodiments of the present invention will be further described below with reference to 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 information age update process is represented by a simplified diagram, where Figure 1 The timeline on the right shows the impact of data updates on data freshness at different iterations (t-2, t-1, t, t+1), quantified using the AoI. Blue blocks represent the state of information, with darker colors indicating older data. Furthermore, the system monitors and adjusts the data update frequency of each device to ensure data timeliness and accuracy, ultimately optimizing the performance and responsiveness 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, the expected dynamic change of the client's local data information age is obtained;

[0046] This embodiment 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 the local data in the t-th iteration (t∈{0, 1, ..., T}). In the t-th iteration, if the client i updates the local data, it is recorded as k i (t) = 1, and the probability that the i-th client updates the local data in the t-th round of iteration is p i (t) represents, that is, P(k i (t) = 1) = p i (t); otherwise, k i (t)=0.

[0047] In the t+1 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 client's information age A at the t+1 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 changes of the client's local data information age are as follows:

[0048]

[0049] Where 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 local data; k i (t)=0 Client i does not update local data.

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

[0051]

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

[0053] S2) Establishing the central server utility function and the client utility function based on the client's local data update probability and information age expectation; 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] Where θ i represents the proportion of the local data volume of the i-th client to the total local data volume of the 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 will be. Therefore, the utility function U of the central server is T (p, R) can be established as follows based on the convergence error function and the reward that motivates the client to update:

[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 between the values ​​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 j-th client at the t-th iteration; represents the expected information age 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 the client actively participates and contributes fresh data. It maintains the accuracy and timeliness of the global model by incentivizing the client 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 uses a 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 probability vector of local data update 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 represents the preference of the i-th client for immediate cost and future cost; is the cost function; represents the expected information age 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 central server utility function and the client utility function 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 The design of (t) affects the utility of the central server. In addition, the utility of each client is 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 probability vector of local data update 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, 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 its designed local data update probability p i (t), which not only changes the client's expected age of local data information, but also further affects 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 the local data update probability p i (t) The determination of age is significantly affected by other clients' information expectations 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 the multi-client joint dynamic data update strategy that changes 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 into the solution, the solution scale will grow exponentially with the increase of iteration rounds, thus causing the curse of dimensionality. 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 a 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. Training is performed based on the updated or unupdated local data. Each client performs mini-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 its 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] After 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 total 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 error, the global model converges, and the target model is obtained. The loss function is expressed as:

[0094]

[0095] Where 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 total local data volume of all clients.

[0096] In addition, this embodiment conducts 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 in the figure show that the method of this embodiment (FedAdd) accelerates the convergence of the FL system compared to classic baseline algorithms (FedAvg, FedProx, FedBABU, and FedGH) on different datasets (from top to bottom: MNIST, Fashion-MNIST, CIFAR-10, and CIFAR-100). The larger increase in the accuracy curve in the initial iterations highlights the ability of this embodiment method to accelerate the learning process, enabling the model to achieve higher accuracy compared to the baseline methods. Furthermore, the consistently high accuracy demonstrates 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 function to jointly incentivize the client to actively update local data. This approach 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. By combining this method of information age and incentive mechanism, the present invention ensures that the global model is synchronized with the latest data, providing an effective federated learning solution for sensitive fields that require rapid response 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 explaining 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, which shall fall within the scope of the 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, the expected dynamic change of the client's local data information age is obtained; The dynamic change of the client local data information age is expressed as: Where 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 local data; k i (t) = 0 Client i does not update local data; The expected age of local data information of client i in the t+1th round of iteration The dynamic change process is as follows: Where p i (t) represents the probability that client i updates local data in the tth iteration; S2) Establishing a central server utility function and a client utility function based on 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 central server utility function and the client utility function 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. The method for dynamically updating local data in federated learning based on information age incentive according to claim 1, characterized in that: In step S2), the central server utility function and the 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.

3. The method for dynamically updating local data in federated learning based on information age incentive according to claim 2, characterized in that: In step S21), the utility function U of the central server T (p, R) is established based on the convergence error function and the reward that incentivizes client updates: 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 between the values ​​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 j-th client at the t-th iteration; represents the expected information age of the i-th client at the t-th iteration.

4. The method for dynamically updating local data in federated learning based on information age incentive according to claim 3, 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 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),y∈{0,1,…,T}},p -i represents the probability vector of local data update 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 represents the preference of the i-th client for immediate cost and future cost; is the cost function; represents the expected information age of the i-th client at the t-th iteration.

5. The method for dynamically updating local data in federated learning based on information age incentive according to claim 4 is characterized by: 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 probability vector of local data update except for the i-th client; p i Represents the local data update probability vector of the i-th client.

6. The method for dynamically updating local data in federated learning based on information age incentive according to claim 5, 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.

7. The method for dynamically updating local data in federated learning based on information age incentive according to claim 6, 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 * .

8. 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 the client's local data update in the current iteration round, and trains based on the updated or unupdated local data. Each client performs mini-batch stochastic gradient descent training in parallel to update its local model parameters; After 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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