Semi-asynchronous satellite federated learning model training method and system based on old control

Abstract

The invention provides a semi-asynchronous satellite federated learning model training method and system based on old control. The method comprises the steps of 1, inputting space-based computing power constellation parameters; 2, broadcasting the global model to a visible satellite; step 3, the satellite receiving the global model is trained by using a local data set; 4, the trained satellite which is visible to the ground uploads the local model obtained through training to a ground parameter server; 5, the ground parameter server selects the optimal aggregation number of the round and judges whether the number of the local models reaches the optimal aggregation number or not, if not, the second step is executed, and if not, the sixth step is executed; 6, the ground parameter server adopts a gradient compensation strategy to carry out aggregation updating on the global model; and 7, judging whether the global model converges or not, if not, returning to the step 2, and otherwise, ending training. The method has the advantages that the problems that a synchronization method is limited by a satellite-ground communication window, and an asynchronous method is unstable in convergence and low in accuracy are solved.

Description

Technical Field

[0001] This invention relates to the field of satellite communication technology, and in particular to a training method and system for a semi-asynchronous satellite federated learning model based on stagnation control. Background Technology

[0002] With the rapid development of aerospace and space communication technologies, satellite communication, with its advantages of wide-area coverage, high-capacity transmission, and lack of geographical limitations, has become an important research direction in modern communication, playing an irreplaceable role in military, navigation, and remote sensing fields. Satellite-based federated learning, as an emerging branch of federated learning, treats satellites as edge computing nodes, directly using onboard remote sensing data for local model training, and replacing raw data backhaul with model parameter transmission. This method fully utilizes the distributed computing resources within the low-Earth orbit satellite constellation to achieve real-time collaborative processing of massive amounts of data in orbit, significantly reducing the communication load and transmission latency of the satellite-to-ground link, while effectively avoiding the privacy risks that may arise from the downlink of raw data. However, due to the high-speed movement of satellites relative to ground parameter servers, the satellite-to-ground communication window is short and highly intermittent. Therefore, when a satellite node misses a communication window, it must endure a long waiting period to re-establish a connection and complete model upload, severely restricting overall training efficiency. Compared to synchronous methods that require waiting for all nodes, semi-asynchronous satellite federated learning triggers aggregate updates upon receiving a specified number of satellite models, mitigating the impact of communication window limitations. In semi-asynchronous update mechanisms, the local model used for satellite training may not be updated from the latest global model, resulting in model staleness. This local update based on outdated parameters deviates from the current global optimization direction, affecting the model's convergence path and final performance. In systems without inter-satellite links, satellites can only communicate with the parameter server through a limited satellite-to-ground visibility window, further reducing the model update frequency and exacerbating the staleness problem. Furthermore, the non-independent and identically distributed nature of data among satellites also exacerbates the negative impact of staleness on the training process. These issues limit the training efficiency of semi-asynchronous satellite federated learning, making existing semi-asynchronous federated learning methods with a fixed number of aggregates difficult to directly apply to low-Earth orbit satellite constellation scenarios.

[0003] Current research on semi-asynchronous satellite federated learning mainly focuses on switching strategies between synchronous and asynchronous mechanisms, and has not yet developed an adaptive adjustment method for the number of aggregates based on the dynamic characteristics of communication windows and model obsolescence control.

[0004] Currently, semi-asynchronous federated learning methods for low-Earth orbit satellite constellations still have shortcomings in design and analysis. Most existing research focuses on switching between asynchronous and semi-asynchronous strategies based on indicators such as satellite connection density and model staleness. While these methods aim to achieve as many aggregation rounds as possible within the communication window, they neglect the fact that frequent asynchronous updates can exacerbate local model staleness when the number of participating clients is small, potentially leading to ineffective acceleration of the training process. Furthermore, the non-independent and identically distributed nature of satellite data is not fully considered, affecting model convergence accuracy. In research on semi-asynchronous federated learning for terrestrial wireless networks, although some work has attempted to introduce dynamic aggregation mechanisms, effective control over the overall system staleness remains lacking, making it difficult to guarantee a balance between convergence speed and performance. Summary of the Invention

[0005] To address the problems in the prior art, this invention provides a method for training a semi-asynchronous satellite federated learning model based on staleness control, comprising the following steps: Step 1: Input the parameters of the space-based computing constellation; Step 2: The ground parameter server broadcasts the latest global model to visible satellites; Step 3: Receive satellite data from the global model, train the model using the local dataset, and generate a local model update; Step 4: Once the training is complete and the satellites are visible to the Earth, they will upload the trained local model to the ground parameter server; Step 5: The ground parameter server selects the optimal number of aggregations for this round based on the model's staleness, and determines whether the number of all received local models has reached the optimal number of aggregations. If the optimal number of aggregations has not been reached, return to step 2; otherwise, jump to step 6. Step 6: The ground parameter server uses the received local model and employs a gradient compensation strategy to aggregate and update the global model; Step 7: Determine if the global model has converged. If it has not converged, return to step 2; otherwise, end the training.

[0006] As a further improvement of the present invention, in step 1, the space-based computing constellation parameters include satellite orbital altitude, number of satellites, orbital inclination, ground station location, satellite-to-ground communication channel parameters, model size, model computational load, and satellite computational throughput.

[0007] As a further improvement of the present invention, in step 2, when the satellite is within the visible window of the ground parameter server and is in an idle state, if the current global model is a new version that the satellite has not yet trained, the ground parameter server will broadcast the global model to the satellite through the satellite-to-ground link.

[0008] As a further improvement of the present invention, in step 3, the satellite Upon receiving the global model Then, based on its local dataset conduct Step stochastic gradient descent Update its local model ,in Indicates satellite In the r In the global training round i The local model after +1 iterations i Indicates the number of steps in the local iteration. r Indicates training rounds, Indicates the learning rate. Represents the local loss function. Indicates satellite In the r In the global training round i The local model after the next iteration , Indicates satellite k In the r Round iteration The local model obtained after the step.

[0009] As a further improvement of the present invention, step 5 further includes: The first step is to construct an optimization problem with the goal of minimizing the global loss function. Under the premise of satisfying the constraints of total training time and model staleness, the original coupled problem is decomposed into independent single-round optimization subproblems using a Lyapunov optimization-based method. The second step is to design a dynamic aggregation strategy for staleness control based on the single-round optimization framework of the first step, so as to achieve adaptive adjustment of the number of satellites participating in aggregation in each round.

[0010] As a further improvement of the present invention, the first step further includes: Step a1: Establish the optimization problem as follows: (9) (9-a) (9-b) (9-c) Equation (9-a) represents the training duration constraint, which stipulates that the total training time must not exceed the training time threshold. , Represents the global loss function. R Indicates the total number of training rounds. T r Indicates the first rThe time required for each training round; Equation (9-b) is the obsoleteness constraint, which stipulates that the obsoleteness of the models uploaded by all satellites in any training round must not exceed the obsoleteness threshold. , For satellite The difference between the round number of the last received global model and the current round; Equation (9-c) is the aggregation quantity constraint, that is, the upper limit of the number of new models received in each round is the total number of satellites. Indicates the first r The number of wheels in aggregation, r Indicates the number of training rounds. K Indicates the total number of satellites; Step a2: Problem Solving; By analyzing and deriving the upper bound of the convergence of the global loss function, the optimization problem in step a1 is transformed into a substitute problem of optimizing the upper bound of convergence. This is solved using a Lyapunov optimization-based method, with the learning rate... In the case of this invention, the convergence bound of the method is: (10) in, , , , , , Indicates the optimal loss. Represents the initial global model. Indicates satellite Is it in the first r Upload new models in rounds. For the total number of satellites, This represents the number of local iterations. The antiquity threshold, For learning rate, , , , , , These are all hyperparameters determined by the initial system settings and are unrelated to the specific training process.

[0011] In equation (10), the upper bound of convergence consists of three terms: the first term The second term represents the difference between the initial global loss and the optimal loss, and its value is determined by the system hyperparameters and the initial model. Determined by system hyperparameters; the third item This reflects the cumulative effect of model staleness over multiple training rounds. Due to the learning rate... ,so ,lead to The effect of obsolescence increases exponentially with each training round, reflecting that obsolescence has a more significant impact in the later stages of training. Furthermore, all three parameters increase exponentially with the number of training rounds. The obsolescence level increases with the increase in age, so it is necessary to set an appropriate obsolescence threshold and control the obsolescence level to be below that threshold. In summary, weights are introduced. Measure the first r The impact of obsolescence in round training transforms problem (9) into (11) (11-a) (11-b) (11-c) To overcome the coupling problem between rounds, the Lyapunov optimization method is adopted, and the following virtual queue is defined: (12) Based on this, to measure the stability of the training process, the Lyapunov equation is defined as follows: (13) This function represents the deviation between the actual training time in each round and the preset latency budget. Furthermore, the single-step Lyapunov drift function is defined as follows: (14) To simultaneously control system obsolescence, a drift plus penalty function is constructed: (15) in, It is a weighting coefficient that balances training time and accuracy. Let represent the weights that increase with each round. Based on this, the optimization problem in equation (11) is transformed into... (16) (16-a) (16-b).

[0012] As a further improvement of the present invention, the second step further includes: Step S1: Sort the clients in ascending order based on satellite visibility time to obtain an ordered set of satellites. Initialize the cumulative staleness array. and collection of highly outdated clients ; Step S2: Iterate through the sorted clients, calculate the cumulative sum of squares of obsolescence, and classify clients whose obsolescence exceeds the threshold. The client is added to the collection of highly outdated clients. A collection of outdated client applications H cardinality and The maximum value in is the minimum number of aggregates. , To maintain a stable number of polymers Lower limit; Step S3: Traverse the candidate values ​​for the number of aggregates Construct an aggregate client collection Calculate the aggregate client set Time required for the next round of training and the objective function value; Step S4: Determine the optimal number of aggregations and the corresponding aggregated satellite set ; Step S5: Update the virtual queue to complete this round of scheduling.

[0013] As a further improvement of the present invention, in step S3, the aggregated client set is calculated. Time required for the next round of training The specific steps are as follows: Taking into account the communication window, for a given satellite In its first r The first round of global training n The duration of each visible window is Its starting time is If the satellite In the r If there is no trainable global model, then the satellite... In the r The time frame for the round-robin upload model is defined as: (8) If the satellite can complete training within the current visible window, the model will be uploaded immediately after training. T k To transmit data from the parameter server to the satellite without considering the communication window Send global model to parameter server and receive satellite data. The total latency required for the local model, N For satellite In the r The total number of visible windows on the ground during each training round; if it cannot be completed in the current window, it must wait until the next available visible window after training ends to upload. For satellite Propagation delay between PS and PS for Transmission latency between PS and PS

[0014] Therefore, the first r The time required for round training is .

[0015] Considering the first r The satellites used in the rotation may already have a trained model or be in the process of training. r The actual time required for round training is less than or equal to Therefore, this formula is used as an upper bound in the analysis. In subsequent experiments, Calculated based on the actual training situation of the satellite.

[0016] As a further improvement of the present invention, step 6 specifically includes: definition Indicates satellite Is it in the first r Upload new models in rounds, among which This indicates uploading, and vice versa, it indicates not uploading. Therefore, there is... ,in Represents a collection of satellites. ; definition For satellite The difference between the last received global model iteration and the current iteration represents the staleness resulting from semi-asynchronous training. Therefore, the satellite... In the r The actual model uploaded in the wheel is ; Introduce a gradient compensation strategy to construct a model buffer: (5) Among them, for those belonging to the set For satellites that upload new models in this round, the server will wait until it receives them. A new local model is created; for satellites that have not uploaded a new model, their historical models are used for aggregation and updating; definition for The obsolescence of the model, specifically for satellites whose models were uploaded in this round, i.e. Its age For satellites using historical models, i.e. Its age The difference between the global epoch on which the model training was based in the last upload and the current epoch; Ground parameter server utilizes model cache Perform a global model update: (6) in, To normalize the aggregate weights, For obsolescence perception weight, This is a hyperparameter.

[0017] The present invention also discloses a system for training a semi-asynchronous satellite federated learning model based on staleness control, comprising: a memory, a processor, and a computer program stored in the memory, the computer program being configured to implement the steps of the method described in the present invention when invoked by the processor.

[0018] The beneficial effects of this invention are as follows: 1. This invention proposes a dynamic aggregation mechanism for staleness control: by using Lyapunov optimization, the multi-round coupling problem is transformed into a sequential single-round decision-making process. While strictly constraining model staleness, it achieves synergistic optimization of training latency and model accuracy, overcoming both the limitations of synchronous methods due to satellite-to-ground communication windows and the unstable convergence and low accuracy of asynchronous methods; 2. A gradient compensation strategy is designed: to address the model update loss caused by satellite-to-ground link interruptions, a gradient compensation mechanism is introduced. By constructing a dynamic model cache queue, historical models of unupdated nodes are reused, significantly mitigating the negative impact of non-independent and identically distributed data on model convergence; 3. An optimal balance between training latency and model accuracy is achieved: by establishing a latency-accuracy joint optimization model, training efficiency and model quality are considered simultaneously when dynamically adjusting the aggregation scale. This ensures that training is completed within a limited time while guaranteeing model convergence accuracy through staleness control, thereby maximizing the overall system performance. Attached Figure Description

[0019] Figure 1 This is a flowchart of the training method of the present invention; Figure 2 This is a schematic diagram of the semi-asynchronous satellite on-orbit federated learning of the present invention; Figure 3 This is the timing diagram of the on-orbit federated learning training of semi-asynchronous satellites based on obsolescence control in this invention; Figure 4 is a comparison chart of the accuracy of the model of the present invention; Figure 4(a) MNIST, Figure 4(b) MNIST Figure 4(c) CIFAR-10 Figure 4(d) CIFAR-10 . Detailed Implementation

[0020] Current research on semi-asynchronous satellite federated learning mainly focuses on switching strategies between synchronous and asynchronous mechanisms, and has not yet developed an adaptive adjustment method for the number of aggregates based on the dynamic characteristics of communication windows and model staleness control. To address this, this invention, targeting low-Earth orbit satellite constellation architectures without inter-satellite links, proposes a staleness-controlled semi-asynchronous federated learning method by systematically analyzing the latency characteristics during semi-asynchronous training. This method aims to alleviate the model staleness problem caused by the intermittency of communication windows and its constraint on training efficiency. Simultaneously, a gradient compensation strategy is constructed to address the problem of non-independent and identically distributed data affecting model convergence. This research lays the technical foundation for the application of semi-asynchronous satellite on-orbit federated learning.

[0021] The core objective of this invention is to construct a semi-asynchronous federated learning framework in a low-Earth orbit satellite constellation without inter-satellite links. This avoids transmitting large amounts of raw data back to ground parameter servers and dynamically adjusts the number of local models in each aggregation round while controlling model staleness, thereby improving training efficiency while making efficient use of the communication window. Furthermore, by introducing a gradient compensation strategy, historical models of satellites that have not updated their models in a timely manner are reused for aggregation, mitigating the impact of non-independent and identically distributed on-board data on model accuracy. This method can adaptively determine the optimal number of aggregations per round based on the satellite constellation configuration and model parameters. Combined with the gradient compensation mechanism, it effectively improves model accuracy while reducing training time and mitigating the negative impact of the visible window and non-independent and identically distributed data on training.

[0022] The specific implementation method of the staleness control semi-asynchronous satellite federated learning model training method disclosed in this invention is as follows: First, a system model for a semi-asynchronous on-orbit satellite federated learning task is established, describing the model distribution, local training, and model aggregation processes between the parameter server and satellite nodes. A gradient compensation mechanism is designed to mitigate the impact of non-independent and identically distributed data on the training process by introducing historical models during the global aggregation phase. Addressing the intermittency of satellite-to-ground communication windows and the heterogeneity of satellite computing resources, a system training latency expression incorporating communication and computation delays is further derived. Second, an optimization problem is constructed with the objective of minimizing the global loss function. This problem requires decomposing the original coupled problem into a series of independently solvable single-round optimization subproblems while satisfying constraints on total training time and model staleness. Finally, based on this single-round optimization framework, a dynamic aggregation strategy with staleness control is designed to adaptively adjust the number of satellites participating in each aggregation round.

[0023] The semi-asynchronous satellite on-orbit federated learning method based on staleness control proposed in this invention has the following characteristics: 1. Joint Optimization: The Lyapunov optimization framework is adopted to decouple the multi-round joint optimization problem into a sequential single-round decision problem. While effectively controlling the model staleness to not exceed the threshold, the training latency and model accuracy are optimized in a coordinated manner to improve the training efficiency and ensure that the overall algorithm maintains a low complexity.

[0024] 2. Obsolescence Control: By defining the round difference as an obsolescence quantification index, a threshold constraint mechanism is designed to ensure that the model's obsolescence does not affect the global optimization direction. Based on satellite visibility time sorting and cumulative obsolescence calculation, Lyapunov optimization is used to adaptively determine the optimal aggregation number in each round, effectively balancing training efficiency and convergence stability.

[0025] 3. Gradient Compensation: To address model gaps caused by semi-asynchronous training, a gradient compensation mechanism is introduced. By constructing a dynamic model cache queue, historical models are used to compensate for unupdated nodes, significantly mitigating the negative impact of non-independent and identically distributed data on model convergence and improving model accuracy.

[0026] (1) Implementation process like Figure 1 As shown, this invention discloses a method for training a semi-asynchronous satellite federated learning model with staleness control. The specific steps are as follows: Step 1: Input the space-based computing constellation parameters, including satellite orbital altitude, number of satellites, orbital inclination, ground station location, satellite-to-ground communication channel parameters, model size, model computational load, and satellite computational throughput; Step 2: The ground parameter server broadcasts the latest global model to visible satellites; Step 3: Receive satellite data from the global model, train the model using the local dataset, and generate a local model update; Step 4: Once the training is complete and the satellites are visible to the Earth, they will upload the trained local model to the ground parameter server; Step 5: The ground parameter server selects the optimal number of aggregations for this round based on the model staleness, and determines whether the number of all received local models has reached the optimal number of aggregations. If the optimal number of aggregations has not been reached, return to step 2; otherwise, jump to step 6. Step 5 also includes: The first step is to construct an optimization problem with the goal of minimizing the global loss function. Under the premise of satisfying the constraints of total training time and model staleness, the original coupled problem is decomposed into independent single-round optimization subproblems using a Lyapunov optimization-based method. The second step: Based on the single-round optimization framework of the first step, design a dynamic aggregation strategy for staleness control to achieve adaptive adjustment of the number of satellites participating in aggregation in each round.

[0027] Step 6: Based on the received local model, the ground parameter server uses a gradient compensation strategy to aggregate and update the global model; Step 7: Determine if the global model has converged. If it has not converged, return to step 2; otherwise, end the training.

[0028] (2) System Model Consider deploying a semi-asynchronous federated learning framework on a low-Earth orbit satellite network. Assume the system consists of… Each satellite orbital plane, It consists of one satellite and one ground parameter server. Assuming the communication channel between the satellite and the parameter server is a Gaussian channel, according to Shannon's formula, the satellite... The maximum data transfer rate achievable between the parameter server and the parameter server is (1) in, Boltzmann's constant, The receiver noise temperature; This refers to the bandwidth of the satellite-to-ground link channel. This refers to the transmission power. Transmitter antenna gain; This refers to the antenna gain at the receiving end. For satellite Path loss between the parameter server and the parameter server: (2) in, For free space path loss, For carrier frequency, At the speed of light, For satellite The altitude of the orbit; For shadow fading, it follows a normal distribution, i.e. ; This indicates signal power attenuation caused by surrounding buildings and ground objects, determined by elevation angle. carrier frequency Determined by environmental characteristics; This indicates a decrease in signal power due to atmospheric effects.

[0029] In the satellite federated learning framework, each satellite independently trains its local model based on its local dataset. Let the total size of all satellite datasets be... ,in For satellite The local dataset. If... Samples in As the training input, the local loss function is defined as (3) in, For model parameters, For example, the loss function can be a sample loss function, such as linear regression or support vector machine. The global loss function is defined as: (4) The goal of satellite federated learning is to obtain optimal model parameters through collaborative training. This minimizes the global loss function, i.e. .

[0030] The specific process of semi-asynchronous satellite federated learning is as follows: Figure 2 As shown, it includes the following four stages: 1) During the model broadcast phase, when a satellite is within the visible window of the parameter server and is in an idle state, if the current global model... For a new version that has not yet been trained on the satellite, the ground parameter server will broadcast the global model to the satellite via the satellite-to-ground link.

[0031] 2) During the local training phase, the satellite Upon receiving the global model Then, based on its local dataset conduct Step stochastic gradient descent Update its local model ,in Indicates satellite In the r In the global training round i The local model after +1 iterations i Indicates the number of steps in the local iteration. r Indicates training rounds, Indicates the learning rate. Represents the local loss function. Indicates satellite In the r In the global training round i The local model after the next iteration , Indicates satellite In the r Round iteration The local model obtained after the step.

[0032] 3) During the local model upload phase, once the satellite completes local training and becomes visible to the Earth, it will upload the trained local model. Uploaded to the ground parameter server.

[0033] 4) During the global aggregation update phase, the parameter server determines the optimal aggregation quantity for each round. and satellite collection .definition Indicates satellite Is it in the first Upload new models in rounds, among which This indicates uploading, and vice versa, it indicates not uploading. Therefore, there is... ,in Represents a collection of satellites. .definition For satellite The difference between the last received global model epoch and the current epoch represents the staleness resulting from semi-asynchronous training. Therefore, satellite In the r The actual model uploaded in the wheel is .like Figure 3 As shown, to mitigate the impact of non-independent and identically distributed data, this invention introduces a gradient compensation strategy and constructs a model buffer: (5) Among them, for those belonging to the set For satellites that upload new models in this round, the server will wait until it receives them. A new local model is created; for satellites that have not uploaded a new model, their historical models are used for aggregation and updating. Definition for The obsolescence of the model, specifically for satellites whose models were uploaded in this round, i.e. Its age For satellites using historical models, i.e. Its age This is the difference between the global epoch on which the model was last uploaded for training and the current epoch. Based on this, the parameter server utilizes... Update the global model (6) in, To normalize the aggregate weights, For obsolescence perception weight, This is a hyperparameter.

[0034] (3) Training time analysis For satellites In an ideal scenario where ground communication window constraints are not considered, the data is transmitted from the parameter server to the satellite. Send global model to parameter server and receive satellite data. The total latency required for the local model is (7) in, For transmission delay, For model size; To delay the transmission time, The orbital height; To reduce training latency, To determine the size of the training mini-batch, For local training sessions, For the computational load of the model, For satellite The computational throughput.

[0035] Taking into account the communication window, for a given satellite In its first r The first round of global training n The duration of each visible window is Its starting time is If the satellite In the r If there is no trainable global model, then the satellite... In the r The time frame for the round-robin upload model is defined as: (8) If the satellite can complete training within the current visible window, the model will be uploaded immediately after training. T k To transmit data from the parameter server to the satellite without considering the communication window Send global model to parameter server and receive satellite data. The total latency required for the local model, N For satellite k In the r The total number of visible windows on the ground during each training round; if it cannot be completed in the current window, it must wait until the next available visible window after training ends to upload. For satellite k Propagation delay between PS and PS for k Transmission delay between PS and PS.

[0036] Therefore, the first r The time required for round training is .

[0037] Considering the first r The satellites used in the rotation may already have a trained model or be in the process of training. r The actual time required for round training is less than or equal to This formula can be used as an upper bound in the analysis. In subsequent experiments, Calculated based on the actual training situation of the satellite.

[0038] (4) Optimization problem establishment Given that the number of new models participating in each round of aggregation directly affects the training effect, this invention aims to control the obsolescence of system models to not exceed a preset threshold and dynamically adjust the number of aggregations, while ensuring that the total training time does not exceed a certain threshold. Under the constraints, minimize the global loss function. To this end, the following optimization problem is established: (9) (9-a) (9-b) (9-c) Among them, (9-a) is the training duration constraint, which restricts the total training time from exceeding the training time threshold. , Represents the global loss function. R Indicates the total number of training rounds. T r Indicates the first r The time required for each training round; (9-b) is the obsoleteness constraint, which requires that the obsoleteness of the models uploaded by all satellites in any training round must not exceed the obsoleteness threshold. , For satellite The difference between the last received global model round and the current round represents the staleness generated by semi-asynchronous training; (9-c) is the aggregation quantity constraint, that is, the upper limit of the number of new models received in each round is the total number of satellites. Indicates the first r The number of wheels in aggregation, r Indicates the number of training rounds. K This indicates the total number of satellites.

[0039] (5) Problem Solving Problem (9) is difficult to solve directly because it is hard to obtain a closed-form expression for the global loss function. Therefore, this invention analyzes and derives the upper bound of the convergence of the global loss function and transforms the original problem into an optimization problem of this upper bound. (Regarding the learning rate...) In the case of this invention, the convergence bound of the method is (10) in, , , , , , Indicates the optimal loss. Represents the initial global model. Indicates satellite Is it in the first r Upload new models in rounds. For the total number of satellites, This represents the number of local iterations. The antiquity threshold, For learning rate, , , , , , These are all hyperparameters determined by the initial system settings and are unrelated to the specific training process.

[0040] In equation (10), the upper bound of convergence consists of three terms: the first term The second term represents the difference between the initial global loss and the optimal loss, and its value is determined by the system hyperparameters and the initial model. Determined by system hyperparameters; the third item This reflects the cumulative effect of model staleness over multiple training rounds. Due to the learning rate... ,so ,lead to The effect of obsolescence increases exponentially with each training round, reflecting that obsolescence has a more significant impact in the later stages of training. All three parameters increase exponentially with each training round. The obsolescence level increases with the increase in age, so it is necessary to set an appropriate obsolescence threshold and control the obsolescence level to be below that threshold. In summary, weights are introduced. Measure the first The impact of obsolescence in round training, and transforming problem (9) into (11) (11-a) (11-b) (11-c) Directly solving problem (11) remains impractical because it requires optimal allocation of latency budgets across training rounds. Furthermore, the interdependence between staleness and aggregation quantity across rounds necessitates a long-term strategy. Therefore, we employ the Lyapunov optimization method to overcome the challenges posed by inter-round coupling, specifically defining the following virtual queue: (12) Based on this, to measure the stability of the training process, the Lyapunov equation is defined as follows: (13) This function represents the deviation between the actual training time in each round and the preset latency budget. Further, we define the single-step Lyapunov drift function as... (14) To simultaneously control system obsolescence, a drift plus penalty function is constructed: (15) in, It is a weighting coefficient that balances training time and accuracy. This represents the weight that increases with each round. Based on this, the present invention transforms the optimization problem in equation (11) into... (16) (16-a) (16-b) To satisfy constraint (16-a), namely ensuring that the model obsolescence of all satellites does not exceed a threshold, this invention sets a minimum number of aggregations. To achieve this goal, specifically, in each training round, the algorithm will select all satellites whose current obsoleteness equals a threshold and include them all in the aggregation set. The number of these satellites is the candidate value for the minimum number of aggregations required. Based on this, as shown in Table 1, we propose Algorithm 1, which achieves flexible aggregation based on obsoleteness control, with a complexity of O(n log n). The main steps are as follows: Step S1: Sort the clients in ascending order based on satellite visibility time to obtain an ordered set of satellites. Initialize the cumulative staleness array. and collection of highly outdated clients (lines 2-4).

[0041] Step S2: Iterate through the sorted clients, calculate the cumulative sum of squares of obsolescence, and set the obsolescence equal to the threshold. The client is added to the collection of highly outdated clients. A collection of outdated client applications H cardinality and The maximum value in is the minimum number of aggregates. , To maintain a stable number of polymers Lower limit; (lines 5-11).

[0042] Step S3: Traverse the candidate values ​​for the number of aggregates Construct an aggregate client collection Calculate the time required for this round of training for this set. And calculate the objective function value (lines 12-16).

[0043] Step S4: Determine the optimal number of aggregations and the corresponding aggregated satellite set (lines 17-18).

[0044] Step S5: Update the virtual queue to complete this round of scheduling. (line 19) Table 1 Adaptive Aggregation Algorithm Based on Antiquity Control

[0045] (5) Simulation experiment verification To verify the performance of the proposed algorithm, we conducted experiments on a system consisting of a parameter server located in Beijing and 10 low-Earth orbit satellites operating at an altitude of 500 kilometers and an orbital inclination of 30 degrees. The experimental platform used two classic models for performance evaluation: a CNN model based on the MNIST dataset and a ResNet-18 model based on the CIFAR-10 dataset. To analyze the training performance under different data distribution conditions, we used a Dirichlet distribution to partition all datasets into non-independent and identically distributed subsets, setting... Two levels of heterogeneity, the smaller of which The value indicates a higher degree of data heterogeneity among clients. See Table 2 for specific constellation simulation parameters. To maintain a stable number of aggregates, select... .

[0046]

[0048] The following schemes were used for comparison: 1) FedAvg: A synchronous federated learning scheme where the ground parameter server must wait for all satellites to complete local training and successfully upload their local models before performing global aggregation and model updates; 2) FedAsync: An asynchronous federated learning scheme where the parameter server immediately updates and distributes the global model once it receives a local model uploaded by any satellite. 3) FedBuff: A semi-asynchronous federated learning scheme that sets up a cache queue on the parameter server side, and performs global aggregation only after a specified number of local models have been collected. The specified number is fixed for each round.

[0049] Figures 4(a) and 4(b) show the accuracy comparison results on the MNIST dataset. Experiments show that the asynchronous satellite federated learning method suffers from the worst performance due to neglecting model temporal consistency, while the semi-asynchronous method exhibits significant fluctuations due to the non-independent and identically distributed nature of the data. In contrast, the method proposed in this invention achieves better performance. and The methods achieved accuracies of 0.9373 and 0.8763 under the two settings, respectively, which are superior to the baseline method and relatively stable. In terms of training efficiency, the methods of this invention can achieve accuracies of over 0.9 and 0.75 for five consecutive rounds in only 29.31 hours and 49.54 hours, respectively, which is 1.75 times and 1.50 times faster than the best benchmark method.

[0050] Figures 4(c) and 4(d) show the experimental results of different schemes on the CIFAR-10 dataset, further verifying the superiority of the proposed method. Both asynchronous and semi-asynchronous methods exhibited severe oscillations. The FedAvg algorithm was relatively stable, but its highest accuracy was low within the set time range. The proposed method, however, showed a faster convergence speed, with accuracies improved to 0.6005 and 0.4866, respectively. Notably, the proposed method maintained an accuracy exceeding 0.5 and 0.4 for five consecutive rounds in only 50.58 hours and 99.58 hours, respectively, achieving speedups of 1.95 times and 1.25 times compared to the best comparison method.

[0051] By comparing the performance under different degrees of non-independent and identically distributed characteristics, it can be seen that the proposed scheme exhibits stronger adaptability in heterogeneous data scenarios. Its staleness control mechanism and gradient compensation strategy effectively suppress model fluctuations and mitigate the impact of data distribution differences on convergence.

[0052] The present invention also discloses a system for training a semi-asynchronous satellite federated learning model based on staleness control, comprising: a memory, a processor, and a computer program stored in the memory, the computer program being configured to implement the steps of the method described in the present invention when invoked by the processor.

[0053] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A training method for a semi-asynchronous satellite federated learning model based on staleness control, characterized in that, Includes the following steps: Step 1: Input the parameters of the space-based computing constellation; Step 2: The ground parameter server broadcasts the latest global model to visible satellites; Step 3: Receive satellite data from the global model, train the model using the local dataset, and generate a local model update; Step 4: Once the training is complete and the satellites are visible to the Earth, they will upload the trained local model to the ground parameter server; Step 5: The ground parameter server selects the optimal number of aggregations for this round based on the model's staleness, and determines whether the number of all received local models has reached the optimal number of aggregations. If the optimal number of aggregations has not been reached, return to step 2; otherwise, jump to step 6. Step 6: The ground parameter server uses the received local model and employs a gradient compensation strategy to aggregate and update the global model; Step 7: Determine if the global model has converged. If it has not converged, return to step 2; otherwise, end the training.

2. The semi-asynchronous satellite federated learning model training method according to claim 1, characterized in that, In step 1, the space-based computing constellation parameters include satellite orbital altitude, number of satellites, orbital inclination, ground station location, satellite-to-ground communication channel parameters, model size, model computational load, and satellite computational throughput.

3. The semi-asynchronous satellite federated learning model training method according to claim 1, characterized in that, In step 2, when the satellite is within the visible window of the ground parameter server and is in an idle state, if the current global model is a new version that has not been trained on the satellite, the ground parameter server will broadcast the global model to the satellite via the satellite-to-ground link.

4. The semi-asynchronous satellite federated learning model training method according to claim 1, characterized in that, In step 3, the satellite Upon receiving the global model Then, based on its local dataset conduct Step stochastic gradient descent Update its local model ,in Indicates satellite k In the r In the global training round i The local model after +1 iterations i Indicates the number of steps in the local iteration. r Indicates training rounds, Indicates the learning rate. Represents the local loss function. Indicates satellite In the r In the global training round i The local model after the next iteration , Indicates satellite In the r Round iteration The local model obtained after the step.

5. The semi-asynchronous satellite federated learning model training method according to claim 1, characterized in that, Step 5 also includes: The first step is to construct an optimization problem with the goal of minimizing the global loss function. Under the premise of satisfying the constraints of total training time and model staleness, the original coupled problem is decomposed into independent single-round optimization subproblems using a Lyapunov optimization-based method. The second step is to design a dynamic aggregation strategy for staleness control based on the single-round optimization framework of the first step, so as to achieve adaptive adjustment of the number of satellites participating in aggregation in each round.

6. The semi-asynchronous satellite federated learning model training method according to claim 5, characterized in that, The first step also includes: Step a1: Establish the optimization problem as follows: (9) (9-a) (9-b) (9-c) Equation (9-a) represents the training duration constraint, which stipulates that the total training time must not exceed the training time threshold. , Represents the global loss function. R Indicates the total number of training rounds. T r Indicates the first r The time required for each training round; Equation (9-b) is the obsoleteness constraint, which stipulates that the obsoleteness of the models uploaded by all satellites in any training round must not exceed the obsoleteness threshold. , For satellite The difference between the last received global model round and the current round represents the staleness generated by semi-asynchronous training; Equation (9-c) is the aggregation quantity constraint, that is, the upper limit of the number of new models received in each round is the total number of satellites. Indicates the first r The number of wheels in aggregation, r Indicates the number of training rounds. K Indicates the total number of satellites; Step a2: Problem Solving; By analyzing and deriving the upper bound of the convergence of the global loss function, the optimization problem in step a1 is transformed into a substitute problem of optimizing the upper bound of convergence. This is solved using a Lyapunov optimization-based method, with the learning rate... In this case, the convergence bound is: （10）, in, , , , , , Indicates the optimal loss. Represents the initial global model. Indicates satellite Is it in the first r Upload new models in rounds. For the total number of satellites, This represents the number of local iterations. The antiquity threshold, For learning rate, , , , , , These are all hyperparameters determined by the initial system settings; In equation (10), the first term The second term represents the difference between the initial global loss and the optimal loss, and its value is determined by the system hyperparameters and the initial model. Determined by system hyperparameters; the third item This reflects the cumulative effect of model obsolescence over multiple training rounds; Introducing weights Measure the first r The impact of obsolescence in round training transforms problem (9) into （11） (11-a) (11-b) (11-c) To overcome the coupling problem between rounds, the Lyapunov optimization method is adopted, and the following virtual queue is defined: （12） Based on this, to measure the stability of the training process, the Lyapunov equation is defined as follows: （13） This function represents the deviation between the actual training time in each round and the preset latency budget. Furthermore, the single-step Lyapunov drift function is defined as follows: （14） To simultaneously control system obsolescence, a drift plus penalty function is constructed: （15） in, It is a weighting coefficient that balances training time and accuracy. Let represent the weights that increase with each round. Based on this, the optimization problem in equation (11) is transformed into... （16） (16-a) (16-b)。 7. The semi-asynchronous satellite federated learning model training method according to claim 5, characterized in that, The second step also includes: Step S1: Sort the clients in ascending order based on satellite visibility time to obtain an ordered set of satellites. Initialize the cumulative staleness array. and collection of highly outdated clients ; Step S2: Iterate through the sorted clients, calculate the cumulative sum of squares of obsolescence, and classify clients whose obsolescence exceeds the threshold. The client is added to the collection of highly outdated clients. A collection of outdated client applications H cardinality and The maximum value in is the minimum number of aggregates. , To maintain a stable number of polymers Lower limit; Step S3: Traverse the candidate values ​​for the number of aggregates Construct an aggregate client collection Calculate the aggregate client set Time required for the next round of training and the objective function value; Step S4: Determine the optimal number of aggregations and the corresponding aggregated satellite set ; Step S5: Update the virtual queue to complete this round of scheduling.

8. The semi-asynchronous satellite federated learning model training method according to claim 7, characterized in that, In step S3, the aggregated client set is calculated. Time required for the next round of training The specific steps are as follows: Taking into account the communication window, for a given satellite In its first r The first round of global training n The duration of each visible window is Its starting time is If satellite In the r If there is no trainable global model, then the satellite... k In the r The time frame for the round-robin upload model is defined as: （8） If the satellite can complete training within the current visible window, the model will be uploaded immediately after training. T k To transmit data from the parameter server to the satellite without considering the communication window Send global model to parameter server and receive satellite data. The total latency required for the local model, N For satellite In the r The total number of visible windows on the ground during each training round; if it cannot be completed in the current window, it must wait until the next available visible window after training ends to upload. For satellite Propagation delay between PS and PS for Transmission latency between PS and PS Therefore, the first r The time required for round training is .

9. The semi-asynchronous satellite federated learning model training method according to claim 1, characterized in that, Step 6 specifically involves: definition Indicates satellite Is it in the first r Upload new models in rounds, among which This indicates uploading, and vice versa, it indicates not uploading. Therefore, there is... ,in Represents a collection of satellites. ; definition For satellite The difference between the last received global model iteration and the current iteration represents the staleness resulting from semi-asynchronous training. Therefore, the satellite... In the r The actual model uploaded in the wheel is ; Introduce a gradient compensation strategy to construct a model buffer: （5）， Among them, for those belonging to the set For satellites that upload new models in this round, the server will wait until it receives them. A new local model is created; for satellites that have not uploaded a new model, their historical models are used for aggregation and updating; definition for The obsolescence of the model, specifically for satellites whose models were uploaded in this round, i.e. Its age For satellites using historical models, i.e. Its age The difference between the global epoch on which the model training was based in the last upload and the current epoch; Ground parameter server utilizes model cache Perform a global model update: （6） in, To normalize the aggregate weights, Weighting for obsolescence perception. This is a hyperparameter.

10. A system for training a semi-asynchronous satellite federated learning model based on staleness control, characterized in that, include: A memory, a processor, and a computer program stored on the memory, the computer program being configured to implement the steps of the method of any one of claims 1-9 when invoked by the processor.

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