A joint communication and computing resource allocation method for multi-cluster aerial federated edge learning

Abstract

This invention discloses a joint communication and computing resource allocation method for multi-cluster aerial federated edge learning. This invention achieves a comprehensive improvement in system performance by jointly optimizing the clustering affiliation relationships between edge devices and servers, CPU frequency, transmit power, and the receiver factor of parameter servers. Specifically, this invention first derives the theoretical bound of the system loss through convergence analysis and constructs a long-term optimization problem to minimize the average total resource consumption cost of the system. For this non-convex problem, this invention decomposes it into two sub-problems: dynamic clustering affiliation and joint communication and computing resource allocation. By constructing a non-cooperative game model among mobile edge devices, the optimal clustering affiliation decision is derived based on Nash equilibrium. Then, the non-convex resource allocation problem is further decomposed into multiple computationally feasible sub-problems, and the corresponding structured optimal solutions are derived. Simulation results show that the proposed algorithm has significant advantages in both training latency and energy consumption.

Description

Technical Field

[0001] This invention relates to the field of communications, specifically to a joint communication computing resource allocation method based on multi-cluster aerial federated learning, and more particularly to a game theory-based dynamic cluster partitioning and resource allocation algorithm that can jointly optimize the edge device layer, edge server layer, and parameter server layer. Background Technology

[0002] With the continuous development of IoT, AI, and edge computing technologies, bandwidth and computing resource constraints in wireless networks have become a core bottleneck limiting the participation of massive edge devices in collaborative tasks. Federated learning provides a practical solution for global model collaborative training across large-scale heterogeneous edge devices, while Federated Edge Learning (FEEL) is specifically optimized for the distributed training needs of mobile edge scenarios. However, the communication-computation decoupling architecture adopted by traditional Federated Edge Learning significantly restricts its operating efficiency in resource-constrained environments. Over-the-air (OTA) computing technology, leveraging the inherent broadcast and electromagnetic superposition characteristics of wireless channels, has pioneered a new paradigm for efficient distributed data processing. In this context, the fusion architecture of OTA computing and Federated Edge Learning can significantly improve the efficiency of collaborative training, demonstrating significant technical advantages. However, existing Over-the-Air Federated Edge Learning (OTA-FEEL) research schemes still have key shortcomings: First, single-cluster scenarios struggle to meet the scalability requirements of large-scale heterogeneous wireless networks, and their performance is also limited by the influence of channel characteristics and gradient distribution features on aggregation accuracy and training efficiency. Second, the performance ceiling of OTA-FEEL is limited by the energy constraints of edge devices, highlighting the urgent need to design efficient communication and computing resource allocation strategies to balance energy consumption and training performance. Third, multi-cluster OTA-FEEL deployed in urban scenarios faces the challenge of dynamic changes in device mobility and wireless channel states. Existing static optimization schemes lack the ability to adapt to frequent cluster switching and time-varying channel characteristics, making it difficult to meet the needs of this dynamic operating scenario. Therefore, researching game-theoretic dynamic clustering and resource allocation algorithms suitable for multi-cluster OTA-FEEL systems has significant research value and exploratory significance. Summary of the Invention

[0003] The purpose of this invention is to address some shortcomings in existing research by proposing a game-theoretic dynamic clustering and resource allocation method for multi-cluster OTA-FEEL systems. It employs a game-theoretic-based dynamic cluster partitioning and resource allocation algorithm that jointly optimizes the edge device layer, edge server layer, and parameter server layer.

[0004] The technical solution adopted in this invention is: a joint communication computing resource allocation method for multi-cluster aerial federation edge learning, comprising the following steps:

[0005] 1) Construct a system model and jointly optimize cluster affiliation decisions. CPU frequency Edge device transmit power Edge server transmit power and parameter server receiving factor The optimization problem is constructed with the objective of minimizing long-term average resource consumption.

[0006] 2) Solve the dynamic cluster partitioning subproblem of the optimization problem in step 1) using a game theory-based method;

[0007] 3) Based on the dynamic cluster in step 2), the alternating optimization algorithm is used to solve the joint communication and computational resource allocation subproblem in the optimization problem to obtain the system resource allocation.

[0008] Specifically, the system model includes N mobile edge devices, S edge servers and 1 parameter server. Each edge server is responsible for providing intermediate data processing and computing services, while the parameter server is responsible for task distribution and global model parameter aggregation services. In each round of communication, all mobile edge devices are divided into different clusters through a clustering method. Gradient aggregation between clusters is performed between each cluster, while gradient aggregation within a cluster is implemented within each cluster through OTA.

[0009] Furthermore, the optimization problem described in step 1) is:

[0010]

[0011]

[0012]

[0013]

[0014]

[0015]

[0016]

[0017]

[0018] in The communication rounds are represented by the set of mobile edge devices denoted as . The cluster set is denoted as , The set of indices representing the maximum number of communication rounds in a cluster is denoted as . , , These are the trade-off factors between the costs of mobile edge devices and edge servers. and Let n be the cost function of the mobile edge device and s be the cost function of the edge server. This indicates its corresponding cluster affiliation. This indicates the CPU frequency of the mobile edge device. This indicates the maximum value of its corresponding CPU frequency. This indicates its corresponding transmission power. This represents the maximum power budget for mobile edge device n. Indicates the transmit power of the edge server. This represents the number of mobile edge devices within cluster s. Represents the compensated real-valued channel coefficients. This represents the noise variance at the edge server. This represents the maximum power budget for edge servers s. This indicates the parameter server accept factor. This represents the cumulative average optimal gap. It indicates its upper bound limit.

[0019] Constraint 1 and Constraint 2 ensure that each device belongs to only one cluster, binary variables. Indicates cluster affiliation. This indicates that device n in round r is assigned to cluster s, otherwise it is 0; Constraint 3 limits the maximum CPU frequency of the device; Constraints 4 and 5 limit the maximum transmit power of the edge device and the server, respectively; Constraint 6 defines the range of values ​​for the parameter server receive factor; Constraint 7 limits the cumulative average optimality gap between the expected global loss and the optimal global loss.

[0020] In step 2), to address the dynamic cluster partitioning subproblem within the optimization problem, we first optimize the clustering component: by designing a static clustering strategy that integrates distance awareness and channel quality awareness, we initialize the cluster state; then, based on Nash equilibrium, we construct a non-cooperative game model among edge devices to dynamically adjust the cluster affiliation of mobile edge devices. This process is one of the core modules of the game-theoretic alternation algorithm, responsible for determining the association structure between mobile edge devices and edge servers.

[0021] Furthermore, step 2) specifically includes the following processing steps:

[0022] definition Let n be the distance between the mobile edge device and the edge server s. The coverage area, distance metric, and channel state stability metric for each edge server are defined as follows:

[0023]

[0024] in and Let represent the standard deviation and mean of the signal-to-noise ratio, respectively; based on this, the stability index at the beginning of communication round r is:

[0025]

[0026] in and Used to balance distance and channel stability metrics, satisfying The parameter server assigns the mobile edge device n to make... Maximize the edge server ,Right now:

[0027]

[0028] Subsequently, the dynamic cluster affiliation is modeled as a non-cooperative game among mobile edge devices, represented by triples: , where: the set of participants Each device acts as an independent decision-making entity, responsible for selecting its cluster; policy space: ,in , It is the policy set for mobile edge device n. Indicates that device n selects cluster s, Includes selection of all devices; cost-utility function Cluster affiliation decision Mapping to real numbers, i.e. ,in The selection by the mobile edge device n itself The cluster affiliation optimization problem for each mobile edge device n is determined jointly with the strategies of other devices, in order to minimize the overall resource cost:

[0029]

[0030]

[0031]

[0032] in Indicates the affiliation selection for all mobile edge devices. This represents the selection of all mobile edge devices except n. This indicates the resource consumption of mobile edge devices. This represents the corresponding loss function.

[0033] The problem is solved using Nash equilibrium to obtain the optimal cluster affiliation decision.

[0034] In step 3) of this invention, based on the dynamic cluster, we further address the communication computing resource allocation subproblem: using the Lagrange duality and penalty function method, we decompose the non-convex resource allocation problem, ultimately deriving an optimal solution with a tractable structure, achieving joint optimization of CPU frequency, edge device transmission power, edge server transmission power, and parameter server receiving factor. This subproblem, in conjunction with the cluster subproblem, constitutes a complete game-theoretic alternation algorithm.

[0035] Furthermore, after obtaining the solution to step 2), the following problem is constructed to optimize the CPU frequency. Edge device transmission power Edge server transmission power and parameter server receiving factor :

[0036]

[0037]

[0038] This indicates the cluster affiliation of mobile edge device n. This represents the energy consumption factor.

[0039] The problem Since this is a non-convex problem, it is decomposed into two sub-problems: one responsible for calculating resource allocation. And the issue of allocating communication resources. ,question The problem is solved directly using a convex optimization solver. The problem is decomposed by using an alternating minimization method, combined with Lagrange duality and penalty function methods, and then solved.

[0040] Specifically, the problem For: given transmission power , and receiving factor Optimize CPU frequency by addressing the following issues. :

[0041]

[0042]

[0043] , These represent the power consumption and latency of mobile edge devices, respectively. , These represent the corresponding energy consumption and delay, respectively.

[0044] By introducing auxiliary variables and constraints , the problem The problem is transformed into a convex problem and then solved directly using a standard convex optimization solver.

[0045] Specifically, the problem For: given CPU frequency Optimize transmit power by constructing the following problem. , and receiving factor :

[0046]

[0047]

[0048] , These represent the edge server's energy consumption and latency, respectively. , These represent the corresponding energy consumption and delay, respectively.

[0049] Will Rewritten as:

[0050]

[0051] in ,and , and Represents the relevant linearly independent terms. and These represent the real-valued coefficients of the corresponding channel. , , Let these represent the transmit power of the mobile edge device, the denormalization factor, and the transmit power of the edge server, respectively. Then, a penalty factor is introduced. The penalty function method is used to apply nonlinear constraints. Integrating into the problem From the objective function, we obtain the reconstructed problem:

[0052]

[0053]

[0054] Among the problems The objective function is:

[0055]

[0056] in This represents the corresponding noise variance.

[0057] An alternating minimization method is used to alternately optimize the transmission power of edge devices. Edge server transmission power and parameter server receiving factor ;

[0058] First, given and Optimize by constructing the following problem :

[0059]

[0060]

[0061]

[0062] in ,and Subsequently, the Lagrange duality method was used to derive the solution to the problem. ;

[0063] Then, given and Optimize the following issues :

[0064]

[0065]

[0066]

[0067] in , , ; the problem objective function pair The first derivative is zero, so we solve for it;

[0068] Given and Optimize the following issues :

[0069]

[0070]

[0071] Similarly, setting the first derivative to zero yields the optimal solution.

[0072] The present invention also provides a communication system comprising N mobile edge devices, S edge servers and 1 parameter server, which is capable of executing the above-described joint communication computing resource allocation method for multi-cluster aerial federated edge learning.

[0073] The present invention has the following beneficial effects:

[0074] To address the challenges of scalability in large-scale heterogeneous wireless networks, energy constraints on edge devices, and dynamic changes in device mobility and wireless channel states, this invention proposes a game theory-based dynamic cluster affiliation and resource allocation algorithm. With the objective of minimizing the long-term average resource consumption of the COTA-FEEL system, we jointly optimize cluster affiliation, CPU frequency, transmission power of edge devices and edge servers, and the receiver factor of the parameter server. Specifically, we design a cluster affiliation strategy and a non-cooperative game model to dynamically adjust device affiliation relationships; subsequently, we employ an alternating optimization method to decompose this non-convex problem into convex subproblems for efficient solution. Simulation results demonstrate that the proposed algorithm exhibits significant advantages in both training latency and energy consumption. Attached Figure Description

[0075] Figure 1 This is a multi-cluster aerial federation edge learning framework.

[0076] Figure 2 The test accuracy curves of different algorithms on the MNIST dataset are shown.

[0077] Figure 3 The test accuracy curves of different algorithms on the CIFAR-10 dataset are shown.

[0078] Figure 4 The test accuracy curves of different algorithms on the EMNIST dataset are shown.

[0079] Figure 5 This section describes the resource consumption of different algorithms on the MNIST dataset as the number of edge servers changes.

[0080] Figure 6 This section describes the resource consumption of different algorithms on the CIFAR-10 dataset when the number of edge servers changes.

[0081] Figure 7 This section describes the resource consumption of different algorithms on the EMNIST dataset as the number of edge servers changes.

[0082] Figure 8 Comparison of the average error gap of different algorithms on the MNIST dataset when the number of edge devices varies.

[0083] Figure 9 Comparison of the average error gap of different algorithms on the CIFAR-10 dataset when the number of edge devices varies.

[0084] Figure 10 Comparison of the average error gap of different algorithms on the EMNIST dataset when the number of edge devices changes. Detailed Implementation

[0085] To make the objectives, technical solutions, and advantages of the present invention clearer, the specific embodiments of the present invention will be described in further detail below.

[0086] This invention provides a method for allocating joint communication computing resources for multi-cluster aerial federated learning, the method comprising:

[0087] Step 1: Construct a system model and derive the theoretical upper bound of the system loss.

[0088] We consider a COTA-FEEL system consisting of N mobile edge devices, S edge servers, and 1 parameter server. The set of mobile edge devices and the cluster set are denoted as follows: and Each edge server is responsible for providing intermediate data processing and computation services, while the parameter server is responsible for task distribution and global model parameter aggregation services. The index set of communication rounds is defined as follows: , This indicates the maximum number of communication rounds. In each round of communication, all devices are divided into different clusters using a clustering method. ,in This represents the s-th cluster. The number of devices in the cluster, and the total number of devices satisfies Furthermore, inter-cluster gradient aggregation occurs between clusters, while intra-cluster gradient aggregation is implemented within each cluster via OTA. We define... The local dataset of devices n managed by edge server s, where and Let the features and labels of the i-th sample from device n be represented respectively. Let be the total number of local samples possessed by device n. Therefore, the local loss function for device n can be expressed as:

[0089]

[0090] in This represents the model corresponding to the quantized sample. This represents the empirical sample loss function. Represents edge server The clusters and edge devices under my responsibility are from A small batch of samples is randomly selected from the local dataset to calculate the local loss gradient. The updated model is then uploaded to the corresponding edge server for cluster aggregation. Based on this, the local gradient vector can be calculated as follows:

[0091]

[0092] in The dataset representing device n (containing (Number of samples). We normalize the local gradient vector using gradient statistics, and the local mean and variance for device n can be expressed as:

[0093]

[0094] in This indicates the dimension of the quantized sampled data.

[0095] Subsequently, the edge server uploads the gradient statistics to the parameter server, and the corresponding global mean and variance can be expressed as:

[0096]

[0097] Finally, the parameter server broadcasts the statistics to all edge devices in the corresponding cluster. The normalization notation can be represented as:

[0098]

[0099] in This represents the global variance of the gradient statistic.

[0100] This invention adopts the Ricean fading channel model commonly used in urban scenarios. The channel between device n and edge server s can be represented as:

[0101]

[0102] in Indicates reference distance The corresponding channel power gain, and These represent the path loss factor and the Ricean fading factor, respectively. This represents the non-line-of-sight (NLOS) scattering component. This represents the distance between the mobile edge device n and the edge server s. We define... Let be the transmission factor of device n, where and They are respectively The phase and compensated transmission power. Therefore, the aggregated signal received by the edge server via air interface calculation can be expressed as:

[0103]

[0104] in Represents the compensated real-valued channel coefficients. This represents a normalized sign vector (mean 0, variance 1). This represents additive white Gaussian noise (AWGN). This indicates the transmit power of the edge server. To suppress signal interference while improving communication efficiency and model training performance, this invention performs intra-cluster gradient aggregation in different frequency bands; therefore, the device's transmission power must meet the following constraints:

[0105]

[0106] in This represents the maximum power budget for edge device n. This indicates the expectation of the parameter. This represents a normalized symbol vector. The parameter server receives the aggregated signals uploaded by all edge servers via air interface computation, and its goal is to find the optimal model parameters. The global loss function can be expressed as:

[0107]

[0108] Let n be the local loss function for the mobile edge device n.

[0109] Similarly, we define Let be the transmission factor of edge server s, where and They are respectively The phase and compensated transmission power. Therefore, the signal received by the parameter server can be expressed as:

[0110]

[0111] in This represents the amplitude of the channel coefficients between the edge server s and the parameter server. This indicates the corresponding AWGN. Therefore, the transmission power of the edge server must meet the following constraints:

[0112]

[0113] in This represents the maximum power budget for edge server s. The parameter server uses a noise reduction factor. with inverse normalization factor The global gradient vector is estimated by the following expression:

[0114]

[0115]

[0116] Subsequently, the parameter server via Update the global model, where This represents the learning rate of stochastic gradient descent. Let represent the global gradient vector. The expectation of the global gradient vector can be expressed as the mean of the local gradient estimates of all edge devices, i.e.:

[0117]

[0118] This represents the local gradient vector.

[0119] Therefore, the total transmission estimation error of the COTA-FEEL system can be calculated as follows:

[0120]

[0121] in , The first term in the formula represents the signal misalignment error, and the second term represents the noise-induced error. This invention refines the communication and computational consumption models based on air interface computing. In the COTA-FEEL scenario, the execution of the learning task requires gradient uploading and model broadcasting, as well as cluster-wide and global aggregation. Due to the high transmission power and insufficient downlink bandwidth of the parameter server, we ignore its downlink transmission latency and energy consumption. To achieve aggregation based on air interface computing, each element of the gradient parameter is modulated into an independent analog symbol for transmission. Therefore, the transmission latency from the edge device to the edge server in communication round r is:

[0122]

[0123] Where q and These represent the number of symbols and resource blocks transmitted by each device, respectively. This represents the duration of each resource block. Similarly, the transmission latency between edge device n and edge server s... Represented as:

[0124]

[0125] in This represents the number of symbols and resource blocks transmitted by each device.

[0126] The communication energy consumption of device n and the communication energy consumption of edge server s can be expressed as:

[0127]

[0128] , Adjust the transmit power of the edge device and the parameter server respectively.

[0129] Then, define and Given the CPU cycle count and frequency of device n, the computation delay of device n is:

[0130]

[0131] This indicates the number of CPU cycles required per bit. , Indicates the size of the data sample.

[0132] The calculated power of device n is (in Energy loss coefficient, (Indicates CPU frequency), the computational energy consumption of device n is:

[0133]

[0134] The total energy cost of device n is:

[0135]

[0136] The cost functions for device n and edge server s are as follows:

[0137]

[0138] in This represents the total latency of cluster s. , Let be the consumption coefficient for latency and energy consumption, and satisfy . , Therefore, the total resource consumption cost of cluster s is:

[0139]

[0140] in , This is a trade-off factor between the cost of equipment and edge servers.

[0141] The upper bound of the optimality gap between the expected global loss function value and the optimal global loss function value can be expressed as:

[0142]

[0143]

[0144] in , Represents the initial global model. It is a non-negative constant vector. This represents the optimal loss function value. Represents the relevant constant terms

[0145] To ensure the convergence of federated learning while efficiently utilizing limited resources, the optimization objective of this invention is to jointly optimize cluster affiliation decisions. CPU frequency Edge device transmit power Edge server transmit power and parameter server receiving factor Minimize the long-run average resource consumption cost. Definition The corresponding optimization problem can be constructed as follows:

[0146]

[0147]

[0148]

[0149]

[0150]

[0151]

[0152]

[0153]

[0154] Constraint 1 and Constraint 2 ensure that each device belongs to only one cluster, binary variables. Indicates cluster affiliation. This indicates that device n in round r is assigned to cluster s, otherwise it is 0; Constraint 3 limits the maximum CPU frequency of the device; Constraints 4 and 5 limit the maximum transmit power of the edge device and the server, respectively; Constraint 6 defines the range of values ​​for the parameter server receive factor; Constraint 7 limits the cumulative average optimality gap between the expected global loss and the optimal global loss.

[0155] Step 2: Solve the dynamic cluster partitioning subproblem of the optimization problem in Step 1) using a game theory-based method.

[0156] We define variables Let n be the distance between edge device n and edge server s, and let s be the variable. The coverage area for each edge server. Distance metrics and channel state stability metrics are defined as follows:

[0157]

[0158] in and Let represent the standard deviation and mean of the signal-to-noise ratio, respectively. Based on this, the stability index at the beginning of communication round r is:

[0159]

[0160] in and Used to balance distance and channel stability metrics, satisfying The parameter server assigns device n to the device that makes... Maximize the edge server ,Right now:

[0161]

[0162] This approach provides a reasonable initial attribution and accelerates convergence by reducing the search space. Subsequently, we model dynamic cluster attribution as a non-cooperative game among edge devices, represented by triples: ,in:

[0163] Participant set Each device acts as an independent decision-making entity, responsible for selecting its cluster; policy space: ,in , It is the policy set of device n ( (Indicates that device n selects cluster s). Includes selection of all devices; cost-utility function: cluster affiliation decision. Mapping to real numbers, i.e. ,in The choice of device n itself The cluster affiliation is determined jointly with the strategies of other devices. To minimize the overall resource cost, we construct the following cluster affiliation optimization problem for each device n:

[0164]

[0165]

[0166]

[0167] in Indicates the affiliation selection for all mobile edge devices. This represents the selection of all mobile edge devices except n. This indicates the resource consumption of mobile edge devices. This represents the corresponding loss function.

[0168] To solve this problem, we derive the optimal cluster affiliation decision using Nash equilibrium. For a finite exact potential game, if each player's strategy set is finite, then there exists at least one pure strategy Nash equilibrium.

[0169] According to the potential game theory of Mondler-Shapley potential games: due to It is a finite set, each It is a finite discrete set, and the potential function is... Defined in a finite-dimensional space, each cluster affiliation operation constitutes an independent better response update, ensuring Non-decreasing. Because... The system exhibits monotonicity in a finite state space and converges after a finite number of updates, eventually reaching a stable Nash equilibrium. ,satisfy:

[0170]

[0171] Indicates the updated policy for mobile edge devices

[0172] If precise game theory Utility function for each device If a system's own strategy is strictly monotonic, then there exists a unique pure strategy Nash equilibrium.

[0173] For any device in a potential game, when the strategies of other devices are fixed, the utility function is... about Strictly monotonous, that is ,have Therefore, the potential function There exists a unique maximizer, corresponding to a unique pure strategy Nash equilibrium in the game.

[0174] The pseudocode for dynamic cluster ownership in game theory is as follows:

[0175]

[0176] Step 3: Solve the joint communication and computational resource allocation subproblem in Step 2) using the alternating optimization algorithm.

[0177] Solve the problem Then, we obtain the cluster allocation strategy. Subsequently, the CPU frequency was optimized by constructing the following problem. Edge device transmission power Edge server transmission power and parameter server receiving factor :

[0178]

[0179]

[0180] This indicates the cluster affiliation of mobile edge device n. This represents the energy consumption factor.

[0181] However, due to the presence of coupling variables in the objective function, the problem... It remains a non-convex problem. Therefore, we employ an efficient alternating minimization method to decompose it into two sub-problems: one responsible for computational resource allocation. And the issue of allocating communication resources. .

[0182] Given transmission power , and receiving factor Optimize CPU frequency by constructing the following problem :

[0183]

[0184]

[0185] , These represent the power consumption and latency of mobile edge devices, respectively. , These represent the corresponding energy consumption and delay, respectively.

[0186] By introducing auxiliary variables and constraints The problem can be solved The problem is transformed into a convex problem and then solved directly using a standard convex optimization solver.

[0187] Given CPU frequency Optimize transmit power by constructing the following problem. , and receiving factor :

[0188]

[0189]

[0190] , These represent the edge server's energy consumption and latency, respectively. , These represent the corresponding energy consumption and delay, respectively.

[0191] To handle non-convex constraints Let's rewrite it as follows:

[0192]

[0193] in ,and , and Represents the relevant linearly independent terms. and These represent the real-valued coefficients of the corresponding channel. , , Let represent the transmit power of the mobile edge device, the denormalization factor, and the transmit power of the edge server, respectively. Then, we introduce a penalty factor. The penalty function method is used to apply nonlinear constraints. Integrating into the problem From the objective function, we obtain the reconstructed problem:

[0194]

[0195]

[0196] Among the problems The objective function is:

[0197]

[0198] in This represents the corresponding noise variance.

[0199] But the problem Since the problem remains non-convex, we employ an alternating minimization method to alternately optimize the transmission power of edge devices. Edge server transmission power and parameter server receiving factor .

[0200] First, given and Optimize by constructing the following problem :

[0201]

[0202]

[0203]

[0204] in ,and Subsequently, we used the Lagrange duality method to derive the problem. Structured optimal solution: introducing constraints and Corresponding Lagrange multipliers and The corresponding Lagrange function is:

[0205]

[0206]

[0207] Based on the KKT optimality condition, the optimal primary and dual variables satisfy:

[0208]

[0209]

[0210]

[0211]

[0212] , Let represent the optimal transmit power of mobile edge device n and the optimal transmit power of cluster s, respectively. , The corresponding Lagrange multipliers, This indicates the maximum transmit power of the edge server.

[0213] Therefore, the problem The structured optimal solution can be expressed as:

[0214]

[0215] Negative optimal dual variable Satisfying the KKT complementary relaxation condition:

[0216]

[0217] The original optimal power scaling strategy simplifies to a channel reversal strategy, expressed as:

[0218]

[0219] This indicates the optimal transmit power for the edge server.

[0220] Given and Optimize by constructing the following problem :

[0221]

[0222]

[0223]

[0224] in , , .question objective function pair The first derivative is:

[0225]

[0226]

[0227] Setting the first derivative to zero, we get:

[0228]

[0229] Similarly, the original optimal solution is ,Right now ,in It's a problem The optimal solution is expressed as:

[0230]

[0231]

[0232] Given and Optimize by constructing the following problem :

[0233]

[0234]

[0235] This problem is also a convex problem. Setting the first derivative to zero yields the optimal solution. :

[0236]

[0237] Step 4: Build a simulation model for Step 3) to simulate and compare the advantages of the proposed algorithm.

[0238] This invention utilizes an integrated environment of PyTorch 2.3.0 and Python 3.12 (running on Ubuntu 22.04) to verify the effectiveness of the proposed algorithm (GDCRA, a game-theoretic dynamic cluster affiliation and resource allocation algorithm). We validated the performance of GDCRA on a 500m × 500m Manhattan map, with the movement trajectories of edge devices generated based on the corresponding mobility model. Specifically, our constructed COTA-FEEL system includes one parameter server and five edge servers (randomly distributed within the area) to support the system. The simulation parameters are set as follows: the path loss at 1 meter is... The path loss factor between device n and edge server s is: Rice's fading factor is CPU frequency The range of values ​​is - CPU cycle count It is 13,876,800; energy consumption coefficient for Performance constraints The noise figure is 0.95. and All are -80 dBm; the number of edge devices N is 40; the maximum transmission power of the devices is... Server maximum transmission power The power consumptions are 0.2W and 3W, respectively. Simulation results show that the proposed algorithm has significant advantages in both training latency and energy consumption.

[0239] The pseudocode for allocating communication resources for joint computing is as follows:

[0240]

[0241] The above description describes specific embodiments of the present invention and the technical principles employed. Any changes made in accordance with the concept of the present invention that do not exceed the spirit of the specification and drawings should still fall within the protection scope of the present invention.

Claims

1. A joint communication computing resource allocation method for multi-cluster aerial federated edge learning, characterized in that, Includes the following steps: 1) Construct a system model and jointly optimize cluster affiliation decisions. CPU frequency Edge device transmit power Edge server transmit power and parameter server receiving factor The optimization problem is constructed with the objective of minimizing long-term average resource consumption. 2) Solve the dynamic cluster partitioning subproblem of the optimization problem in step 1) using a game theory-based method; 3) Based on the dynamic cluster in step 2), the alternating optimization algorithm is used to solve the joint communication and computational resource allocation subproblem in the optimization problem to obtain the system resource allocation.

2. The method for allocating joint communication computing resources for multi-cluster aerial federated edge learning according to claim 1, characterized in that: The system model includes N mobile edge devices, S edge servers and 1 parameter server. Each edge server is responsible for providing intermediate data processing and computing services, while the parameter server is responsible for task distribution and global model parameter aggregation services. In each round of communication, all mobile edge devices are divided into different clusters through a clustering method. Gradient aggregation between clusters is performed between each cluster, while gradient aggregation within a cluster is implemented within each cluster through OTA.

3. The method for allocating joint communication computing resources for multi-cluster aerial federated edge learning according to claim 1, characterized in that: The optimization problem described in step 1) is: in The communication rounds are represented by the set of mobile edge devices denoted as . The cluster set is denoted as , The set of indices representing the maximum number of clusters and communication rounds is denoted as . , , These are the trade-off factors between the costs of mobile edge devices and edge servers. and Let n be the cost function of the mobile edge device and s be the cost function of the edge server. This indicates its corresponding cluster affiliation. This indicates the CPU frequency of the mobile edge device. This indicates the maximum value of its corresponding CPU frequency. This indicates its corresponding transmission power. This represents the maximum power budget for mobile edge device n. Indicates the transmit power of the edge server. This represents the number of mobile edge devices within cluster s. Represents the compensated real-valued channel coefficients. This represents the noise variance at the edge server. This represents the maximum power budget for edge servers s. This indicates the parameter server accept factor. This represents the cumulative average optimal gap. Indicates its upper bound; Constraint 1 and Constraint 2 ensure that each device belongs to only one cluster, binary variables. Indicates cluster affiliation. This indicates that device n in round r is assigned to cluster s, otherwise it is 0; Constraint 3 limits the maximum CPU frequency of the device; Constraints 4 and 5 limit the maximum transmit power of the edge device and the server, respectively; Constraint 6 defines the range of values ​​for the parameter server receive factor; Constraint 7 limits the cumulative average optimality gap between the expected global loss and the optimal global loss.

4. The method for allocating joint communication computing resources for multi-cluster aerial federated edge learning according to claim 1, characterized in that: Step 2) includes initializing the cluster state by designing a static cluster strategy that integrates distance awareness and channel quality awareness; then, based on Nash equilibrium, constructing a non-cooperative game model among edge devices to dynamically adjust the cluster affiliation of mobile edge devices and determine the association structure between mobile edge devices and edge servers.

5. The method for allocating joint communication computing resources for multi-cluster aerial federated edge learning according to claim 4, characterized in that: The specific processing steps in step 2) include: definition Let n be the distance between the mobile edge device and the edge server s. The coverage area, distance metric, and channel state stability metric for each edge server are defined as follows: in and Let represent the standard deviation and mean of the signal-to-noise ratio, respectively; based on this, the stability index at the beginning of communication round r is: in and Used to balance distance and channel stability metrics, satisfying The parameter server assigns the mobile edge device n to make... Maximize the edge server ,Right now: Subsequently, the dynamic cluster affiliation is modeled as a non-cooperative game among mobile edge devices, represented by triples: , where: the set of participants Each device acts as an independent decision-making entity, responsible for selecting its cluster; policy space: ,in , It is the policy set for mobile edge device n. Indicates that device n selects cluster s, Includes selection of all devices; cost-utility function Cluster affiliation decision Mapping to real numbers, i.e. ,in The selection by the mobile edge device n itself The cluster affiliation optimization problem for each mobile edge device n is determined jointly with the strategies of other devices, in order to minimize the overall resource cost: in Indicates the affiliation selection for all mobile edge devices. This represents the selection of all mobile edge devices except n. This indicates the resource consumption of mobile edge devices. This represents the corresponding loss function; The problem is solved using Nash equilibrium to obtain the optimal cluster affiliation decision.

6. The method for allocating joint communication computing resources for multi-cluster aerial federated edge learning according to claim 5, characterized in that: Step 3) describes a sub-problem that, after obtaining the solution to step 2), constructs the following problem to optimize CPU frequency. Edge device transmission power Edge server transmission power and parameter server receiving factor : This indicates the cluster affiliation of mobile edge device n. This represents the energy consumption factor.

7. The method for allocating joint communication computing resources for multi-cluster aerial federated edge learning according to claim 6, characterized in that: The problem Since this is a non-convex problem, it is decomposed into two sub-problems: one responsible for calculating resource allocation. And the issue of allocating communication resources. ,question The problem is solved directly using a convex optimization solver. The problem is decomposed by using an alternating minimization method, combined with Lagrange duality and penalty function methods, and then solved.

8. The method for allocating joint communication computing resources for multi-cluster aerial federation edge learning according to claim 7, characterized in that: The problem For: given transmission power , and receiving factor Optimize CPU frequency by addressing the following issues. : , These represent the power consumption and latency of mobile edge devices, respectively. , These represent the corresponding energy consumption and delay, respectively. By introducing auxiliary variables and constraints , the problem The problem is transformed into a convex problem and then solved directly using a standard convex optimization solver.

9. The method for allocating joint communication computing resources for multi-cluster aerial federated edge learning according to claim 7, characterized in that: The problem For: given CPU frequency Optimize transmit power by constructing the following problem. , and receiving factor : , These represent the edge server's energy consumption and latency, respectively. , These represent the corresponding energy consumption and delay, respectively. Will Rewritten as: in ,and , and Represents the relevant linearly independent terms. and These represent the real-valued coefficients of the corresponding channel. , , These represent the transmit power of the mobile edge device, the denormalization factor, the transmit power of the edge server, and the introduced penalty factor, respectively. The penalty function method is used to apply nonlinear constraints. Integrating into the problem From the objective function, we obtain the reconstructed problem: Among the problems The objective function is: in Indicates the corresponding noise variance; An alternating minimization method is used to alternately optimize the transmission power of edge devices. Edge server transmission power and parameter server receiving factor ; First, given and Optimize by constructing the following problem : in ,and Subsequently, the Lagrange duality method was used to derive the solution to the problem. ; Then, given and Optimize the following issues : in , , ; the problem objective function pair The first derivative is zero, so we solve for it; Given and Optimize the following issues : Similarly, setting the first derivative to zero yields the optimal solution.

10. A communication system comprising N mobile edge devices, S edge servers, and 1 parameter server, characterized in that: The system is capable of executing the joint communication computing resource allocation method for multi-cluster aerial federated edge learning as described in any one of claims 1-9.

Images