A communication-efficient decentralized federated learning method based on subgraph partitioning

Abstract

The application relates to a communication-efficient decentralized federated learning method based on subgraph division, comprising the following steps: constructing a physical network topology graph of a decentralized federated learning environment; dividing the physical network topology graph into non-conflict subgraphs, and setting a mixing matrix for each non-conflict subgraph; constructing a problem constraint model with the minimum total iteration time as the target; optimizing a bandwidth allocation matrix with the delay value of the link with the maximum communication delay in the current non-conflict subgraph as the optimization target; optimizing the mixing matrix with the minimum expected communication delay as the optimization target; optimizing the non-conflict subgraph sampling probability based on the optimized mixing matrix with the minimum expected communication delay as the optimization target; and performing global updating of the decentralized federated learning model based on the optimized non-conflict subgraph sampling probability. The application can significantly reduce the global model convergence delay.

Description

Technical Field

[0001] This invention relates to the field of federated learning technology, and in particular to a communication-efficient decentralized federated learning method based on subgraph partitioning. Background Technology

[0002] With the rapid development of artificial intelligence technology, the importance of data as a core driving force is becoming increasingly prominent. However, in practical applications, "data silos" and "privacy protection" have become two key bottlenecks restricting the development of machine learning. On the one hand, data from different institutions (such as hospitals, enterprises, and research units) is often stored in a scattered manner. Due to privacy regulations (such as the EU's General Data Protection Regulation and my country's Personal Information Protection Law), commercial competition, and industry barriers, it is impossible to directly share or centrally store data, making it difficult to effectively utilize data resources. On the other hand, traditional machine learning models require data to be centralized on a central server for model training. This process not only may lead to the risk of data leakage, but also brings high communication costs and computational pressure due to massive data transmission. Especially in wireless edge networks, problems such as limited bandwidth, unstable links, and heterogeneous terminal devices further exacerbate the instability of the system and the bottleneck of training efficiency.

[0003] Against this backdrop, Federated Learning emerged as a distributed machine learning paradigm. First proposed by Google in 2016, this technology addresses model training challenges on mobile devices. Its core idea is that, without sharing the original data, each participating party (client) retains the original data locally, only uploading parameters generated during model training (such as gradients and weights) to a central server or interacting with other participants to collaboratively train a global model. This model avoids the leakage of original data while enabling cross-node data collaboration, perfectly balancing the needs of model performance and privacy protection. In recent years, Federated Learning has been widely applied in various fields such as medical image analysis, financial risk control, intelligent manufacturing, and connected vehicles, becoming one of the key technological paths for the implementation of distributed AI.

[0004] From a technical architecture perspective, federated learning is mainly divided into two modes: centralized federated learning (Centralized FL) and decentralized federated learning (Decentralized FL). Centralized federated learning adopts a "parameter server-worker node" architecture, with the central server coordinating global model training. Its workflow includes: (1) the server distributes the initial model; (2) each client trains the model based on local data; (3) the client uploads model parameters (rather than the original data); (4) the server aggregates the parameters to generate a global model. This mode has been applied in scenarios such as Google's Gboard input method, Apple's Siri, and federated recommendation systems. However, the centralized architecture has the following limitations: the central server may become a performance bottleneck; server failure can lead to the paralysis of the entire system; all clients need to maintain continuous communication with the server, and the resulting communication latency is also one of the performance bottlenecks; in addition, the central node is easy to become a target of attack, and there is a risk of privacy leakage and single point of failure.

[0005] Decentralized federated learning completely eliminates the central server, with each participant exchanging model parameters directly through peer-to-peer communication. This model is particularly suitable for the following scenarios: (1) IoT device networks, such as smart homes, vehicle networks, and industrial sensor networks; (2) edge computing environments, such as base station collaboration and edge AI inference in 5G networks; and (3) cross-institutional collaboration scenarios, such as multi-hospital joint medical research and cross-bank anti-fraud model training. In cross-bank anti-fraud model training, a single bank is limited by its customer base and business type, resulting in incomplete coverage of fraud samples and weak model generalization ability. Furthermore, sensitive customer data cannot be shared due to compliance requirements. At the same time, there are significant differences in information technology architecture between banks, and nodes are highly dynamic (temporary withdrawal / joining, network instability). The central node of traditional centralized federated learning is prone to computing power bottlenecks, single-point failures, and privacy leakage risks. Decentralized federated learning achieves equal interaction between nodes through peer-to-peer networks, transmits only encrypted model parameters, supports elastic node adaptation, and combines distributed verification to ensure security, making it the optimal technical path for this scenario. In bandwidth-constrained scenarios, although decentralized federated learning avoids the bottleneck of central nodes, it still has major problems such as high communication overhead, high latency, significant link heterogeneity, and dynamic joining and leaving of nodes, which seriously restrict its deployment and expansion capabilities in actual systems. Summary of the Invention

[0006] The purpose of this invention is to address the problem that existing work ignores the differences in link quality. Previous work has ignored the channel quality of heterogeneous nodes. This invention is based on the wireless communication environment of heterogeneous nodes, and generates collision-free subgraphs based on greedy coloring of the collision graph to reduce redundant communication. It also adaptively optimizes bandwidth allocation, the spectral radius of the hybrid matrix, and the sampling probability of the subgraph to reduce the global convergence delay.

[0007] To achieve the above objectives, the present invention provides the following solution:

[0008] An efficient decentralized federated learning method for communication based on subgraph partitioning includes:

[0009] Construct the physical network topology of the decentralized federated learning environment;

[0010] The physical network topology is divided into conflict-free subgraphs, and a hybrid matrix is ​​set for each conflict-free subgraph.

[0011] Based on the conflict-free subgraph after setting the mixing matrix, a problem constraint model is constructed with the goal of minimizing the total iteration time.

[0012] Based on the problem constraint model, the bandwidth allocation matrix is ​​optimized with the goal of minimizing the latency of the link with the largest communication latency in the current conflict-free subgraph.

[0013] Based on the optimized bandwidth allocation matrix, the hybrid matrix is ​​optimized with the goal of minimizing the expected communication delay;

[0014] Based on the optimized hybrid matrix, the sampling probability of the conflict-free subgraph is optimized with the goal of minimizing the expected communication delay;

[0015] The decentralized federated learning model is updated globally based on the optimized sampling probability of conflict-free subgraphs.

[0016] Optionally, dividing the physical network topology graph into conflict-free subgraphs includes:

[0017] In the physical network topology diagram, an edge is added to a preset node to construct a conflict graph; wherein, the preset node refers to two nodes that have at least one common neighbor;

[0018] The greedy coloring algorithm is used to combine the graphs into R conflict-free subsets based on the number of time slots in each iteration, which is equivalent to dividing the graph into R conflict-free subgraphs.

[0019] Optionally, the mixing matrix is:

[0020] W r =I-εL(t)

[0021] Where ε is the weight, I is the identity matrix, and L(t) is the Laplace matrix at the t-th iteration.

[0022] Optionally, the problem constraint model is:

[0023]

[0024] ρ(W)<1, (4)

[0025] WT =W, (5)

[0026] W·u=u, (6)

[0027] P r ≥0, r=1,…R, (7)

[0028]

[0029] Where st represents being constrained by P r The sampling probability W for each subgraph r The mixing matrix for each subgraph, where r = 1, ..., R, B = [B i,j ] represents the bandwidth allocation matrix for the global link, B i,j Representing links i,j, The allocated bandwidth, B budget For the global bandwidth budget, W T Let W be the transpose of W, u be an N×1 unit column vector, and ρ(W) be the spectral radius of W. L represents the maximum node latency under the current hybrid matrix and bandwidth allocation. i,j (B i,j ) indicates that the bandwidth is B i,j The total delay of time link i,j

[0030] Optionally, the method for optimizing the mixing matrix includes:

[0031]

[0032] st(4)-(6).

[0033] Where B is the bandwidth allocation matrix for the global link. W r r = 1, ..., R, corresponding to the mixing matrix of each subgraph, P r r = 1, ..., R, which represents the sampling probability of each subgraph.

[0034] Optionally, the goal of optimizing the hybrid matrix is ​​to minimize the expected communication delay while satisfying the convergence condition ρ(W)<1, thereby accelerating the global convergence speed.

[0035] Optionally, optimizing the mixing matrix includes:

[0036] The Tinkerbach algorithm is used to transform the minimization of expected communication delay into a convex subproblem model for iterative solution.

[0037] In each iteration, an auxiliary variable σ is introduced. kThe problem of minimizing the expected communication latency is transformed into:

[0038] Step 0: Initialization: K = 0, ε = 10 -6 ;

[0039] Step 1: Let

[0040]

[0041] Step 2: Determine |g(W) k ,B)-σ k (1-ρ(W k ))|<ε, no, let k=k+1, Proceed to step 1;

[0042] Where K represents the number of iterations, σ k To update the step size, ε is the preset error, g(W) k B) represents the maximum node delay under the mixing matrix and bandwidth allocation at the k-th iteration, ρ(W) k ) is the spectral radius of W at the k-th iteration;

[0043] For the problem in step 1, two auxiliary variables S1 and S2 are introduced as g(W) k ,B) and ρ(W k The upper bound of ) is to solve the following problem:

[0044]

[0045] (4)-(6)

[0046] Where ≤ indicates that the matrix is ​​positive semi-definite, that is, for any matrices A and B, A≤B means that BA is a positive semi-definite matrix, L i,j (B i,j ) indicates that the bandwidth is B i,j The total delay of time link i,j I is the identity matrix, the transformed objective function is linear, and the constraints are linear matrix inequality constraints and linear inequality constraints. The problem is transformed into a semidefinite programming problem, which is solved using an existing convex programming solver.

[0047] Optionally, the objective function for minimizing the desired communication delay is:

[0048]

[0049] st(7)-(8),

[0050] The Tinkerbach algorithm is used to solve the objective function of minimizing the expected communication delay to obtain the optimized collision-free subgraph sampling probability.

[0051] The beneficial effects of this invention are as follows:

[0052] In a wireless communication environment based on heterogeneous nodes, this invention generates collision-free subgraphs by greedy coloring of the collision graph, reducing redundant communication; and adaptively optimizes bandwidth allocation, the spectral radius of the hybrid matrix, and the sampling probability of the subgraph to reduce global convergence latency. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0054] Figure 1 This is a schematic diagram of a communication-efficient decentralized federated learning method based on subgraph partitioning, according to an embodiment of the present invention.

[0055] Figure 2 This is a schematic diagram illustrating the auxiliary graph design and collision-free subset partitioning in an embodiment of the present invention;

[0056] Figure 3 This is a schematic diagram of a system model according to an embodiment of the present invention;

[0057] Figure 4 This is a time slot diagram for each iteration of an embodiment of the present invention. Detailed Implementation

[0058] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0059] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0060] Traditional federated learning employs a server-client architecture, where a central server distributes an initial model to all slave nodes. Each node updates its model using local private data (e.g., calculating gradients). The central server collects the calculated gradients or parameters from the slave nodes and updates the global model by weighted averaging of the collected parameters. This architecture relies on the coordination of the central server and is vulnerable to attacks or outages, presenting a single point of failure. Decentralized architectures have emerged to address this issue, where each node acts as both a computation node and a communication relay. All nodes initially load the same initial model, calculate gradients using local data, and fuse neighbor node models using a weighted average based on a weight matrix. In bandwidth-constrained scenarios, communication latency caused by low-quality links becomes a bottleneck that needs to be addressed. While a large number of nodes participating in communication can accelerate global model convergence, it also increases communication latency. To avoid these problems, the trade-off between communication latency and global convergence speed has received increasing attention and research. This invention discloses an optimized method for weight matrices, bandwidth allocation, and subgraph sampling probabilities in subgraph communication scenarios to reduce global model convergence latency in bandwidth-constrained scenarios.

[0061] This embodiment considers jointly modeling the "actual delay per round" and the "convergence speed" under bandwidth-constrained wireless channels to minimize the total communication latency. For example... Figure 1 As shown, this embodiment proposes a communication-efficient decentralized federated learning method based on subgraph partitioning, including:

[0062] Construct the physical network topology of the decentralized federated learning environment;

[0063] The physical network topology is divided into conflict-free subgraphs, and a mixing matrix is ​​set for each conflict-free subgraph; wherein, a single mixing matrix is ​​an N×N matrix, where N is the total number of nodes in the network, and the elements W in the matrix are... i,j This represents the weight of the information received by node i from node j when node i updates its own model. The sum of each row and each column is 1, meaning the matrix is ​​doubly random, ensuring that all nodes eventually converge to consistency.

[0064] Based on the conflict-free subgraph after setting the mixing matrix, a problem constraint model is constructed with the goal of minimizing the total iteration time.

[0065] Based on the problem constraint model, the bandwidth allocation matrix is ​​optimized with the goal of minimizing the latency of the link with the largest communication latency in the current conflict-free subgraph.

[0066] Based on the optimized bandwidth allocation matrix, the hybrid matrix is ​​optimized with the goal of minimizing the expected communication delay;

[0067] Based on the optimized hybrid matrix, the sampling probability of the conflict-free subgraph is optimized with the goal of minimizing the expected communication delay;

[0068] The decentralized federated learning model is updated globally based on the optimized sampling probability of conflict-free subgraphs.

[0069] Furthermore, dividing the physical network topology graph into conflict-free subgraphs includes:

[0070] In the physical network topology diagram, an edge is added to a preset node to construct a conflict graph; wherein, the preset node refers to two nodes that have at least one common neighbor;

[0071] The greedy coloring algorithm is used to group the graph into R conflict-free subsets based on the number of time slots in each iteration, resulting in R conflict-free subgraphs. The conflict-free subsets are as follows: Figure 2 As shown.

[0072] Specifically, in this embodiment, a decentralized federated learning environment consisting of N computing nodes, N = {1, 2, ..., n}, is considered for training a model. The system model is as follows: Figure 3 As shown, the physical network topology is represented by an undirected graph G = (N, E), where E is the edge set. If there is a link between node i and node j and i ≠ j, then (i, j) ∈ E. We assume G is connected, meaning there is a path between any two nodes. Based on the communication topology, we construct a conflict graph G. a In G, a node i and j is considered to have at least one common neighbor (or i and j are neighbors themselves) if and only if they have at least one common neighbor. a Add an edge to them, which means that if i and j broadcast at the same time, their neighbors will receive a collision signal, so they cannot be placed in the same time slot. After constructing the collision graph, use a greedy coloring algorithm to combine them into R collision-free subsets according to the number of time slots in each iteration, and the sampling probability P of each subset is given. r , In each iteration, a subset is selected for communication aggregation based on the sampling probability of the subset, while the remaining nodes perform local gradient calculations. The time slots for each iteration are as follows: Figure 4 As shown. Definition Let represent the loss function for local training at node i, x represent the model parameters, and δ represent the loss function for local training at node i. i f represents the local data sample set. i (·) is the loss function defined by the model, such as cross-entropy; let Let represent the global loss function. The problem of decentralized federated learning can be formulated as minimizing the global loss function, as follows:

[0073] minF(x)

[0074]

[0075] Where X represents the feasible set of parameters for training the model, and the above problem is generally solved using the stochastic gradient descent algorithm. The process of training a model in decentralized federated learning is as follows: In the t-th iteration, each node first calculates the gradient g using its local data. i (t) and update its own model, then send the model to the neighbors; subsequently, the received neighbor models are weighted according to the weight matrix W = [W i,j ] Perform a weighted average, W i,j Let represent the aggregate weight between node i and node j. The update rule for the global model can be expressed as follows:

[0076] X(t+1)=P x {(X(t)-β(t)G(t))W}

[0077] Where X(t) = [x1(t),...,x i (t),...,x n [(t)],P x () represents the projection onto X, β(t) represents the step size at the t-th iteration, and G(t) = [g1(t),...,g i (t),...,g n (t)]. The above iterative process continues until the model converges or reaches the preset number of iterations. Finally, the parameter values ​​of the final global model are determined by the average of the parameters of all node models.

[0078] This invention considers a bandwidth-constrained environment with a bandwidth budget of B. budget In a frequency division multiple access wireless communication environment, B i,j Let represent the bandwidth of the link from node i to node j. Then, the communication delay from node i to node j can be expressed as follows:

[0079]

[0080] D i This represents the size of the model parameters for node i. θ i,j To express the spectral efficiency from node i to node j, according to Shannon's formula, θ i,j It can be represented as follows:

[0081]

[0082] Where p i d represents the transmission power of the i-th node. i,j Let be the distance between node i and node j. For the power gain of the wireless channel, Let be the white noise power between i and j.

[0083] For the same node, its transmission delay The total time delay from node i to node j can be expressed as:

[0084]

[0085] B represents the computation delay when node i calculates the gradient locally, defined as B = [B i,j [A bandwidth allocation matrix for all nodes. The latency of a single iteration is determined by selecting the node with the largest latency in a subset. Define...] This is the delay matrix for all nodes at the k-th iteration, used to distinguish the quality of each link:

[0086]

[0087] When i = j, the delay is equal to 0, defined as follows: Let W be the maximum latency in each iteration (depending on the node with the highest current communication latency), where ⊙ is the Hadamard product, and W is the maximum latency in each iteration. i,j The delay is 0 if and only if the value is 0, which means that node i has no parameters transmitted to node j.

[0088] The mixture matrix also plays a significant role in the global model. Let... Among them ||·|| 2 The spectral norm of the matrix is ​​represented by T, where u is an N×1 column vector. ∈ T represents the number of iterations by which the ideal trained model approximates ∈. Typically, T... ∈ It is inversely proportional to 1-ρ(W), that is:

[0089]

[0090] When the spectral radius ρ(W) < 1, the convergence of decentralized federated learning can be guaranteed. The smaller the spectral radius, the faster the convergence speed. In order to achieve faster convergence, our system designed a hybridization matrix W for each communication subgraph. r , Among them W r The design method is: W r =I-εL(t), where ε is the weight, I is the identity matrix, and L(t) is the Laplace matrix at the t-th iteration. This design satisfies the double randomness of the hybrid matrix, that is, the matrix satisfies the property of being symmetric and having a row / column sum of 1.

[0091] Training T ∈ The training time required for the number of iterations in each round is T. ∈ To minimize the convergence time of the global model, g(W,B) should be minimized. Therefore, considering minimizing the total iteration time, we model the problem as follows:

[0092]

[0093] ρ(W)<1, (4)

[0094] W T =W, (5)

[0095] W·u=u, (6)

[0096] P r ≥0, r=1,…R, (7)

[0097]

[0098] Initially, both the bandwidth and sampling probability are equally divided. Constraints (2) and (3) restrict the allocated bandwidth from exceeding the specified total bandwidth. (4) ensures the convergence of the system. (5) and (6) ensure that the matrix remains symmetric, with the row / column sum being 1. A symmetric matrix will lead to a decrease in convergence speed but will also significantly reduce the computational load. (7) and (8) restrict the sampling probability P. r Non-negative and sum to 1. In (1), due to the existence of the indicator function, the objective function is non-convex and non-smooth with respect to W. The optimal value of each variable is solved by alternating optimization. W is fixed to optimize B, B is fixed to optimize W, and finally W and B are fixed to optimize the sampling probability P. r , r=1,…R.

[0099] Furthermore, the specific method for optimizing the bandwidth allocation matrix is ​​as follows:

[0100] When W r r = 1, ..., R and P r When r = 1, ..., R are fixed quantities, optimizing the bandwidth allocation matrix B can be viewed as a resource allocation problem for a single subgraph. It is modeled as a minimum-maximum bandwidth allocation problem, with the goal of minimizing the latency of the link with the highest communication latency in the current subgraph, thereby improving overall training efficiency. Optimizing B can be seen as optimizing g(W,B) for a single subgraph, specifically expressed as:

[0101]

[0102] st(2)-(3)

[0103] Among them W r Given the mixing matrix of the communication subgraphs participating in the current iteration, the above objective function can be expanded as follows:

[0104]

[0105] st(2)-(3)

[0106] The above problem is a convex problem with respect to B, which can be solved using the primal-dual method or the Lagrange multiplier method. In the actual implementation, the CVXPY library is used for modeling, and the MOSEK solver is called for efficient solution.

[0107] Furthermore, the method for optimizing the mixture matrix is ​​as follows:

[0108] Optimizing the mixture matrix requires solving the following fractional programming subproblem:

[0109]

[0110] st(4)-(6).

[0111] A common approach to solving fractional programming problems is to optimize the mixture matrix W, where the objective is to minimize the expected communication delay while satisfying the convergence condition ρ(W) < 1, thus accelerating global convergence. Since the spectral radius optimization problem is essentially a non-convex fractional programming problem, the Tinkelbach algorithm is used to transform it into a series of convex subproblems for iterative solving. Specifically, in each iteration, we introduce an update step size σ. k The solution steps are as follows:

[0112] Step 0: Initialization: K = 0, ε = 10 -6

[0113] Step 1: Let

[0114]

[0115] Step 2: Determine |g(W) k ,B)-σ k (1-ρ(W k ))|<ε, no, let k=k+1, Proceed to step 1

[0116] Where K represents the number of iterations, σ k To update the step size, ε is a preset error. For the problem in step 1, two auxiliary variables S1 and S2 are introduced as g(W) k ,B) and ρ(W k Find the upper bound of ), and transform the problem into solving the following problem:

[0117]

[0118] (4)-(6).

[0119] The transformed objective function is linear, and the constraints are linear matrix inequality constraints and linear inequality constraints, thus transforming the problem into a semidefinite programming problem for solution.

[0120] Furthermore, the optimization method for the sampling probability is as follows:

[0121] The optimization objective of the subgraph sampling probability π is to minimize the expected communication delay while also considering the convergence speed. We model this problem as a constrained stochastic optimization problem with the objective function:

[0122]

[0123] st(7)-(8)

[0124] in The Tinkelbach algorithm is also used to solve this problem:

[0125] Step 0: Initialization: K = 0, ε = 10 -6

[0126] Step 1: Let

[0127]

[0128] Step 2: Determine |g(W) k ,B)-μ k (1-ρ(W k ))|<ε, no, let k=k+1, Proceed to step 1

[0129] In step 1, g(W) k ,B) in B and W k When fixed, it is treated as a constant, and γ is introduced as ρ(W) k Find the upper bound of the problem, transforming it into an SDP problem to be solved. As follows:

[0130]

[0131] Specifically, the pseudocode of the efficient decentralized federated learning algorithm based on subgraph partitioning proposed in this embodiment is as follows:

[0132]

[0133] When jointly training a credit card fraud detection model across multiple banks, the method described in this embodiment first constructs an initial physical topology, treating each bank as a training node (the initial physical topology exhibits significant heterogeneity in link quality, with varying link quality). An auxiliary graph is then constructed from this initial physical topology, and a greedy coloring algorithm is used to divide it into collision-free subsets. These subsets are then combined into several communication subgraphs, with the number of combinations equal to the number of time slots in one iteration. Each communication subgraph corresponds to a certain number of mixing matrices and sampling probabilities. Next, the delay moments of the global nodes are calculated. Initially, the bandwidth allocation is optimized by solving the minimum-maximum bandwidth optimization problem of this method to reduce the maximum latency of the current subgraph links. After the bandwidth optimization of each subgraph is completed, the Tinkerbach algorithm is used to optimize the mixing matrix and sampling probabilities of each subset. Finally, efficient joint training of the model is achieved based on the optimized mixing matrices and sampling probabilities of each subset.

[0134] The advantage of this embodiment is that it solves the problem of ignoring link quality differences in existing work. Previous work ignored the channel quality of heterogeneous nodes. This embodiment is based on the wireless communication environment of heterogeneous nodes. It generates collision-free subgraphs based on greedy coloring of the collision graph to reduce redundant communication. It adaptively optimizes bandwidth allocation, hybrid matrix spectral radius and subgraph sampling probability to reduce global convergence delay.

[0135] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A communication-efficient decentralized federated learning method based on subgraph partitioning, characterized in that, include: Construct the physical network topology of the decentralized federated learning environment; The physical network topology is divided into conflict-free subgraphs, and a hybrid matrix is ​​set for each conflict-free subgraph. Based on the conflict-free subgraph after setting the mixing matrix, a problem constraint model is constructed with the objective of minimizing the total iteration time; the problem constraint model is as follows: in The sampling probability for each subgraph. The mixing matrix for each subgraph, where , A bandwidth allocation matrix for global links. Indicates link , The allocated bandwidth For the global bandwidth budget, for transpose, for unit column vector, for spectral radius, This represents the maximum node latency under the current hybrid matrix and bandwidth allocation. Indicates that the bandwidth is Time Link Total latency, ; Based on the problem constraint model, the bandwidth allocation matrix is ​​optimized with the goal of minimizing the latency of the link with the largest communication latency in the current conflict-free subgraph. Based on the optimized bandwidth allocation matrix, the hybrid matrix is ​​optimized with the goal of minimizing the expected communication delay; Based on the optimized hybrid matrix, the sampling probability of the conflict-free subgraph is optimized with the goal of minimizing the expected communication delay; The decentralized federated learning model is updated globally based on the optimized sampling probability of conflict-free subgraphs.

2. The efficient decentralized federated learning method for communication based on subgraph partitioning according to claim 1, characterized in that, Dividing the physical network topology graph into conflict-free subgraphs includes: In the physical network topology diagram, an edge is added to a preset node to construct a conflict graph; wherein, the preset node refers to two nodes that have at least one common neighbor; The greedy coloring algorithm is used to combine the elements based on the number of time slots in each iteration. A conflict-free subset, that is, divided into A conflict-free subgraph.

3. The efficient decentralized federated learning method for communication based on subgraph partitioning according to claim 1, characterized in that, The mixing matrix is: in As weight, For the first The Laplace matrix at the next iteration.

4. The efficient decentralized federated learning method for communication based on subgraph partitioning according to claim 1, characterized in that, The methods for optimizing the mixture matrix include: Where B is the bandwidth allocation matrix for the global link. , The mixing matrix corresponding to each subgraph, This corresponds to the sampling probability of each subgraph.

5. The efficient decentralized federated learning method for communication based on subgraph partitioning according to claim 1, characterized in that, The goal of optimizing the mixture matrix is ​​to satisfy the convergence condition. Under the premise of minimizing the expected communication latency, the global convergence speed is accelerated.

6. The efficient decentralized federated learning method for communication based on subgraph partitioning according to claim 5, characterized in that, Optimizing the hybrid matrix includes: The Tinkerbach algorithm is used to transform the minimization of expected communication delay into a convex subproblem model for iterative solution. In each iteration, an auxiliary variable is introduced. The problem of minimizing the expected communication latency is transformed into: Step 0: ; ； ； Step 2: 1; in, Indicates the number of iterations. To update the step size, As a preset error, Given the hybrid matrix and bandwidth allocation at the k-th iteration, the maximum node latency is... For the k-th iteration spectral radius; For steps The problem introduces two auxiliary variables and As and The upper bound is the solution to the following problem: in, This indicates that the matrix is ​​positive semi-definite, meaning that for any matrices A and B, A ≠ 0. B means that B−A is a positive semi-definite matrix. Indicates that the bandwidth is Time Link Total latency, Given an identity matrix, the transformed objective function is linear, and the constraints are linear matrix inequality constraints and linear inequality constraints. This transforms the problem into a semidefinite programming problem, which can be solved using an existing convex programming solver.

7. The efficient decentralized federated learning method for communication based on subgraph partitioning according to claim 1, characterized in that, The objective function for minimizing the desired communication delay is: The Tinkerbach algorithm is used to solve the objective function of minimizing the expected communication delay to obtain the optimized collision-free subgraph sampling probability.

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