Wireless network distributed average consensus method based on graph neural network

Abstract

The invention relates to the technical field of wireless communication, and discloses a wireless network distributed average consensus method based on a graph neural network, which comprises the following steps of: establishing an undirected connected graph according to a wireless network, and determining an arithmetic mean value of initial state values of all nodes in the undirected connected graph; setting a consensus target, wherein the consensus target is that the final state values of all the nodes converge to the arithmetic mean value; calculating the number of communication time slots required for realizing the consensus target; establishing an optimization problem by taking minimization of the communication time slot number as a target; constructing and training a message passing neural network based on a graph neural network, obtaining a final embedded vector of each node, and obtaining a broadcast probability of each node by using the embedded vector; and solving the optimization problem by using the broadcast probability of each node to obtain an optimal time slot, and realizing the consensus target by using a distributed linear iteration method based on the broadcast probability. The consensus efficiency can be improved, and the communication cost can be reduced.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a wireless network distributed average consensus method based on graph neural network. Background Art

[0002] The goal of distributed average consensus is to make all nodes in the network converge to the arithmetic mean of their initial state values ​​through iterative communication. With the rapid development of emerging technologies such as drone swarm control, decentralized federated learning, and data fusion, people are increasingly demanding efficient and low-latency wireless communications. However, traditional wireless networks face many challenges in achieving distributed average consensus, mainly in terms of signal interference, network congestion, and energy constraints. Therefore, it is particularly important to optimize the distributed average consensus algorithm in wireless networks.

[0003] Existing average consensus algorithms usually use linear iterative methods, which are popular for their simplicity and scalability, but have certain limitations in ensuring fast convergence and reducing communication overhead. To address these problems, researchers have proposed a variety of improved methods, such as hybrid matrix optimization based on semidefinite programming and consensus schemes that consider the randomness of network topology. However, these methods face the problems of high communication cost and low efficiency in practical applications. Summary of the invention

[0004] The primary purpose of the present invention is to overcome the problems existing in the prior art and provide a wireless network distributed average consensus method based on graph neural network. The present invention can improve consensus efficiency and reduce communication costs.

[0005] In order to achieve the above object, the present invention provides a wireless network distributed average consensus method based on graph neural network, comprising: Establishing an undirected connected graph according to the wireless network, and determining an arithmetic mean of initial state values ​​of all nodes in the undirected connected graph; A consensus target is set, where the final state values ​​of all nodes converge to the arithmetic mean; Calculating the number of communication time slots required to achieve the consensus goal; Establishing an optimization problem with the goal of minimizing the number of communication time slots; Construct and train a message passing neural network based on a graph neural network to obtain the final embedding vector of each node, and use the embedding vector to obtain the broadcast probability of each node; The optimization problem is solved using the broadcast probability of each node to obtain the optimal time slot, and the consensus goal is achieved using a distributed linear iterative method based on the broadcast probability.

[0006] Furthermore, the consensus target is determined by the following formula: 1 T x(0) in, is the number of nodes in the wireless network, For nodes, , For the The initial state value of a node.

[0007] Furthermore, the number of communication time slots required to achieve the consensus goal is calculated as follows:

[0008] in, is the expected error tolerance of consensus, , For the Random mixing matrix in the consensus step.

[0009] Furthermore, the optimization problem is as follows:

[0010] in, , K is the average number of nodes scheduled for broadcasting in each consensus step, is the minimum scheduling probability of all nodes.

[0011] Furthermore, the construction and training of a message passing neural network based on a graph neural network to obtain a final embedding vector of each node and using the embedding vector to obtain a broadcast probability of each node specifically includes: (1) Establishing a message passing neural network, wherein the message passing neural network includes a message passing phase, an aggregation phase, and an update phase; (2) Iteratively train the message passing neural network to obtain the final graph embedding of each node; (3) The final graph of each node is embedded into the input rescale function, specifically:

[0012] Get the broadcast probability of each node.

[0013] Further, iteratively training the message passing neural network specifically includes: (1) In each training, in the message passing stage, each node generates a first message based on local features and edge features of neighboring nodes, and passes the first message to the neighboring nodes, wherein the local features are at least one of the initial state value, node degree, PageRank value and betweenness centrality, and the edge features are at least one of the strength, bandwidth and distance between nodes; in the aggregation stage, each node aggregates the first messages from all neighbors to generate a second message; in the update stage, each node updates its own node features based on the second message and local features, and the node features of each node after the previous training are used as local features of the next training to participate in the training; (2) Repeat the above steps until the message passing neural network converges and obtains the final graph embedding of each node.

[0014] Furthermore, the loss function used in iteratively training the message passing neural network is as follows:

[0015] in, , is the number of nodes, For small batch sizes.

[0016] Furthermore, the optimization problem is solved using the broadcast probability of each node to obtain the optimal time slot, including: (1) Based on the monotonicity of the logarithmic function, the optimization problem is reformulated as follows:

[0017] in, , ; (2) Input the broadcast probability of each node into the above formula to obtain the optimal time slot.

[0018] Furthermore, based on the broadcast probability, a distributed linear iteration method is used to achieve the consensus goal, specifically including: (1) In each iteration step, each node determines whether to send its current state value to its neighbor node based on the broadcast probability, which is specifically represented by a Bernoulli random variable:

[0019] when When the node The state value of is broadcast to all neighboring points. ,node No broadcasting; (2) Each node updates its state value by linear weighted average based on its current state value and the state value received from its neighbors; (3) Repeat the above steps until the consensus goal is achieved.

[0020] Furthermore, the communication mode adopted by each node to broadcast its current state value to its neighboring nodes is time division multiple access and / or orthogonal frequency division multiple access.

[0021] Compared with the prior art, the present invention has the following beneficial effects: The present invention improves the consensus efficiency in wireless networks and effectively reduces communication costs by utilizing graph neural networks to dynamically adjust the broadcast probability according to the wireless network topology and node importance. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 This is a flow chart of a distributed average consensus method for a wireless network based on a graph neural network in Example 1; Figure 2 It is a structural diagram of the neural network of Example 1; Figure 3 This is a message passing neural network framework diagram of Example 1; Figure 4 It is the convergence of the neural network in Example 2 with different numbers of nodes; Figure 5 is a comparison diagram of the neural network and other broadcasting methods at different network scales in Example 2; Figure 6 is a performance comparison diagram of the neural network and other broadcasting methods in Example 2 when the network scale is the same but the K value is different; Figure 7 This is a comparison chart of the root mean square error performance of the neural network and other broadcasting methods in the entire consensus process in Example 2. DETAILED DESCRIPTION

[0023] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0024] In the description of the present invention, it should be noted that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", and "third" are used for descriptive purposes only and cannot be understood as indicating or implying relative importance.

[0025] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0026] Furthermore, in the description of the present invention, unless otherwise specified, “plurality” means two or more.

[0027] Example 1 like Figure 1 As shown, a distributed average consensus method for a wireless network based on a graph neural network in a preferred embodiment of the present invention includes: S1: establishing an undirected connected graph according to the wireless network, and determining the arithmetic mean of the initial state values ​​of all nodes in the undirected connected graph; In one embodiment, consider a A wireless network with nodes. The wireless network is represented as an undirected connected graph ,in Represents a collection of nodes. Represents a set of edges. Indicates The node can directly communicate with The connectivity of the graph can also be measured through the adjacency matrix To describe, if and There is a connection between ),but for , otherwise .set up Representation Node The neighbor set of a node. The degree is defined as ,Right now No. The sum of the row elements can also be expressed as ,in represents the cardinality of the set. The degree matrix is ​​recorded as , which is a diagonal matrix whose diagonal elements are the degrees of each node, that is, The Laplace matrix is ​​recorded as , through the degree matrix Subtract the adjacency matrix Get, that is .

[0028] The initial state value of a node represents the state of the node at the beginning of consensus. Optionally, the initial state value may be a data value or a signal value held by the node.

[0029] S2: Set the consensus target. The consensus target is that the final state values ​​of all nodes converge to the arithmetic mean. In one embodiment, the consensus goal is as follows:

[0030] in , Indicates To achieve this goal, the following distributed linear iterative method is used:

[0031] in represents the index of the consensus step, It is Step 1 The state value of a node, Indicates that the The node is The weight assigned to each node status value. The meaning is: node When updating its status value, it will take into account its own current status value and the current status values ​​of all neighboring nodes. Representation Node The impact on its own state value, and the weight Representation Node To its neighboring nodes These weights determine the degree of dependence of the state value of each neighbor node on the node. The proportion of state updates, which in turn affects the convergence speed and stability of the consensus algorithm in the entire network. The distributed linear iterative method can be more concisely expressed as:

[0032] in , the weight matrix Also called a mixing matrix. Since not all nodes can communicate directly with each other, the mixing matrix The sparse pattern constraints must be followed according to the connectivity of the network, namely:

[0033] Given any initial state value and with a fixed weight matrix Iterative mixing, the final state value of each node is expected to converge to the arithmetic mean of its initial state value, that is:

[0034] in . The above is also equivalent to:

[0035] According to, the formula is valid if and only if the following conditions are met:

[0036] A simple choice of mixing matrix is ,in , , The matrix represents the identity matrix. In the above formula, the spectral radius Also known as the asymptotic convergence factor, it is closely related to the convergence speed of the average consensus process.

[0037] S3: Calculate the number of communication slots required to achieve the consensus goal; In one embodiment, the number of steps required for the consensus process to converge can be estimated as:

[0038] in represents the expected error tolerance of consensus. nodes, each consensus step requires Therefore, the entire consensus process requires communication time slots.

[0039] In order to reduce communication costs, this embodiment proposes a probabilistic broadcasting scheme. In this scheme, only some nodes are scheduled to broadcast information to their neighbors in each consensus step. The broadcast probability of a node is recorded as ,satisfy ,in is predefined, and This means that on average, each consensus step involves about nodes are scheduled to broadcast. For this probabilistic broadcast scheme, the number of steps required for the consensus process to converge can be estimated as:

[0040] in Indicates The random mixing matrix in the consensus step, whose elements are defined as:

[0041] In the above formula, is a Bernoulli random variable with probability The value is ,Right now Indicates The node in Selected for broadcast in the consensus step, otherwise It should be mentioned that in order to ensure The row randomness of , its diagonal elements need to be adjusted. Therefore, The elements of can be represented as:

[0042] S4: Establish an optimization problem with the goal of minimizing the number of communication time slots; In one embodiment, it is proposed to numerically optimize the broadcast probability vector To minimize the number of communication time slots required to achieve average consensus in wireless networks. The optimization problem can be expressed as:

[0043] In the constraints, Indicates the minimum scheduling probability of all nodes. This value is set to prevent the broadcast probability from reaching zero. This is necessary because if the broadcast probability of some nodes is zero, then during the entire consensus process, these nodes will not be scheduled to broadcast values ​​to their neighbors, and the average consensus of the network cannot be achieved.

[0044] S5: Build and train a message passing neural network based on graph neural network to obtain the final embedding vector of each node, and use the embedding vector to obtain the broadcast probability of each node; In one embodiment, S5 specifically includes: (1) Establishing a message passing neural network, wherein the message passing neural network includes a message passing phase, an aggregation phase, and an update phase. Figure 2 It is the structural diagram of the graph neural network. Figure 3 It is a diagram of the message passing neural network framework; (2) Iteratively train the message passing neural network to obtain the final graph embedding of each node; (3) The final graph of each node is embedded into the input rescale function, specifically:

[0045] Get the broadcast probability of each node.

[0046] It should be noted that iterative training of the message passing neural network specifically includes: (1) In each training, in the message passing stage, each node generates a first message based on the local features and the edge features of the neighboring nodes, and passes the first message to the neighboring nodes, wherein the local features are at least one of the initial state value, the node's degree, the PageRank value and the betweenness centrality, and the edge features are at least one of the strength, bandwidth and distance between nodes; in the aggregation stage, each node aggregates the first messages from all neighbors to generate a second message; in the update stage, each node updates its own node features based on the second message and local features, and the node features of each node after the previous training are used as local features for the next training to participate in the training; formally, the message passing, aggregation and update stages of the MPNN framework can be expressed as:

[0047] In GNN Layer, It is from Node to Messages generated by each node; It is The graph embedding of nodes, It is from Aggregate messages of neighbor nodes of each node; and All are GNN Characteristics of the layer. The function is They have substitutional variability, so The output of does not change with the order of the input messages. The message function of all nodes in the graph and update function are parameters and After N rounds of updates, each node The final embedding of determines the broadcast probability of network nodes, see Figure 2 Diagram of the message passing neural network framework.

[0048] The proposed learning algorithm is trained offline in an unsupervised manner using mini-batches of samples, where the training data is uniformly sampled from the training set. The final embedding of each node is obtained Then, the rescale function is used to make , the specific expression is:

[0049] in is the scaling factor, so that , and Represent the minimum and maximum values ​​of the broadcast probability respectively; (2) Repeat the above steps until the message passing neural network converges and obtains the final graph embedding of each node.

[0050] Furthermore, the loss function used in iteratively training the message passing neural network is as follows:

[0051] in, , is the number of nodes, is the size of a small batch, so that the loss function can directly link the optimization of the broadcast probability with the improvement of the consensus speed, achieving the goal of fast average consensus among distributed nodes. By optimizing this loss function by the gradient descent method, the model in this study can learn how to dynamically adjust the broadcast probability according to the structure of the network and the characteristics of the nodes to optimize the communication efficiency of the entire wireless network.

[0052] S6: Use the broadcast probability of each node to solve the optimization problem, obtain the optimal time slot, and use a distributed linear iterative method based on the broadcast probability to achieve the consensus goal.

[0053] In one embodiment, solving the optimization problem using the broadcast probability of each node to obtain the optimal time slot includes: (1) Based on the monotonicity of the logarithmic function, the optimization problem is reformulated as follows:

[0054] in, , ; (2) Input the broadcast probability of each node into the above formula to obtain the optimal time slot.

[0055] The consensus goals achieved using a distributed linear iterative method based on broadcast probability include: (1) In each iteration step, each node determines whether to send its current state value to its neighbor node based on the broadcast probability, which is specifically represented by a Bernoulli random variable:

[0056] when When the node The state value of is broadcast to all neighboring points. ,node No broadcasting; In order to effectively implement the above consensus algorithm in a wireless network and take advantage of the broadcast characteristics of the wireless medium, several key factors need to be considered. In each consensus step, each node Need to get from its neighbor nodes Collect the values ​​and use the mixing matrix No. The row updates its own value, as described in the distributed linear iteration method, for To ensure that there is no mutual interference between nodes, one possible approach is to schedule nodes to broadcast information to their neighbors using an orthogonal multiple access scheme, such as time division multiple access (TDMA) or orthogonal frequency division multiple access. This embodiment considers the TDMA strategy without loss of generality. By adopting this strategy, each node can broadcast information to its neighbors without causing interference to other nodes.

[0057] (2) Each node updates its state value by linear weighted average based on its current state value and the received neighbor state value. The linear weighted average method is as follows:

[0058] (3) Repeat the above steps until the consensus goal is achieved, that is: .

[0059] This embodiment uses a graph neural network to dynamically adjust the broadcast probability according to the wireless network topology and node importance, thereby improving the consensus efficiency in the wireless network and effectively reducing the communication cost.

[0060] Example 2 In order to evaluate the performance of the graph neural network (GNN) based method, the following baseline algorithm is proposed for comparative experiments. In the experimental simulation, all graphs are The random graph model is randomly generated. The edge between each two nodes in the graph is The probability of is established. The mixing matrix is ​​set to ,in . The minimum broadcast probability of all nodes is set to For each training iteration, a batch of 50 samples is used to estimate the gradient of the loss function in an unsupervised manner. The parameters of the GNN-based model are updated by the ADAM algorithm with a learning rate of 0.001. The dimension of the graph embedding of each node is set to 16. The number of convolutional layers of the GNN is set to 3.

[0061] 1. Use the PageRank value of the node, the degree of the node, and the betweenness of the node as the broadcast probability method.

[0062] Figure 4 The convergence behavior of the proposed GNN method is illustrated, and the performance of the considered framework during training is described. For comparison, this example also shows the convergence of N=50, N=40, N=30, where K=0.8*K, as shown in Figure 4 As shown in the figure, when N=30, the network converges in the 6th epoch, and the others converge within the 10th epoch.

[0063] exist Figure 5 In this paper, we consider training on networks with N = 50 and K = 40. After training, we freeze these strategies, i.e., keep their parameters unchanged, which shows that the proposed GNN method has good performance in different Value The network is evaluated and it can be seen that the method of directly using the PageRank value, degree and betweenness centrality of the node as the broadcast probability is the best method. Therefore, the betweenness centrality is selected as the feature of the GNN node, but the proposed GNN method is better than the other three methods.

[0064] exist Figure 6 In this paper, we consider the case where N=30 is fixed and K has different values. From the performance of training on the network, it can be seen that the proposed GNN method is better than the other three methods. Note that when N=30, K=30, the probability of all nodes is 1, so the performance of the four methods is the same.

[0065] 2. In addition to the optimization effect of the broadcast probability, the following indicators are used to further evaluate the performance of the GNN method.

[0066] The average number of iterations required for the consensus process to converge; the total number of communication slots required to reach consensus; the root mean square error between the state values ​​of all nodes in each consensus step and the average value.

[0067] like Figure 7 As shown in Figure 2, the comparison of the root mean square error (RMSE) performance of different schemes in the entire consensus process is shown. and . Due to the time-varying mixing matrix It is row random rather than double random, so although all nodes can reach a consensus, the final state value may not be the average of the initial state value. To solve this problem, a deviation correction method based on pre-compensation is adopted. In the consensus step, RMSE can be calculated as or In the figure, “unscheduled” means that all nodes are scheduled to broadcast information to their neighbors in each consensus step, i.e. .from Figure 7 As can be seen from the above, the performance of the proposed scheme is much better than other benchmark schemes. This emphasizes the importance of optimizing the broadcast probability and the effectiveness of the scheme proposed in Example 1.

[0068] In summary, an embodiment of the present invention provides a wireless network distributed average consensus method based on a graph neural network, which improves the consensus efficiency in the wireless network and effectively reduces the communication cost by utilizing the graph neural network to dynamically adjust the broadcast probability according to the wireless network topology and node importance.

[0069] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and substitutions can be made without departing from the technical principles of the present invention. These improvements and substitutions should also be regarded as the scope of protection of the present invention.

Claims

1. A distributed average consensus method for wireless networks based on graph neural networks, characterized in that: The method comprises the following steps: Establishing an undirected connected graph according to the wireless network, and determining an arithmetic mean of initial state values ​​of all nodes in the undirected connected graph; A consensus target is set, where the final state values ​​of all nodes converge to the arithmetic mean; Calculating the number of communication time slots required to achieve the consensus goal; Establishing an optimization problem with the goal of minimizing the number of communication time slots; Construct and train a message passing neural network based on a graph neural network to obtain the final embedding vector of each node, and use the embedding vector to obtain the broadcast probability of each node; The optimization problem is solved using the broadcast probability of each node to obtain the optimal time slot, and the consensus goal is achieved using a distributed linear iterative method based on the broadcast probability.

2. According to claim 1, a distributed average consensus method for wireless networks based on graph neural networks is characterized in that: The consensus target is determined by the following formula: 1 T x(0) in, is the number of nodes in the wireless network, For nodes, , For the The initial state value of a node.

3. According to claim 2, a distributed average consensus method for wireless networks based on graph neural networks is characterized in that: The number of communication slots required to achieve the consensus goal is calculated as follows: in, is the expected error tolerance of consensus, , For the Random mixing matrix in the consensus step.

4. According to claim 3, a distributed average consensus method for wireless networks based on graph neural networks is characterized in that: The optimization problem is as follows: in, , K is the average number of nodes scheduled for broadcasting in each consensus step, is the minimum scheduling probability of all nodes.

5. According to claim 4, a distributed average consensus method for wireless networks based on graph neural networks is characterized in that: The step of constructing and training a message passing neural network based on a graph neural network, obtaining a final embedding vector of each node, and using the embedding vector to obtain a broadcast probability of each node specifically includes: (1) Establishing a message passing neural network, wherein the message passing neural network includes a message passing phase, an aggregation phase, and an update phase; (2) Iteratively train the message passing neural network to obtain the final graph embedding of each node; (3) The final graph of each node is embedded into the input rescale function, specifically: Get the broadcast probability of each node.

6. A wireless network distributed average consensus method based on graph neural network according to claim 5 The method is characterized in that Iteratively training the message passing neural network specifically includes: (1) In each training, in the message passing stage, each node generates a first message based on local features and edge features of neighboring nodes, and passes the first message to the neighboring nodes, wherein the local features are at least one of the initial state value, node degree, PageRank value and betweenness centrality, and the edge features are at least one of the strength, bandwidth and distance between nodes; in the aggregation stage, each node aggregates the first messages from all neighbors to generate a second message; in the update stage, each node updates its own node features based on the second message and local features, and the node features of each node after the previous training are used as local features of the next training to participate in the training; (2) Repeat the above steps until the message passing neural network converges and obtains the final graph embedding of each node.

7. A wireless network distributed average consensus method based on graph neural network according to claim 6 The method is characterized in that The loss function used for iterative training of the message passing neural network is as follows: in, , is the number of nodes, For small batch sizes.

8. A wireless network distributed average consensus method based on graph neural network according to claim 6 The method is characterized in that The optimization problem is solved using the broadcast probability of each node to obtain the optimal time slot, including: (1) Based on the monotonicity of the logarithmic function, the optimization problem is reformulated as follows: in, , ; (2) Input the broadcast probability of each node into the above formula to obtain the optimal time slot.

9. A wireless network distributed average consensus method based on graph neural network according to claim 1 The method is characterized in that The consensus goal is achieved using a distributed linear iterative method based on the broadcast probability, specifically including: (1) In each iteration step, each node determines whether to send its current state value to its neighbor node based on the broadcast probability, which is specifically represented by a Bernoulli random variable: when When the node The state value of is broadcast to all neighboring points. ,node No broadcasting; (2) Each node updates its state value by linear weighted average based on its current state value and the state value received from its neighbors; (3) Repeat the above steps until the consensus goal is achieved.

10. A distributed average consensus method for wireless networks based on graph neural networks according to claim 9, characterized in that: The communication method adopted by each node to broadcast its current state value to its neighboring nodes is time division multiple access and / or orthogonal frequency division multiple access.

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