A transmission scheme design method and system for RIS-assisted sparse federated learning networks

Abstract

The present invention proposes a transmission scheme design method and system for a RIS-assisted sparse federated learning network. The present invention first models the local gradient information sparsity rate and constructs a transmission scheme design optimization problem for maximizing federated learning performance. By finding the second-order derivative of the optimization problem with respect to the transmission code length, it is proved that the optimization problem is a convex problem with respect to the transmission code length, and then the KKT condition is used to derive the closed-form solution of the optimal code length, and based on this, the dimension reduction of the optimization problem is achieved. Then, the optimization problem after dimension reduction is solved based on the block coordinate descent algorithm, and an efficient design scheme for coding rate, transmission power and RIS phase matrix is ​​obtained. The present invention significantly improves the performance of RIS-assisted sparse federated learning networks, can be widely used in many practical application scenarios, and has extremely high scalability and economic benefits.

Description

Technical Field

[0001] The present invention belongs to the field of communications, and in particular relates to a transmission scheme design method and system for a RIS-assisted sparse federated learning network. Background Art

[0002] The widespread deployment of mobile edge computing applications in recent years has enabled edge devices to process and store data locally, which has promoted the rapid development of data-driven federated learning (FL) technology. In FL networks, edge devices independently train their local models based on local datasets and only upload local gradient information to the server, effectively avoiding the sharing of a large amount of sensitive data and reducing the risk of data leakage. Although uploading local gradient information instead of the original dataset in FL can reduce communication overhead, local model parameters (such as neural networks) still contain a large number of parameters.

[0003] To solve this problem, the sparse federated learning network reduces the amount of transmitted information while ensuring the performance of the federated learning network by sparsely storing the local gradients to be uploaded. However, all existing works assume that the server successfully receives the local gradient information. In actual systems, the instability of the wireless channel causes transmission errors during the upload of local gradient information, which in turn affects the amount of local gradient information successfully received. As one of the key technologies of 6G, the Reconfigurable Intelligent Surface (RIS) technology realizes intelligent control of the wireless propagation environment by manipulating the reflection unit to finely adjust the phase angle of the reflected signal. RIS technology provides a higher degree of freedom for the design of wireless communication systems in FL networks. At present, a large number of related research works have emerged at home and abroad. In 2022, M. Naseri Tehran et al. further studied the multi-user scenario and proposed a block coordinate descent method to alternately iteratively optimize the transmitter beamforming and RIS phase to achieve the minimum transmit power while meeting QoS requirements. In 2021, H. Liu et al. analyzed the convergence of federated learning in a single RIS-assisted federated learning scenario, and jointly designed the beamforming of the transmitter and RIS through the continuous convex approximation (SCA) method. To further improve communication efficiency, in 2022, W. Ni et al. proposed a multi-RIS-assisted federated learning framework, and proposed a joint transmit power, RIS beamforming and device selection algorithm based on an alternating iterative method.

[0004] At present, existing work has assumed that the transmission block length tends to infinity when designing wireless transmission schemes in federated learning networks. In actual scenarios, since wireless resources are limited, local information transmission uses finite block length coding, which is the so-called finite block length (FBL) communication. According to the transmission rate model proposed by Polyanskiy in 2012, decoding errors cannot be ignored even when the coding rate is lower than the Shannon capacity, and the probability of decoding errors increases when the block length becomes shorter. Considering that information transmission errors when using finite block lengths will reduce the convergence speed of federated learning and the accuracy of federated learning solutions, it is crucial to consider the impact on finite code length transmission when designing sparse federated learning networks. Therefore, considering the impact of finite block length communication on the performance of sparse federated learning networks, a design method for an efficient wireless transmission scheme needs to be studied. Summary of the invention

[0005] Aiming at the problem that the sparse error of local information and transmission error in RIS-assisted sparse federated learning network lead to low federated learning performance, the present invention proposes a transmission scheme design method based on alternating iterative optimization, which improves the performance of sparse federated learning network by jointly designing RIS phase, transmission power and coding rate.

[0006] The present invention proposes a transmission scheme design method for a RIS-assisted sparse federated learning network, comprising:

[0007] A transmission scheme design method for a RIS-assisted sparse federated learning network includes the following steps:

[0008] Step 1: Based on the RIS-assisted sparse federated learning network scenario, the transmission error probability expression of the communication system is calculated in combination with the finite code length theory, and the sparse coefficient expression of the local gradient information is obtained;

[0009] Step 2: Construct the objective function of the optimization problem based on the expression of transmission error probability and the sparse coefficient expression of local gradient information, define a constant modulus constraint based on beamforming at the RIS, and define a total transmission power constraint based on the sum of the transmission powers of the server and edge devices to construct a joint resource allocation and beamforming design optimization problem for maximizing federated learning performance;

[0010] Step 3: Obtain an analytical expression for the optimal solution of the coding rate, and based on this, reduce the dimension of the constructed optimization problem to transform the original problem into a reduced-dimensional optimization problem only about the transmit power and the RIS phase matrix;

[0011] Step 4: Solve the optimization problem after dimensionality reduction and obtain the efficient solution of the edge device's coding rate, transmit power, and RIS phase matrix to obtain the transmission solution;

[0012] Step 5: Based on the transmission scheme in step 4, the edge device calculates local sparse gradient information based on local data, and uses the sparse algorithm to aggregate the local coefficient gradient information to obtain the global gradient information, and then sends the global gradient to all edge devices in the form of broadcast for model update.

[0013] Furthermore, the transmission error probability ε of the communication system is calculated in step 1 in combination with the finite code length theory. k The expression is:

[0014]

[0015] where r k represents the coding rate of edge device k, m represents the transmission code length, C k =log2(1+γ k ) represents the Shannon transmission capacity between the server and edge device k, W k =1-(1+γ k ) -2 represents the channel dispersion between the server and edge device k; represents the received signal-to-noise ratio between the server and edge device k, p k represents the transmit power of edge device k, σ 2 represents the noise power; G represents the channel gain between the server and the edge device k, represents the Gaussian Q function.

[0016] Furthermore, the sparse coefficient β of the edge device k in step 1 is k Set to:

[0017]

[0018] in, Represents the sparse gradient information of edge device k The number of remaining non-zero elements in , q G and q L Respectively The number of information bits occupied by the non-zero elements and the corresponding position coordinates, T represents the total number of transmissions during the local gradient information upload of the edge device k, and Z represents the number of elements in the original local gradient information.

[0019] Furthermore, in step 2, the transmission error probability and the sparse coefficient are minimized by optimizing the transmission power, coding rate and phase matrix of the edge device, and the objective function of the optimization problem constructed is:

[0020]

[0021] where a c,k and a s,kThey represent the transmission error probability coefficient and sparse error performance coefficient of edge device k respectively;

[0022] The constant modulus constraint is:

[0023]

[0024] Where θ j represents the phase of the jth reflection unit on the RIS, and L represents the number of reflection units on the RIS;

[0025] The transmission power constraint is:

[0026]

[0027] Where p k represents the transmit power allocated to edge device k, P sum Indicates the total transmit power;

[0028] The joint resource allocation and beamforming design optimization problem P0 for maximizing federated learning performance is constructed as:

[0029]

[0030] Furthermore, the step 3 includes the following sub-steps:

[0031] Step 3.1: Fix the transmit power and RIS phase matrix, calculate the second-order derivative of the objective function with respect to the coding rate, prove that the optimization problem is a convex problem with respect to the coding rate, and calculate the optimal solution expression of the coding rate of edge device k based on the KKT condition:

[0032]

[0033] Step 3.2: Bring the optimal solution of the coding rate of edge device k into the optimization problem P0 for dimensionality reduction. The optimization problem P1 after dimensionality reduction is:

[0034] P1:

[0035]

[0036] in is the transmission error probability obtained based on the optimal solution of the coding rate of edge device k.

[0037] Furthermore, the step 4 solves the optimization problem P1 after dimension reduction based on the block coordinate descent algorithm, including:

[0038] Step 4.1: Initialize the transmit power and RIS phase matrix, and set the iteration threshold And the initial transmission power of the edge device P(0) and the RIS initial phase matrix Θ (0) As a local point of iteration

[0039] Step 4.2: Fix the RIS phase matrix, calculate the second-order derivative of the objective function of the optimization problem P1 after dimension reduction with respect to the transmit power, and prove that the optimization problem P1 after dimension reduction is a convex problem with respect to the transmit power;

[0040] Step 4.3: Fix the RIS phase matrix and use the ellipsoid method to solve the optimization problem P1 after dimension reduction to obtain the optimal solution of the transmission power for this iteration.

[0041] Step 4.3: Fixed transmit power optimization solution for this iteration Based on the first-order Taylor approximation At local point By approximating and introducing trust region constraints, the optimization problem P1 after dimensionality reduction is approximated to the optimization problem P2:

[0042] P2:

[0043]

[0044] in, represents the constant term introduced by the first-order Taylor approximation, and Respectively represent the local point The calculated received signal-to-noise ratio and channel dispersion of the server and edge device k, represents the confidence radius, and

[0045] Step 4.4: Introduce auxiliary variables y = {y1, y2, ..., y K}, α={α1,α2,...,α K}, perform a quadratic transformation on the fractional terms in the objective function and use Lagrange dual transformation on the logarithmic function terms. The optimization problem P2 is equivalent to the optimization problem P3:

[0046] P3:

[0047]

[0048] in C 2k =1+α k +C 1k represents the constant term generated by the quadratic transformation and the Lagrange dual transformation;

[0049] Step 4.5: Perform a convex approximation on the objective function in the optimization problem P3 and introduce the dual variable ψ = {ψ1, ψ2, ..., ψ N} and τ, and calculate the optimal RIS phase matrix and auxiliary variables y and α in the optimization problem P3 based on the KKT condition * The analytical expression of is:

[0050]

[0051] in and Represents auxiliary variables y={y1,y2,...,y K}, α={α1,α2,...,α K} is the optimal solution, represents the optimal solution of the RIS phase matrix in this iteration,

[0052] Represents the constant term generated after mathematical calculation, a k =Fh d,k represents the equivalent channel of the direct line-of-sight communication link, J k =FH H diag(h r,k ) represents the equivalent channel of the RIS reflection communication link, F represents the receive beamforming vector at the base station, and h d,k represents the channel vector between the server and edge device k, H represents the channel between the server and RIS, and h r,k The channel vector between RIS and edge device k is expressed as, and Respectively represent a k and J k The conjugate transposed matrix of n represents an indicator vector of length N, in which only the element at the nth position is 1 and the rest are 0; I N×N represents the unit matrix of length N;

[0053] Step 4.6: If the performance improvement of this iteration is less than the iteration threshold ε, the iteration is stopped. The optimal solution of this iteration is the optimal transmission code length, transmission power and RIS phase matrix (m) of the edge device in the RIS-assisted sparse federated learning network. * ,P * ,θ * )=(m,P,θ); otherwise it will be used as the local point for the next iteration Go back to step 4.2.

[0054] Furthermore, the step 5 comprises:

[0055] Multi-edge devices by index K represents the number of edge devices. The edge device constructs a local sparse gradient information matrix by combining the non-zero elements in the local gradient information and their corresponding position coordinates. in represents the original local gradient information of edge device k at the tth global iteration, Represents sparse operations;

[0056] Based on sparse local gradient information The server performs federated aggregation operations to obtain the global gradient information g (t +1) , expressed as:

[0057]

[0058] Where D represents the total data volume of all edge devices, D k represents the amount of local data of the kth edge device;

[0059] The server broadcasts the global gradient information g (t+1) Sent to all edge devices, the edge devices update their local models based on the received global gradient information, expressed as:

[0060] v (t+1) =v (t) -ηg (t+1)

[0061] where v (t) represents the local model parameters of the tth global iteration, v (t+1) represents the local model parameters of the t+1th global iteration, and η represents the learning rate.

[0062] In another aspect, the present invention provides a transmission scheme design system for a RIS-assisted sparse federated learning network, comprising:

[0063] Module 1: It is used in RIS-assisted sparse federated learning network scenarios, combining finite code length theory to calculate the transmission error probability expression of the communication system and obtain the sparse coefficient expression of the local gradient information;

[0064] Module 2: It is used to construct the objective function of the optimization problem based on the transmission error probability expression and the sparse coefficient expression of the local gradient information, and define the constant modulus constraint according to the beamforming at the RIS, and define the total transmission power constraint according to the sum of the transmission power of the server and the edge device to construct the joint resource allocation and beamforming design optimization problem for maximizing the performance of federated learning;

[0065] Module 3: It is used to obtain the analytical expression of the optimal solution of the coding rate, and based on this, the dimension of the constructed optimization problem is reduced to transform the original problem into a reduced-dimensional optimization problem only about the transmit power and the RIS phase matrix;

[0066] Module 4: It is used to solve the optimization problem after dimensionality reduction and obtain the efficient solution of the coding rate, transmission power and RIS phase matrix of the edge device to obtain the transmission solution;

[0067] Module 5: Based on the transmission scheme, the edge device calculates the local sparse gradient information based on the local data and uploads it to the server. The server uses the sparse algorithm to aggregate the local coefficient gradient information to obtain the global gradient information, and sends the global gradient to all edge devices in the form of broadcast for model update.

[0068] The RIS-assisted sparse federated learning network transmission scheme design system is used to execute the steps in any one of the RIS-assisted sparse federated learning network transmission scheme design methods of claims 1-7.

[0069] Compared with the prior art, the present invention has the following beneficial effects:

[0070] The present invention proposes a transmission scheme design method in a RIS-assisted sparse federated learning network, which jointly designs the transmission power, transmission code length and phase matrix of the edge device at the RIS to minimize the transmission error probability and the local gradient information sparsity error, thereby improving the performance of the sparse federated learning network. The present invention significantly improves the performance of the RIS-assisted sparse federated learning network, can be widely used in many practical application scenarios, and has extremely high scalability and economic benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 : Schematic diagram of RIS-assisted sparse federated learning network according to an embodiment of the present invention;

[0072] Figure 2 : Flow chart of the method implemented by the present invention;

[0073] Figure 3 : A graph showing how the test performance of the RIS-assisted sparse federated learning network changes with the global training cycle in an embodiment of the present invention. DETAILED DESCRIPTION

[0074] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians of the present invention without making creative work are within the scope of protection of the present invention.

[0075] Example 1

[0076] The present invention provides a design method for joint coding rate, transmission power and RIS phase matrix in a RIS-assisted sparse federated learning network, aiming to maximize the performance of the sparse federated learning network by minimizing the transmission error probability and the sparse error of local gradient information.

[0077] Combine the following Figure 1-3 A transmission scheme design method in a RIS-assisted sparse federated learning network according to an embodiment of the present invention is introduced, which is as follows:

[0078] Figure 1 A RIS-assisted sparse federated learning network is considered for a specific embodiment of the present invention, and the network includes a server, K edge devices and a RIS. The edge device transmits local gradient information to the server, and reflects the signal through the RIS to enhance the signal strength of the server receiving signal. In order to improve the performance of the RIS-assisted sparse federated learning network, the resource allocation of the wireless system and the phase matrix at the RIS are jointly designed to minimize the wireless transmission error probability of the local gradient information and the sparse error.

[0079] like Figure 2 The method flow chart of the present invention is shown, and the implementation process includes the following steps:

[0080] Step 1: Modeling the sparse rate of local gradient information in RIS-assisted sparse federated learning networks. First, the distances between the base station and the user, the base station and the RIS, and the RIS and the user are calculated based on the locations of the base station, the user, and the RIS. Secondly, the channel gains between the base station and the user, the base station and the RIS, the base station and the user, the base station and the eavesdropper, and the RIS and the user are calculated by combining the Ricean channel gain coefficient and the Ricean channel path attenuation coefficient under unit distance. Then, based on the channel gain and combined with the finite code length theory, the transmission error probability expression of the communication system is calculated to obtain the sparse rate expression of the local gradient information.

[0081] All wireless transmission channels in step 1 are constructed using the Rice channel model, expressed as:

[0082]

[0083] Where κ represents the Rice coefficient. LoS Represents the sight distance component; h NLoS Represents the small-scale attenuation coefficient, which obeys Gaussian distribution λ=μ(l / l0) -a represents the path loss, a is the path loss coefficient, μ is the path loss per unit distance, l0 is the reference distance, and l is the distance between the server and the edge device.

[0084] The channel vector between the server and edge device k is represented as h d,k , the channel between the server and RIS is denoted as H, and the channel vector between RIS and edge device k is denoted as h r,k Therefore, the channel gain between the server and edge device k can be expressed as G = |f k (h d,k +H H Θh r,k )| 2 , where h k =h d,k +H H Θh r,k , Θ represents the beamforming matrix of RIS, defined as θ represents the phase vector of RIS, N represents the number of RIS reflection units, and f k Represents the server's receive beam vector.

[0085] The transmission error probability ε between the server and edge device k k It is expressed as:

[0086]

[0087] where r k represents the coding rate of edge device k, m represents the transmission code length, C k =log2(1+γ k ) represents the Shannon transmission capacity between the server and edge device k, W k =1-(1+γ k ) -2 represents the channel dispersion between the server and edge device k. represents the received signal-to-noise ratio between the server and edge device k, where p k represents the transmit power of edge device k, σ 2 Represents the noise power. represents the inverse function of the Gaussian Q function, where the expression of the Gaussian Q function is

[0088] The sparse coefficient β of edge device k in step 1 k Defined as:

[0089]

[0090] Where T represents the total number of transmissions during the local gradient information upload of edge device k, Z represents the number of elements in the original local gradient information, Represents the sparse gradient information of edge device k The number of remaining non-zero elements in , q G and q L Respectively The number of information bits occupied by the non-zero elements and the corresponding position coordinates.

[0091] Step 2: Construct a joint resource allocation and beamforming design optimization problem for maximizing federated learning performance. First, construct the objective function of the optimization problem based on the sparse error and transmission error probability expressions, then define a constant modulus constraint based on beamforming at the RIS, and finally define a total transmission power constraint based on the sum of the transmission powers of the server and edge devices.

[0092] The objective function of the optimization problem described in step 2 is:

[0093]

[0094] where a c,k and a s,k denote the transmission error probability and sparse error performance coefficient of edge device k, respectively, P = {p1, p2, ..., p K} and r={r1,r2,...,r K} represent the transmission power vector and the coding rate vector respectively. The above objectives mean that by optimizing the transmission power, coding rate and phase matrix of RIS of edge devices, the transmission error probability and sparsity coefficient can be minimized, thereby increasing the amount of local gradient information successfully uploaded to the server, thereby improving the performance of sparse federated learning.

[0095] The constant modulus constraint is:

[0096]

[0097] Where θ j represents the phase of the jth reflection unit on the RIS, and L represents the number of reflection units on the RIS. The above constraint means that the modulus of each reflection unit on the RIS must be 1.

[0098] The transmission power constraint in step 2 is:

[0099]

[0100] Where p k represents the transmit power allocated to edge device k, P sumRepresents the total transmit power. The above constraint means that the sum of the transmit powers allocated to edge devices must be less than the total power.

[0101] In step 2, the joint resource allocation and beamforming design optimization problem constructed in the RIS-assisted sparse federated learning network is:

[0102] (P0):

[0103] st|θ j | 2 =1,j=1,...,N

[0104]

[0105] The meaning of the above design optimization problem is to minimize the total transmission error probability and sparsity coefficient of all users under the constant modulus constraint and total transmission power constraint by optimizing the transmission power, coding rate and phase matrix of RIS of the edge device.

[0106] Step 3: Obtain the analytical expression of the optimal solution for the coding rate, and based on this, reduce the dimension of the constructed optimization problem. By calculating the second-order derivative of the objective function with respect to the coding rate and combining the KKT condition, obtain the analytical expression of the optimal solution for the coding rate. Based on this expression, the original problem is transformed into a design problem only about the transmit power and the RIS phase matrix, achieving dimensionality reduction of the complex problem.

[0107] The specific steps for reducing the dimension of the constructed optimization problem described in step 3 are as follows:

[0108] Step 3.1: Fix the transmit power and RIS phase matrix, and calculate the second-order derivative of the objective function with respect to the coding rate. Analysis shows that the second-order derivative of the objective function with respect to the coding rate is greater than or equal to 0, proving that the optimization problem is a convex problem with respect to the coding rate. Subsequently, the optimal solution expression for the coding rate of edge device k is calculated based on the KKT condition, which is expressed as:

[0109]

[0110] Step 3.2: Substitute the coding rate expression into the problem (P0) to achieve dimensionality reduction of the original optimization problem. The optimization problem (P0) after dimensionality reduction can be equivalently rewritten as:

[0111] (P1):

[0112]

[0113] in The meaning of problem (P1) is to minimize the transmission error probability and the sparsity coefficient by jointly designing the transmit power of the edge device and the phase matrix at the RIS.

[0114] Step 4: Solve the optimization problem after dimensionality reduction based on the block coordinate descent algorithm and obtain the efficient solution of the coding rate, transmit power and RIS phase matrix of the edge device.

[0115] The specific steps of the block coordinate descent algorithm described in step 4 are as follows:

[0116] Step 4.1: Initialize the transmit power and RIS phase matrix, and set the iteration threshold And the initial transmission power of the edge device P (0) and the RIS initial phase matrix Θ (0) As a local point of iteration

[0117] Step 4.2: Fix the RIS phase matrix and calculate the second-order derivative of the objective function of the reduced-dimensional optimization problem P1 with respect to the transmit power. Prove that the reduced-dimensional optimization problem P1 is a convex problem with respect to the transmit power.

[0118] Step 4.3: Fix the RIS phase matrix Θ and use the ellipsoid method to solve problem (P1) to obtain the optimal solution of the transmission power for this iteration

[0119] Step 4.3: Fixed transmit power optimization solution for this iteration Based on the first-order Taylor approximation At local point By approximating and introducing trust region constraints, the optimization problem P1 after dimensionality reduction is approximated to the optimization problem P2:

[0120] (P2):

[0121]

[0122] in, represents the constant term introduced by the first-order Taylor approximation, and Respectively represent the local point The calculated received signal-to-noise ratio and channel dispersion of the server and edge device k, represents the confidence radius, and

[0123] Step 4.4: Introduce auxiliary variables y = {y1, y2, ..., y K}, α={α1,α2,...,α K}, perform a quadratic transformation on the fractional terms in the objective function and use Lagrange dual transformation on the logarithmic function terms. The optimization problem P2 is equivalent to the optimization problem P3:

[0124] (P3):

[0125]

[0126] in C 2k =1+α k +C 1k Represents the constant term generated by the quadratic transformation and the Lagrange dual transformation.

[0127] Step 4.5: Perform a convex approximation on the objective function in the optimization problem P3 and introduce the dual variable ψ = {ψ1, ψ2, ..., ψ N} and τ, and calculate the optimal RIS phase matrix and auxiliary variables y and α in the optimization problem P3 based on the KKT condition * The analytical expression of is:

[0128]

[0129] in and Represents auxiliary variables y={y1,y2,...,y K}, α={α1,α2,...,α K} is the optimal solution. Represents the optimized solution of the RIS phase matrix in this iteration.

[0130] Indicates the constant term generated after mathematical calculation. k =Fh d,k represents the equivalent channel of the direct line-of-sight communication link, J k =FH H diag(h r,k ) represents the equivalent channel of the RIS reflection communication link, F represents the receive beamforming vector at the base station, and h d,k represents the channel vector between the server and edge device k, H represents the channel between the server and RIS, and h r,k The channel vector between RIS and edge device k is expressed as . and Respectively represent a k and J k The conjugate transposed matrix of . n represents an indicator vector of length N, in which only the element at the nth position is 1 and the rest are 0; I N×N represents the unit matrix of length N;

[0131] Step 4.6: If the performance improvement of this iteration is less than the iteration threshold ε, the iteration is stopped. The optimal solution of this iteration is the optimal transmission code length, transmission power and RIS phase matrix (m) of the edge device in the RIS-assisted sparse federated learning network. * ,P * ,θ * )=(m,P,θ); otherwise it will be used as the local point for the next iteration Go back to step 4.2.

[0132] Step 5: Based on the transmission scheme, the local gradient information is sparsely distributed and uploaded for federated aggregation. The server broadcasts the aggregated global gradient information to all users. First, the edge device extracts part of the data from the local data set, and uses the gradient descent algorithm to calculate the local gradient information based on the extracted data. Secondly, the local gradient information is sparsely distributed in combination with the sparse algorithm. Finally, all edge users send the sparse local gradient information to the server via wireless transmission. In step 5, the edge device first extracts part of the data from the local data set, and uses the gradient descent algorithm to calculate the local gradient information based on the extracted local data. The local gradient information is based on the transmission scheme designed in step 5. The local gradient information is sparsely processed based on the calculated transmission throughput and the Top-S sparse algorithm, that is, the values ​​of the S elements with the largest amplitude in the gradient information and the corresponding position indexes are retained. Finally, all edge users send the sparse local gradient information to the local user. It is sent to the server via wireless transmission.

[0133] Specifically:

[0134] Multi-edge devices by index The edge device constructs a local sparse gradient information matrix by taking the non-zero element set in the local gradient information and its corresponding position coordinates. in represents the original local gradient information of edge device k at the tth global iteration, Represents a sparse operation. Based on sparse local gradient information The server performs federated aggregation operations to obtain the global gradient information g (t+1) , expressed as:

[0135]

[0136] Where D represents the total data volume of all edge devices, D k Represents the local data volume of the kth edge device.

[0137] The server broadcasts the global gradient information g (t+1)Sent to all edge devices. The edge device updates its local model based on the received global gradient information, expressed as:

[0138] v (t+1) =v (t) -ηg (t+1)

[0139] where v (t) represents the local model parameters of the tth global iteration, and η represents the learning rate.

[0140] Figure 3 A graph showing the variation of the test performance of the RIS-assisted sparse federated learning network with the global training cycle in an embodiment of the present invention is given. As can be seen from the graph, as the training cycle increases, the test performance of the sparse federated learning network improves and is better than the comparison scheme.

[0141] Example 2

[0142] This embodiment provides a transmission scheme design system for a RIS-assisted sparse federated learning network, including:

[0143] Module 1: It is used in RIS-assisted sparse federated learning network scenarios, combining finite code length theory to calculate the transmission error probability expression of the communication system and obtain the sparse coefficient expression of the local gradient information;

[0144] Module 2: It is used to construct the objective function of the optimization problem based on the transmission error probability expression and the sparse coefficient expression of the local gradient information, and define the constant modulus constraint according to the beamforming at the RIS, and define the total transmission power constraint according to the sum of the transmission power of the server and the edge device to construct the joint resource allocation and beamforming design optimization problem for maximizing the performance of federated learning;

[0145] Module 3: It is used to obtain the analytical expression of the optimal solution of the coding rate, and based on this, the dimension of the constructed optimization problem is reduced to transform the original problem into a reduced-dimensional optimization problem only about the transmit power and the RIS phase matrix;

[0146] Module 4: It is used to solve the optimization problem after dimensionality reduction and obtain the efficient solution of the coding rate, transmission power and RIS phase matrix of the edge device to obtain the transmission solution;

[0147] Module 5: Based on the transmission scheme, the edge device calculates the local sparse gradient information based on the local data and uploads it to the server. The server combines the sparse algorithm to perform federated aggregation on the local coefficient gradient information to obtain the global gradient information, and sends the global gradient to all edge devices in the form of broadcast for model update.

[0148] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present invention.

[0149] Obviously, those skilled in the art can make various changes and modifications to the embodiments of the present invention without departing from the spirit and scope of the embodiments of the present invention. Thus, if these modifications and variations of the embodiments of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

[0150] Other parts not described in detail are all prior art.

Claims

1. A transmission scheme design method for a RIS-assisted sparse federated learning network, characterized in that: The following steps are involved: Step 1: Based on the RIS-assisted sparse federated learning network scenario, the transmission error probability expression of the communication system is calculated in combination with the finite code length theory, and the sparse coefficient expression of the local gradient information is obtained; In step 1, the transmission error probability of the communication system is calculated by combining the finite code length theory The expression is: in Representing edge devices k The coding rate, Indicates the transmission code length, Representation Servers and Edge Devices k The Shannon transmission capacity, Representation Servers and Edge Devices k Channel dispersion between Representation Servers and Edge Devices k The received signal-to-noise ratio, Representing edge devices k The transmission power, represents the noise power; Representation Servers and Edge Devices k The channel gain between Gauss function; Edge devices in step 1 k The sparse coefficient Set to: in, Representing edge devices k Sparse gradient information The number of remaining non-zero elements in , and Respectively The number of information bits occupied by the non-zero elements and the corresponding position coordinates, T Indicates on edge devices k Total number of transmissions during local gradient information upload, Z Represents the number of elements in the original local gradient information; Step 2: Construct the objective function of the optimization problem based on the expression of transmission error probability and the sparse coefficient expression of local gradient information, define the constant modulus constraint according to the beamforming at the RIS, and define the total transmission power constraint according to the sum of the transmission power of the server and the edge device to construct the joint resource allocation and beamforming design optimization problem for maximizing the performance of federated learning; the objective function of the constructed optimization problem is: in and Represents edge devices k The transmission error probability coefficient and the performance coefficient of sparse errors; represents the transmit power vector, represents the coding rate vector, represents the RIS phase matrix; The constant modulus constraint is: ， In the formula Indicates the first j The phase of the reflection unit, N Indicates the number of reflection units on the RIS; The transmission power constraint is: ， In the formula Indicates that it is assigned to edge devices k The transmission power, Indicates the total transmit power; The joint resource allocation and beamforming design optimization problem P0 for maximizing federated learning performance is constructed as: Step 3: Obtain an analytical expression for the optimal solution of the coding rate, and based on this, reduce the dimension of the constructed optimization problem to transform the original problem into a reduced-dimensional optimization problem only about the transmit power and the RIS phase matrix; Step 3 includes the following sub-steps: Step 3.1: Fix the transmit power and RIS phase matrix, calculate the second-order derivative of the objective function with respect to the coding rate, prove that the optimization problem is convex with respect to the coding rate, and calculate the edge device based on the KKT condition k The optimal solution expression for the coding rate is: Step 3.2: Connect the edge device k The optimal solution of the coding rate is brought into the optimization problem P0 for dimensionality reduction. The optimization problem P1 after dimensionality reduction is: in For edge devices k The transmission error probability obtained by the optimal solution of the coding rate; Step 4: Solve the optimization problem after dimensionality reduction and obtain the efficient solution of the edge device's coding rate, transmit power, and RIS phase matrix to obtain the transmission solution; Step 5: Based on the transmission scheme in step 4, the edge device calculates local sparse gradient information based on local data, and uses the sparse algorithm to aggregate the local coefficient gradient information to obtain the global gradient information, and then sends the global gradient to all edge devices in the form of broadcast for model update.

2. According to claim 1, a transmission scheme design method for a RIS-assisted sparse federated learning network is characterized in that: The step 4 solves the optimization problem P1 after dimensionality reduction based on the block coordinate descent algorithm, including: Step 4.1: Initialize the transmit power and RIS phase matrix, and set the iteration threshold , and the initial transmit power of the edge device and the RIS initial phase matrix As a local point of iteration ; Step 4.2: Fix the RIS phase matrix, calculate the second-order derivative of the objective function of the optimization problem P1 after dimension reduction with respect to the transmit power, and prove that the optimization problem P1 after dimension reduction is a convex problem with respect to the transmit power; Step 4.3: Fix the RIS phase matrix and use the ellipsoid method to solve the optimization problem P1 after dimension reduction to obtain the optimal solution of the transmission power for this iteration. ; Step 4.3: Fixed transmit power optimization solution for this iteration , based on the first-order Taylor approximation At local point By approximating and introducing trust region constraints, the optimization problem P1 after dimensionality reduction is approximated to the optimization problem P2: in, , , represents the constant term introduced by the first-order Taylor approximation, and Respectively represent the local point Computed servers and edge devices k The received signal-to-noise ratio and channel dispersion, represents the confidence radius, and ; represents the phase vector of RIS, Step 4.4: Introducing auxiliary variables , , perform a quadratic transformation on the fractional terms in the objective function and use Lagrange dual transformation on the logarithmic function terms. The optimization problem P2 is equivalent to the optimization problem P3: in , , represents the constant term generated by the quadratic transformation and the Lagrange dual transformation; Step 4.5: Convex approximation of the objective function in the optimization problem P3 and introduction of dual variables and , based on KKT conditions, calculate the optimal RIS phase matrix and auxiliary variables in the optimization problem P3 and The analytical expression of is: in and Represents auxiliary variables , The optimal solution of represents the optimal solution of the RIS phase matrix in this iteration, , , , , Represents the constant term generated after mathematical calculation, represents the equivalent channel of the direct line-of-sight communication link, represents the equivalent channel of the RIS reflection communication link, represents the receive beamforming vector at the base station, represents the channel vector between the server and edge device k, The channel between the server and RIS is represented as, represents the channel vector between RIS and edge device k, and Respectively and The conjugate transposed matrix of represents an indicator vector of length N, where only n The element at position is 1, and the rest are 0; represents the unit matrix of length N; Step 4.6: If the performance improvement of this iteration compared to the previous iteration is less than the iteration threshold , then the iteration is stopped, and the optimal solution of this iteration is the optimal transmission code length, transmission power and RIS phase matrix of the edge device in the RIS-assisted sparse federated learning network ; otherwise it will be used as the local point for the next iteration , return to step 4.

2.

3. According to claim 2, a transmission scheme design method for a RIS-assisted sparse federated learning network is characterized in that: The step 5 comprises: Multi-edge devices by index To characterize, K Represents the number of edge devices. The edge devices construct a local sparse gradient information matrix with the set of non-zero elements in the local gradient information and their corresponding position coordinates. ,in Representing edge devices k In the t The original local gradient information of the global iteration, Represents sparse operations; Based on sparse local gradient information , the server obtains global gradient information through federated aggregation operations , expressed as: in represents the total data volume of all edge devices, represents the amount of local data of the kth edge device; The server broadcasts the global gradient information Sent to all edge devices, the edge devices update their local models based on the received global gradient information, expressed as: in represents the local model parameters at the tth global iteration, represents the local model parameters of the t+1th global iteration, Represents the learning rate.

4. A transmission scheme design system for RIS-assisted sparse federated learning networks, characterized in that: include: Module 1: It is used in RIS-assisted sparse federated learning network scenarios, combining finite code length theory to calculate the transmission error probability expression of the communication system and obtain the sparse coefficient expression of the local gradient information; Module 2: It is used to construct the objective function of the optimization problem based on the transmission error probability expression and the sparse coefficient expression of the local gradient information, and define the constant modulus constraint according to the beamforming at the RIS, and define the total transmission power constraint according to the sum of the transmission power of the server and the edge device to construct the joint resource allocation and beamforming design optimization problem for maximizing the performance of federated learning; Module 3: It is used to obtain the analytical expression of the optimal solution of the coding rate, and based on this, the dimension of the constructed optimization problem is reduced to transform the original problem into a reduced-dimensional optimization problem only about the transmit power and the RIS phase matrix; Module 4: It is used to solve the optimization problem after dimensionality reduction and obtain the efficient solution of the coding rate, transmission power and RIS phase matrix of the edge device to obtain the transmission solution; Module 5: Based on the transmission scheme, the edge device calculates the local sparse gradient information based on the local data and uploads it to the server. The server uses the sparse algorithm to aggregate the local coefficient gradient information to obtain the global gradient information, and sends the global gradient to all edge devices in the form of broadcast for model update. The RIS-assisted sparse federated learning network transmission scheme design system is used to execute the steps in any one of the RIS-assisted sparse federated learning network transmission scheme design methods of claims 1-3.

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