Distributed acceleration resource allocation method and system for privacy protection

Abstract

The invention relates to a privacy-protected distributed acceleration resource allocation method and system, and belongs to the technical field of information communication. According to the method and the system, a parameterized distributed momentum method and a push-pull distributed resource allocation algorithm are combined to realize accelerated resource allocation in a directed network; a privacy-related variable is decomposed into two variables through a state decomposition scheme, one variable is used for information interaction, and the other variable directly related to privacy is used for local updating, so that privacy is protected, and noise disturbance is introduced in communication by adopting a differential privacy strategy to further enhance privacy protection. The algorithm disclosed by the invention is specially designed for a complex network scene, is suitable for applications needing privacy protection and efficient resource allocation, such as a smart power grid and energy management, shows wide applicability and innovation in distributed optimization, and has a wide application prospect.

Description

Technical Field

[0001] The present invention belongs to the field of information communication technology and relates to a privacy-protected distributed acceleration resource allocation method and system. Background Art

[0002] In recent years, with the popularity of consumer electronics and the continuous enrichment of their functions, traditional centralized resource allocation methods are facing a series of new challenges. Traditional centralized methods usually rely on central nodes to aggregate, process and allocate system resources. Although this simplifies the management process, it also brings a series of problems such as single point failure, privacy leakage and high communication costs. Especially in large-scale distributed networks, long-distance data transmission may significantly increase the energy consumption and latency of the system, affecting the overall performance. In addition, the centralized method has poor scalability and is difficult to flexibly respond to the needs of rapidly expanding systems. These limitations are particularly prominent in modern consumer electronics scenarios, especially in application areas such as smart homes, smart grids, energy management and utility optimization. Traditional centralized resource allocation solutions have gradually become difficult to meet actual needs.

[0003] In contrast, distributed resource allocation methods (DRAPs) have gradually become a hot topic in research and application. Distributed methods improve the robustness, scalability and single-point failure resistance of the system through local communication and collaborative optimization between nodes without relying on central nodes. In scenarios such as smart grids, distributed algorithms can not only optimize the dynamic allocation of energy resources, but also improve communication efficiency in local interactions between nodes. However, although distributed methods have advantages over centralized solutions in many aspects, they still face a series of problems in practical applications, such as the computational efficiency of the algorithm, privacy protection, and communication overhead, which are important factors restricting their widespread application.

[0004] At present, most distributed resource allocation algorithms focus on reaching consensus between nodes through the exchange of local information to ensure the reasonable allocation of system resources. However, in terms of privacy protection, existing methods mostly adopt simple protection strategies and fail to fully consider the privacy needs in different application scenarios. For example, differential privacy, as a popular privacy protection strategy, protects user privacy by adding noise to communication, but this noise disturbance will affect the accuracy of resource allocation to a certain extent, resulting in a decrease in algorithm performance. In addition, existing accelerated distributed algorithms, such as the Nesterov acceleration method and the heavy ball method, can significantly improve the convergence speed of the algorithm and reduce the number of iterations, but often ignore the requirements of privacy protection. Therefore, the application of such algorithms in consumer electronic devices that focus on privacy sensitivity is limited.

[0005] In response to the above challenges, how to design a distributed resource allocation method that takes into account both privacy protection and algorithm efficiency has become an important direction of current research. Existing algorithms often cannot achieve efficient accelerated convergence and strong privacy protection at the same time when dealing with general constraint-coupled distributed resource allocation problems. Therefore, it is urgent to propose an innovative distributed algorithm that can not only ensure privacy security in data exchange between nodes, but also improve the convergence speed of the algorithm through acceleration methods to meet the complex resource management needs in consumer electronic devices. Summary of the invention

[0006] In view of this, the purpose of the present invention is to provide a privacy-preserving distributed accelerated resource allocation method and system. In this solution, state decomposition and differential privacy schemes are used to prevent sensitive information leakage. On the one hand, the method and system introduce momentum method to accelerate the resource allocation process. Combined with the push-pull algorithm framework, the addition of momentum method can improve the convergence speed in a distributed environment and ensure that the resource allocation task is completed in a shorter time; on the other hand, by adopting state decomposition and differential privacy theory, privacy-related variables are decomposed, and random noise is introduced at the same time, so as to complete resource optimization under the premise of privacy protection.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] A privacy-preserving distributed acceleration resource allocation method is proposed. This method combines a parameterized distributed momentum method with a push-pull distributed resource allocation algorithm to realize acceleration resource allocation in a directed network. A state decomposition scheme is used to decompose privacy-related variables into two variables, one variable is used for information interaction, and the other variable directly related to privacy is used for local updates, thereby protecting privacy. A differential privacy strategy is used to introduce noise perturbations in communication to further enhance privacy protection.

[0009] Furthermore, in the present method, defining a time-varying directed network includes: the communication between nodes is regarded as a directed network, described by G = {V, E}, consisting of a node set V = {1, 2, 3, ..., n} and an edge set Composition; This method uses N i in ={j∈V|(j,i)∈E} represents the out-neighborhood of node i; the directed network satisfies the following assumptions:

[0010] 1) Matrix and are the non-negative row random matrix and column random matrix obtained by the network, namely A1 n =1 n and also, Satisfy A ii >0 and Bii >0;

[0011] 2) Network G corresponding to matrices A and B A and Contains at least one spanning tree;

[0012] 3) There is at least one node as G A and The root node of the spanning tree;

[0013] 4) The directed network G satisfies three basic conditions involving network stability, node reliability, and communication integrity;

[0014] The three basic conditions are expressed as follows:

[0015] 4-1) Network stability: Nodes in a directed network can maintain continuous and stable operation within a reasonable time frame, and the network connection is reliable;

[0016] 4-2) Node reliability: The nodes in the network have sufficient computing and data storage capabilities to correctly perform the computing tasks required by the algorithm, and the data will not be damaged or lost when processing data within the node;

[0017] 4-3) Communication integrity: The communication between nodes is reliable, that is, the message can be transmitted to the target node accurately and the message transmission delay is within an acceptable range.

[0018] Furthermore, in this method, the following is the problem definition, and the original problem to be solved is:

[0019]

[0020] in, represents the local decision variable associated with node i, X i is a locally convex and closed set representing x i The local constraints represents the local resource demand, and represents the total demand for resources; in this context, each node i belonging to the set {1,2,...,n} has a unique local function f i : The function represents the local cost of resource allocation for node i; only node i knows X i and d i ; is a coupling matrix with full row rank (p ≥ m), and Right now is reversible; the following assumptions need to be met:

[0021] Each local cost function fi : are strongly convex and have Lipschitz continuous gradients, that is, for all have and Where L ≥ μ > 0;

[0022] Under the assumed conditions, the optimal solution x can be found * ; In addition, the corresponding dual problem of the problem is defined as:

[0023]

[0024] in, is the Lagrange multiplier, Represents the function f i convex conjugate function of , and each Q i (λ) are all concave functions;

[0025] Therefore, the dual problem is reformulated in the framework of convex optimization, namely:

[0026]

[0027] in, Strong duality ensures the equivalence of the primal problem and the dual problem, that is, the optimal value h of the dual problem * =-f * , and the optimal point of the dual problem satisfy Therefore, we focus on solving the dual problem to further exploit the convex conjugate function f i # to achieve the optimal allocation.

[0028] Furthermore, in this method, the state decomposition scheme is used as follows:

[0029] The state decomposition scheme requires that the dual state variables y of each node i (highly related to node privacy information and transmitted in the network) is decomposed into two sub-states and In the overall privacy protection process, only the sub-state is visible and shared with its neighbor nodes, while the sub-state containing private information Remain invisible and private to the network. Before sharing, the substate should be masked with noise as in existing work to prevent accurate estimation, since The update depends on During the noise adding process, we adopt the differential privacy strategy of Laplace noise to ensure the subsequent verifiable security. Here, is the key variable in the entire privacy protection process and the output variable in differential privacy. is related to private information to ensure convergence.

[0030] Furthermore, in this method, differential privacy technology is used as follows:

[0031] Each node can only access its own local parameters about the problem, but the relevant local estimates are shared among the local neighborhood, which may lead to privacy risks, such as model inversion attacks. To address this challenge, this method adopts a differential privacy strategy to protect the local loss function of participating nodes. Next, the relevant definitions of differential privacy are introduced:

[0032] Consider two sets of functions, U = {f1,...,f n} and U′={f1′,...,f n ′}, if there exists i0∈V such that and Then the function sets U and U′ are considered δ-adjacent, where δ>0, Represents two functions and The distance between

[0033] In other words, if only one node's local cost function differs between two sets of functions, the two sets of functions are considered adjacent. In this invention, the method assumes that an external attacker can obtain all auxiliary information except the parameter δ, that is, it can capture all information transmitted by inter-node communication. In this case, for any δ-adjacent function sets U and U′, if:

[0034] P[D(U)∈F]≤exp(ò)·P[D(U′)∈F]

[0035] Then the random algorithm D satisfies ò-differential privacy, where Range(D) represents the set of all possible outputs generated by algorithm D, F represents any subset of Range(D), and the privacy level is quantified by the positive parameter ò;

[0036] From the definition, it can be seen that an external attacker cannot distinguish two δ adjacent function sets based on the output of the random algorithm D. Here, in order to ensure privacy protection, ò should be minimized as much as possible by introducing noise with large variance. However, this may actually lead to a trade-off that may harm the accuracy of the algorithm. In order to analyze the differential privacy level of an algorithm, it is necessary to understand the sensitivity of the algorithm. This method uses Adj(U k ,U′ k ) represents the adjacent data set U at time k k and U′ k proximity;

[0037] At time k, is the sensitivity of the random algorithm D. The size of the random noise can be adjusted by limiting the sensitivity to ensure differential privacy.

[0038] Furthermore, the method specifically comprises the following steps:

[0039] S1. Initialize hyperparameters: constant step size η>0, adjustable parameter γ∈(-∞,+∞), momentum coefficient ν>0, noise parameter σ i > 0, weights of two sub-states α i ,β i ∈(0,1), initial vector

[0040] S2. Initialize parameters for all nodes i∈V:

[0041] S3, set the number of iterations k of all nodes i∈V to 1, and then set a maximum number of iterations K as the criterion for the algorithm to stop iterative updating;

[0042] S4, determine whether k≤K holds. If so, perform S5-S7 on all nodes i∈V. If not, that is, when k=K, the algorithm returns the local average variable of K iterations.

[0043] S5. Update auxiliary variables:

[0044] Nodes from each network Get and And immediately Transmit to each network Then, node i integrates the information and updates the variable z i,k+1 and as follows:

[0045]

[0046] S6. Update main variables:

[0047] At time k ≥ 0, node i updates the dual variable λ using only its own information i,k+1 and the original variable x i,k+1 as follows:

[0048]

[0049] in, is the parametric momentum term with momentum coefficient ν;

[0050] S7, state decomposition:

[0051] In order to protect private information, node i generates a node with the parameter σ i The Laplace distributed random noise vector τ i,k ,Then Subject to the random vector τ i,k Perturbation, that is,

[0052]

[0053] Upon receiving of After that, node i integrates the information and updates its auxiliary variable y using the inexact gradient tracking method. i,k+1 ,Right now,

[0054]

[0055] The present invention also provides a privacy-protected distributed acceleration resource allocation system.

[0056] The beneficial effects of the present invention are:

[0057] The present invention aims at the distributed resource allocation problem with a common set of constraints. First, the differential privacy strategy and state decomposition scheme are used to ensure privacy protection during communication between nodes, and the noise perturbation mechanism further enhances privacy security. Secondly, the parameterized distributed momentum method and the push-pull algorithm are combined to improve the convergence speed of resource allocation, which is particularly suitable for directed networks. The algorithm maintains a high calculation accuracy while protecting privacy, and can effectively balance privacy protection and allocation accuracy. In addition, the algorithm realizes global resource allocation through local communication without the need for a central node. It has strong resistance to single point failures and scalability, and is suitable for large-scale network environments. The algorithm is designed for complex network scenarios and is suitable for applications such as smart grids and energy management that require privacy protection and efficient resource allocation, showing wide applicability and innovation in distributed optimization.

[0058] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0060] Figure 1 It is a schematic diagram of the process of the method of the present invention;

[0061] Figure 2 The convergence effect of the algorithm of the present invention in the general resource allocation problem;

[0062] Figure 3 The effect diagram of the algorithm of the present invention comparing different step sizes and momentum parameters in a general resource allocation problem;

[0063] Figure 4 Comparison of different privacy constants σ in the general resource allocation problem of the algorithm of the present invention i ;

[0064] Figure 5 To compare the effects of the algorithm of the present invention with those of related algorithms in general resource allocation problems;

[0065] Figure 6 Compare the proposed algorithm to time-varying networks and different sparsities in the general resource allocation problem;

[0066] Figure 7 The effect of the algorithm of the present invention on the IEEE 118-bus in the economic dispatch problem;

[0067] Figure 8 The effect of the algorithm of the present invention on dynamic demand in economic dispatch problems;

[0068] Fig. 9 This is the privacy protection effect of the algorithm of the present invention in the economic scheduling problem. DETAILED DESCRIPTION

[0069] The technical solution of the present invention is described in detail below with reference to the accompanying drawings.

[0070] Figure 1 The flowchart of the method of the present invention is shown in the figure. In this embodiment, the distributed acceleration resource allocation method with privacy protection provided by the present invention includes the following steps:

[0071] (1) Initialize hyperparameters: η = 0.08, γ = 0.5, ν = 0.5, σ i =0.09,α i =0.5,β i =0.5, n=50 initial vector

[0072] (2) Initialize parameters for all nodes i∈V:

[0073] (3) Set the number of iterations k of all nodes i∈V to 1, and then set a maximum number of iterations K=1000 as the criterion for the algorithm to stop iterative updating.

[0074] (4) Determine whether k≤K holds. If so, perform (5)-(7) updates on all nodes i∈V. If not, that is, when k=K, the algorithm returns the local average variable of K iterations

[0075] (5) Update auxiliary variables:

[0076] Nodes from each network Get and And immediately Transmit to each network Then, node i integrates the information and updates the variable z i,k+1 and as follows:

[0077]

[0078] (6) Update the main variables:

[0079] At time k ≥ 0, node i updates the dual variable λ using only its own information i,k+1 and the original variable x i,k+1 as follows:

[0080]

[0081] in, is the parametric momentum term with momentum coefficient ν.

[0082] (7) State decomposition:

[0083] In order to protect private information, node i generates a node with the parameter σ i The Laplace distributed random noise vector τ i,k ,Then Subject to the random vector τ i,k Perturbation, that is,

[0084]

[0085] Upon receiving of After that, node i integrates the information and updates its auxiliary variable y using the inexact gradient tracking method. i,k+1 ,Right now

[0086]

[0087] In this embodiment, general resource allocation problems and economic dispatch problems (EDPs) are used to test the effectiveness of the proposed algorithm.

[0088] 1. The present invention adopts a general resource allocation problem to test the effectiveness of the proposed algorithm.

[0089] In this embodiment, the general distributed resource allocation problem with a logarithmic cost function with 2-norm regularization is solved, as follows:

[0090]

[0091] Where: Set p = 1, n = 5. Coefficient a i , b i 、c i and r i Randomly select from the range of (0,2], [-2,2], [-3,3] and [-3,3] to ensure randomness and accuracy. In addition, consider C i =1,X i =[1,3], and d i =2. A strongly connected directed network G with n = 5 nodes randomly established is used as the basis for the study. Then, the simulation results are described in the following three parts. In the comparison scenario, by evaluating the residual to quantify the performance of the algorithm, where the optimal solution is obtained by the centralized method.

[0092] (i) Convergence performance: In this section, the convergence performance of the proposed algorithm is tested with parameters ξ∈(0,1), α∈(0,1), β∈(0,1), ν=0.5, γ=0.5, and η=0.08. The simulation results are shown in Figure 2 shown. Figure 2 (a)-2(b) shows the algorithm of the present invention using differential privacy strategy (σ i =0.09, i=1,…,5) converges to the optimal allocation neighborhood of the problem. Figure 2 (c)-2(d) shows that even with the state decomposition scheme, the algorithm of the present invention without the differential privacy strategy can achieve the optimal allocation. Figure 2 (b) and Figure 2 (d) shows that the weighted sum of states at any termination time is not always equal to the demand, and can only be close to being equal after a certain period of time, which is essentially due to the asymptotic convergence of the algorithm of the present invention.

[0093] (ii) Parameter setting: In this section, the effects of parameters γ, η, and ν on the convergence performance of the proposed algorithm are discussed. Figure 3 shown. Figure 3 (a) and Figure 3 (c) shows the impact of different step length η values ​​(fixed γ and ν) on the convergence results of the differential privacy strategy (σ i =0.09, i=1,…,5). Figure 3 (b) and Figure 3(d) shows the impact of different momentum parameters |γ|ν values ​​(fixed η) on the convergence results without adopting differential privacy strategy. Figure 3 It is shown that the proposed algorithm can achieve linear convergence. Increasing the step size η and the momentum parameter |γ|ν will accelerate the convergence of the algorithm. However, this property is not unconditional, because there are some specific upper limits for the step size and momentum parameters. In addition, Figure 3 It is also concluded that differential privacy strategies do degrade the performance of the algorithm.

[0094] (iii) Differential Privacy: In this section, the differential privacy performance of the proposed algorithm is discussed under the conditions of ν = 0.5, γ = 0.5 and η = 0.1. Figure 4 The results are shown, showing different σ i Convergence mode for values ​​of σ from i = 1 to i = 5 i are 0.2, 5, and 10, respectively. Clearly, the convergence behavior is significantly affected by the parameter σ. It is worth noting that the addition of perturbations to the algorithm leads to a slower convergence process. In addition, the size of these perturbations, i.e., σ i The value of is inversely proportional to the convergence performance of the algorithm.

[0095] (iv) Performance comparison: In this section, the proposed algorithm is compared with related distributed algorithms in terms of convergence speed and convergence time. Figure 5 And as shown in Table 1. Figure 5 It shows that these algorithms are i ) or the convergence without using differential privacy strategy. Table 1 The required residual 10 is achieved by the algorithm -8 Here, the algorithm without differential privacy strategy is considered, because the introduction of random noise will lead to large fluctuations in the convergence estimate and the convergence time will be inaccurate.

[0096] Table 1

[0097]

[0098] (v) Time-varying networks: In this section, the applicability of the proposed algorithm in time-varying networks (real-world network environments) and the impact of different network sparsities on the algorithm performance are further discussed. Figure 6 As shown, no differential privacy strategy (fixed model and algorithm parameters) is adopted. Figure 6 (a) It shows that the algorithm of the present invention is applicable to time-varying networks and exhibits superior acceleration compared with other related algorithms. Figure 6 (b) shows that the convergence is better when the network is denser.

[0099] 2. The present invention uses the application of economic dispatch problem to test the effectiveness of the proposed algorithm.

[0100] In this example, we continue to consider applying EDPs on the IEEE 118-bus test system to demonstrate the performance of the proposed algorithm in a larger-scale actual power system. The IEEE 118-bus test system consists of 54 generators interconnected by bus lines, assuming that these lines are directed and strongly connected. Each generator i faces a quadratic cost function, which is private to generator i and is expressed as Among them, the coefficient w i The range is 0.0024 to 0.0697, v i The range is 8.3391 to 37.6968, r i Between 6.78 and 74.33, in $ / MW 2 , $ / MW and $. Each x i Restricted to a specified range (in MW), where The range is 5 to 150, The range is 150 to 400. The total demand of the system is d = 6000MW, which is initially evenly distributed to each node. There is d(i) = d / n. For simplicity, the same network strategy as in the above example is adopted. Then, the simulation results are described in the following two parts.

[0101] (i) Convergence performance: In this section, the convergence performance of the proposed algorithm is tested using parameters ξ∈(0,1), α∈(0,1), β∈(0,1), ν=0.5, γ=0.5, and η=0.01. The simulation results are shown in Figure 7 As shown, it shows that the algorithm with differential privacy strategy (σ i =10,i=1,…,54) will converge to the optimal allocation neighborhood of the problem. Figure 7 (c) shows that after a certain period of time, the weighted sum of the states is approximately equal to the demand. This approximation is due to the fact that the algorithm of the present invention converges to the neighborhood of the optimal solution when k→∞, and the adoption of the differential privacy strategy.

[0102] (ii) Dynamic demand: Given that demand is not always constant in practical applications of smart grids, the application of the proposed algorithm in dynamic economic dispatch scenarios is explored, especially for the case of time-varying demand. Here, the total iteration time is divided into three equal time periods, and it is assumed that the total demand changes in each time period. Simulation results (ξ∈(0,1), α∈(0,1), β∈(0,1), ν=0.5, γ=0.5, η=0.05, and σ i =10, i=1,…,54) such as Figure 8As shown, it is shown that when the total demand fluctuates, the proposed algorithm converges in a short time, and the generators adjust their power generation according to the current total demand.

[0103] (iii) Privacy protection: In this section, the privacy protection performance of the algorithm of the present invention is verified. The purpose of privacy protection in EDPs is that even if an external attacker knows some information, he cannot obtain the power generation information. Given a cost function f i (x i ), the attacker will use the inferred information in the network to calculate the power generation x of generator i in the next time step i,k+1 , the calculation formula is Consider the worst case scenario that an attacker may obtain, that is, he can obtain the distributed update rule (the algorithm of the present invention without the state decomposition scheme and parameter momentum acceleration) and use the same parameters.

[0104] Fig. 9 Shows x 7,k The inference result and the actual x 7,k In order to better characterize the privacy protection performance, generator 7 is selected to ensure that its optimal solution is not within the constraint boundary. The inference results of other generators are the same as generator 7. Fig. 9 It is shown that after adopting the state decomposition scheme and differential privacy strategy, external eavesdroppers cannot accurately infer x 7,k . Fig. 9 (a) shows that the state decomposition scheme itself has privacy-preserving properties.

[0105] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A privacy-preserving distributed acceleration resource allocation method, characterized in that: This method combines the parameterized distributed momentum method with the push-pull distributed resource allocation algorithm to achieve accelerated resource allocation in directed networks; the privacy-related variables are decomposed into two variables through the state decomposition scheme, one variable is used for information interaction, and the other variable directly related to privacy is used for local updates, thereby protecting privacy, and a differential privacy strategy is used to introduce noise perturbations in communication to further enhance privacy protection.

2. The privacy-preserving distributed acceleration resource allocation method according to claim 1, characterized in that: In this method, the definition of a time-varying directed network includes: the communication between nodes is regarded as a directed network, described by G = {V, E}, which consists of a node set V = {1, 2, 3, ..., n} and an edge set Composition; This method uses N i in ={j∈V|(j,i)∈E} represents the out-neighborhood of node i; the directed network satisfies the following assumptions: 1) Matrix and are the non-negative row random matrix and column random matrix obtained by the network, namely A1 n =1 n and also, Satisfy A ii >0 and B ii >0; 2) Network G corresponding to matrices A and B A and Contains at least one spanning tree; 3) There is at least one node as G A and The root node of the spanning tree; 4) The directed network G satisfies three basic conditions involving network stability, node reliability, and communication integrity; The three basic conditions are expressed as follows: 4-1) Network stability: Nodes in a directed network can maintain continuous and stable operation within a reasonable time frame, and the network connection is reliable; 4-2) Node reliability: The nodes in the network have sufficient computing and data storage capabilities to correctly perform the computing tasks required by the algorithm, and the data will not be damaged or lost when processing data within the node; 4-3) Communication integrity: The communication between nodes is reliable, that is, the message can be transmitted to the target node accurately and the message transmission delay is within an acceptable range.

3. The privacy-preserving distributed acceleration resource allocation method according to claim 2, characterized in that: In this method, the following is the problem definition, and the original problem to be solved is: in, represents the local decision variable associated with node i, X i is a locally convex and closed set representing x i The local constraints represents the local resource demand, and represents the total demand for resources; each node i belonging to the set {1,2,...,n} has a unique local function f i : The function represents the local cost of resource allocation for node i; only node i knows X i and d i ; is a coupling matrix with full row rank (p ≥ m), and Right now is reversible; the following assumptions need to be met: Each local cost function f i : are strongly convex and have Lipschitz continuous gradients, that is, for all Yes||▽f i (x)-▽f i (y)||≤L||xy||and <▽f i (x)-▽f i (y),xy>≥μ||xy|| 2 , where L ≥ μ > 0; Under the assumed conditions, the optimal solution x can be found * ; In addition, the corresponding dual problem of the problem is defined as: in, is the Lagrange multiplier, Represents the function f i convex conjugate function of , and each Q i (λ) are all concave functions; Therefore, the dual problem is reformulated in the framework of convex optimization, namely: in, Strong duality ensures the equivalence of the primal problem and the dual problem, that is, the optimal value h of the dual problem * =-f * , and the optimal point of the dual problem satisfy Therefore, we focus on solving the dual problem to further exploit the convex conjugate function f i # to achieve the optimal allocation.

4. The privacy-preserving distributed acceleration resource allocation method according to claim 3, characterized in that: In this method, the state decomposition scheme and differential privacy technology are used as follows: Related ways of state decomposition: The state decomposition scheme requires that the dual state variables y of each node i is decomposed into two sub-states and In the overall privacy protection process, only the sub-state is visible and shared with its neighbor nodes, while the sub-state containing private information Remain invisible and private to the network; before sharing, substate should be masked with noise as in existing work to prevent accurate estimation, since The update depends on In the process of adding noise, the differential privacy strategy of Laplace noise is adopted to ensure the subsequent verifiable security; here, is the key variable in the entire privacy protection process and the output variable in differential privacy. is related to private information to ensure convergence; Related definitions of differential privacy: Consider two sets of functions, U = {f1,...,f n } and U′={f1′,...,f n ′}, if there exists i0∈V such that and Then the function sets U and U′ are considered δ-adjacent, where δ>0, Represents two functions and The distance between In other words, if only one node’s local cost function differs between two sets of functions, then the two sets of functions are considered adjacent. This approach assumes that an external attacker can obtain all auxiliary information except the parameter δ, i.e., it can capture all information transmitted by inter-node communication. In this case, for any δ-adjacent sets of functions U and U′, if: P[D(U)∈F]≤exp(ò)·P[D(U′)∈F] Then the random algorithm D satisfies ò-differential privacy, where Range(D) represents the set of all possible outputs generated by algorithm D, F represents any subset of Range(D), and the privacy level is quantified by the positive parameter ò; From the definition, it can be seen that an external attacker cannot distinguish two δ adjacent function sets based on the output of the random algorithm D. This method uses Adj(U k ,U′ k ) represents the adjacent data set U at time k k and U′ k proximity; At time k, is the sensitivity of the random algorithm D. The size of the random noise is adjusted by limiting the sensitivity to ensure differential privacy.

5. The privacy-preserving distributed acceleration resource allocation method according to claim 4, characterized in that: This method specifically comprises the following steps: S1. Initialize hyperparameters: constant step size η>0, adjustable parameter γ∈(-∞,+∞), momentum coefficient ν>0, noise parameter σ i > 0, weights of two sub-states α i ,β i ∈(0,1), initial vector S2. Initialize parameters for all nodes i∈V: S3, set the number of iterations k of all nodes i∈V to 1, and then set a maximum number of iterations K as the criterion for the algorithm to stop iterative updating; S4, determine whether k≤K holds. If so, perform S5-S7 on all nodes i∈V. If not, that is, when k=K, the algorithm returns the local average variable of K iterations. S5. Update auxiliary variables: Nodes from each network Get and And immediately Transmit to each network Then, node i integrates the information and updates the variable z i,k+1 and as follows: S6. Update main variables: At time k ≥ 0, node i updates the dual variable λ using only its own information i,k+1 and the original variable x i,k+1 as follows: in, is the parametric momentum term with momentum coefficient ν; S7, state decomposition: In order to protect private information, node i generates a node with the parameter σ i The Laplace distributed random noise vector τ i,k ,Then Subject to the random vector τ i,k Perturbation, that is, Upon receiving of After that, node i integrates the information and updates its auxiliary variable y using the inexact gradient tracking method. i,k+1 ,Right now, 6. A privacy-preserving distributed acceleration resource allocation system, characterized in that: The system adopts the method as claimed in any one of claims 1 to 5.

Images