A privacy-protected distributed multi-agent network optimization method

Abstract

The application provides a privacy-protected distributed multi-agent network optimization method and belongs to the technical field of privacy protection. When information transmission is performed in the multi-agent network, a disturbance is added in a real state to obtain a disguised state to conceal real information for information transmission, and on this basis, an initialization step and an updating law of a variable in an agent are invented. The application can improve the problem that the privacy protection in the distributed multi-agent network is not enough and the optimization process is complex.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of privacy protection, and particularly relates to a privacy-protected distributed multi-agent network optimization method. BACKGROUND

[0002] With the modern world becoming increasingly digitized and interconnected, the scale and complexity of modern data sets are growing exponentially, and methods capable of solving data sets with a large number of features or training data become increasingly important. At the same time, the development of wired and wireless technologies has led to the emergence of large-scale networks, including the Internet, mobile ad hoc networks and wireless sensor networks, which have led to a huge increase in information data sets. In the prior art, distributed optimization methods are commonly used to process huge data sets, and in distributed optimization processing, the decentralized collection, storage and information exchange between nodes of huge data sets inevitably lead to the risk of privacy leakage. Research on privacy protection for distributed algorithms has become increasingly important, such as Chinese invention patents CN110399738B and CN113312635B, which are based on research on information security technology for privacy protection. SUMMARY

[0003] Based on the above analysis, the application provides a privacy-protected distributed multi-agent network optimization method, which can solve the problems of insufficient privacy protection in the prior art in a distributed multi-agent network and complex optimization process.

[0004] The application provides a privacy-protected distributed multi-agent network optimization method, characterized in that the specific steps include:

[0005] Step S1: establishing an optimization problem model of a distributed multi-agent network

[0006] Step S1-1: establishing a topology graph of a multi-agent network G :

[0007] G ={ V , E};

[0008] wherein, V is a set of agent nodes in the multi-agent network, V ={ v 1, v 2,…, v n}, n is the total number of agent nodes; when two agent nodes communicate bidirectionally, the two agent nodes are a pair of neighbor nodes, wherein the pair of neighbor nodes are agent node v i and neighbor agent nodev j , v i ∈ V , v j ∈ V , i≠j each edge between a pair of neighboring nodes is denoted as ( i , j ) and ( j , i ) E is a set of edges between neighboring nodes in a multi-agent network, E ={( i , j ), ( j , i )}; an agent node v i is denoted as N i , N i ={ v j |j =1,2,…, m , ( i , j )∈ E}, m is the total number of neighboring agent nodes of agent node v i ;

[0009] Step S1-2: establish a distributed consensus optimization problem according to the topology graph of the multi-agent network G ;

[0010] Step S2: initialize the initial values of the iteration variables of each agent node:

[0011] the initial value of the state auxiliary variable of agent node v i and neighboring agent node v j :

[0012]

[0013] wherein, x i 0 is the true state of agent node v i at the initial time; ε i 0 is agent node v ​i random perturbation generated at the beginning; Γ i,j 0 auxiliary variable for the multiplier corresponding to the edge ( i , j ) at the beginning; θ non-negative common penalty parameter for all agent nodes;

[0014] Thus, the agent node v i neighbor agent node v j The expression of the initial value of the state auxiliary variable is ;

[0015] Agent node v i and neighbor agent node v j The initial value of the cover multiplier corresponding to the edge ( i , j ) is ∧ i,j 0 :

[0016]

[0017] wherein, λ i,j 0 is the initial value of the real multiplier corresponding to the edge ( i , j );

[0018] Thus, the neighbor agent node v j and the agent node v i The expression of the initial value of the cover multiplier corresponding to the edge ( j , i ) is ∧ j,i 0 The expression of the initial value of the real multiplier corresponding to the edge ( j , i ) is λ j,i 0 ;

[0019] Agent node v i The initial value of the cumulative auxiliary variable is a i 0 :

[0020]

[0021] Thus, the agent node vi a neighbor agent node of v j The initial value of the cumulative auxiliary variable is expressed as a j 0 ;

[0022] Step S3: Establishing an agent node v i a first cover state of a second cover state of :

[0023]

[0024] wherein, x i k a real state of the agent node v i at the first update; k ε i k a random disturbance generated by the agent node v i at the second update; k k =0,1,2,…, K , K a maximum number of updates to meet the error condition;

[0025] Thus, the first cover state expression of a neighbor agent node v j in a multi-agent network is and the second cover state expression is ; the agent node v i and the neighbor agent node v j exchange information with added random disturbance;

[0026] Step S4: Establishing an update law of the agent node:

[0027] the agent node k +1th iteration, the following variables of the agent node v i are updated:

[0028]

[0029] wherein, a i k+1 the agent node​​v i at the k +1th update; a i k for the agent node v i at the k +1th update; x i k+1 for the agent node v i at the k +1th update; i,j k for the masking multiplier corresponding to the edge ( k , i , j ) at the k +1th update; j,i k for the masking multiplier corresponding to the edge ( j , i ) at the +1th update; v i for the non-increasing constant sequence generated at the k +1th update; θ for the non-negative common penalty parameter of the agent node N i |for the number of elements in the set N i i,j k+1 for the masking multiplier corresponding to the edge ( k , i , j ) at the ε +1th update; i k+1 for the agent node v i the random disturbance generated at the k +1th update;

[0030] Step S5: based on the initial value of the agent node in step S2, generating the first masking state and the second masking state according to step S3, and performing iterative parameter updating according to the updating law of step S4 until the number of updates reaches K , traversing all agent nodes v i v i x i K ,​​ .

[0031] Optionally, the specific steps of step S1-2 are as follows:

[0032] Topology graph based on multi-agent network G The optimal solution to the distributed consistency optimization problem can be obtained in the following manner. x * :

[0033]

[0034] in, x i For intelligent agent nodes v i The estimate; x j For neighboring intelligent agent nodes v j The estimate; f i ( x i ) is an agent node v i The cost function.

[0035] Optionally, maximum number of updates K The error condition is || x i K+1 - x i K ||< θ , θ For error condition accuracy.

[0036] The advantages of this invention are:

[0037] (1) The method of the present invention can achieve reliable privacy protection without adding extra communication and computing burden, and has strong operability and adaptability, and high optimization speed.

[0038] (2) The method of the present invention does not require additional restrictions on the disturbance, the whole optimization process is simple, and the work efficiency is improved.

[0039] (3) The method of the present invention targets semi-honest enemies and external eavesdroppers. It adds random perturbation to the privacy information of the honest agent's state (such as the agent's real-time state and gradient information) to generate a mask state without decay. It also designs an update law for agent nodes based on the mask state passed by neighboring agents, so that the state of all normal agents can quickly converge to the optimal solution of the optimization problem. Attached Figure Description

[0040] The accompanying drawings are provided to better understand the invention, but are not intended to limit the invention, wherein:

[0041] θ This is a flowchart illustrating the distributed optimization method of the present invention;

[0042] θ This is a schematic diagram of a 5-node sensor network in Example 1;

[0043] θ The convergence curve of the sensor node real state of the 5-node sensor network in Example 1 is shown.

[0044] θ This is a diagram showing the changes in the first masking state of the sensor nodes in the 5-node sensor network of Example 1.

[0045] θ This is a diagram showing the changes in the second masking state of the sensor nodes in the 5-node sensor network of Example 1.

[0046] θ The curve showing the change of the global cost function of the 5-node sensor network in Example 1;

[0047] θ The image shows the global error curve of the sensor node state in the 5-node sensor network of Example 1. Attached image description:

[0049] 1: Agent node numbered 1; 2: Agent node numbered 2; 3: Agent node numbered 3; 4: Agent node numbered 4; 5: Agent node numbered 5. Detailed Implementation

[0050] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0051] like θ The present invention discloses a privacy-preserving distributed multi-agent network optimization method, the specific steps of which include:

[0052] Step S1: Establish an optimization problem model for a distributed multi-agent network:

[0053] Step S1-1: Establish the topology of the multi-agent network. G :

[0054] G ={ V , E};(1)

[0055] in, V It is the set of agent nodes in a multi-agent network. V ={v 1, v 2,…, v n}, n This represents the total number of agent nodes; when two agent nodes communicate bidirectionally, these two agent nodes form a pair of neighbor nodes, where each neighbor node is an agent node. v i and neighboring intelligent agent nodes v j , v i ∈ n , v j ∈ n , θ The edge between each pair of neighboring nodes is ( i , j )and( j , i ); E It is the set of edges between neighboring nodes in a multi-agent network. E ={( i , j ), ( j , i )};Agent Node v i The set of neighboring intelligent agent nodes is N i , N i ={ v j |j =1,2,…, m , ( i , j )∈ E}

[0056] Optionally, a topology graph of a multi-agent network. G All agent nodes in the system have at least one agent node neighbor.

[0057] Step S1-2: Based on the topology of the multi-agent network G Establishing a distributed consistency optimization problem:

[0058] Topology graph based on multi-agent network G The optimal solution to the distributed consistency optimization problem can be obtained in the following manner. x * :

[0059]

[0060] in, xFor the decision variables of the agent nodes, i.e., the global state. R d for d 3D closed function, R For real numbers, d It refers to the dimension of the variables in the actual problem, which depends on the specific problem. f i ( x ) is the cost function of the agent node. For global cost function;

[0061] The distributed consensus optimization problem is addressed by transmitting masked state information between intelligent agent nodes. The distributed processing expression is as follows:

[0062]

[0063] in, x i For intelligent agent nodes v i The estimate; x j For neighboring intelligent agent nodes v j The estimate; f i ( x i ) is an agent node v i The cost function.

[0064] Optionally, agent nodes v i Cost function f i ( x i ) can be a power generation cost function for a power plant, a loss function in machine learning problems, etc.

[0065] Step S2: Initialize the initial values ​​of the iterative variables of the agent nodes:

[0066] This involves initializing all agent nodes in the set of agent nodes.

[0067] intelligent agent node v i With neighboring intelligent agent nodes v j Initial values ​​of the state auxiliary variables :

[0068] (6)

[0069] in, xi 0 For intelligent agent nodes v i The initial true state; θ i 0 For intelligent agent nodes v i Initial random disturbance; Γ i,j 0 Initially, with the edge ( i , j The corresponding multiplier auxiliary variable; θ is the non-negative common penalty parameter for all agent nodes.

[0070] Understandable θ i 0 For intelligent agent nodes v i The initial random disturbance is an arbitrary random disturbance.

[0071] Therefore, neighboring agent nodes in a multi-agent network v j The expression for the initial value of the state auxiliary variable is: .

[0072] The state auxiliary variables are passed to their respective neighbors.

[0073] intelligent agent node v i With neighboring intelligent agent nodes v j The edge ( i , j The initial value of the corresponding masking multiplier is ∧. i,j 0 :

[0074] (7)

[0075] in, θ i,j 0 For the edge ( i , j The corresponding initial values ​​of the real multipliers.

[0076] Therefore, neighboring intelligent agent nodes v j With agent nodes v i The edge ( j , i The corresponding initial value expression for the masked multiplier is ∧ j,i 0 ,side(j , i The corresponding initial value expression for the real multiplier is: θ j,i 0 .

[0077] intelligent agent node v i Initial values ​​of cumulative auxiliary variables a i 0 :

[0078] (8)

[0079] intelligent agent node v i First, receive the state auxiliary variable, then set the initial value of the cumulative auxiliary variable. a i 0 .

[0080] Therefore, agent nodes in a multi-agent network v i Neighboring intelligent agent nodes v j The expression for the initial value of the cumulative auxiliary variable is: a j 0 .

[0081] Step S3: In the first k The agent node is created in the next update. v i First state of concealment Second concealment state :

[0082]

[0083] in, x i k For intelligent agent nodes v i No. k The actual state at the time of the next update; θ i k For intelligent agent nodes v i No. k Random disturbances generated by the next update; k =0,1,2,…, K , K To satisfy the maximum number of updates required to meet the error condition; agent nodes v i Transmit information to neighboring intelligent agent nodesv j At that time, the agent node with added random perturbation is transmitted. v i The first and second masking states.

[0084] Therefore, neighboring agent nodes in a multi-agent network v j The first masking state expression is The expression for the second masked state is: Neighboring intelligent agent nodes v j Transmit information to intelligent agent nodes v i At that time, the neighboring intelligent agent nodes with added random perturbations are passed on. v j The first and second masking states.

[0085] Step S4: Establish the update law for agent nodes:

[0086] No. k At iteration +1, the neighboring agent node v j Receive agent node v i First state of concealment Second concealment state Intelligent agent node v i Receive neighboring smart agent nodes v j First state of concealment Second concealment state Update agent nodes v i The following variables:

[0087] (11)

[0088]

[0089] in, a i k+1 For intelligent agent nodes v i In the k The cumulative auxiliary variable at +1 update; a i k For intelligent agent nodes v i In the k The cumulative auxiliary variable during the next update; xi k+1 For intelligent agent nodes v i In the k The actual state at +1 update; ∧ i,j k In the first k During the next update, the edge ( i , j The corresponding masking multiplier; ∧ j,i k In the first k During the next update, the edge ( j , i The corresponding masking multiplier; For intelligent agent nodes v i In the k The non-increasing constant sequence generated during the next update; θ The non-negative common penalty parameter for all agent nodes; N i |for sets N i The number of elements; ∧ i,j k+1 In the first k +1 update with edge ( i , j The corresponding masking multiplier; θ i k+1 For intelligent agent nodes v i No. k +1 update generates random perturbations. Preferably, θ =1.

[0090] Understandable θ i k+1 For intelligent agent nodes v i No. k The random perturbation generated by +1 update is an arbitrary random perturbation.

[0091] Step S5: Based on the initial values ​​of the iterative parameters of the agent nodes in Step S2, generate the first and second masking states according to Step S3, and update the iterative parameters according to the update law in Step S4 until the number of updates reaches [a certain number]. K traverse all agent nodes v i Obtain each agent node v i status x i K , .

[0092] Preferably, the maximum number of updates K The error condition is || x i K+1 - x i K ||< θ , θ For the accuracy of error conditions. Preferably, θ =10 -3 .

[0093] Example 1

[0094] To illustrate the effectiveness of the method proposed in this invention, the following detailed description of the above technical solution is provided through a specific embodiment. The specific implementation steps are as follows:

[0095] See θ This embodiment discloses a privacy-preserving distributed sensor network optimization method, the specific steps of which include:

[0096] The distributed sensor network is configured with 5 sensors. n =5, for all 5 sensors in the diagram, each sensor i Measuring the two-dimensional coordinates of a signal source x ∈ R 2 The signal received by the sensor is the value of the signal source after passing through the sensor's measurement matrix and then adding Gaussian noise. Specifically, the sensor... i The received signal value is y i ,satisfy y i = M i x + θ i ,in M i ∈ R 2×2 It is a sensor i The measurement matrix, θ i ∈ R 2 It is a sensor i The received signal contains Gaussian noise, i.e., ... The goal of the sensor network is to use the maximum likelihood method, with each sensor jointly solving for the signal source. x Optimal estimation of coordinate position x * The optimization problem is ,F ( x ) is the global cost function, and correspondingly, for each sensor i The cost function is Then the optimal estimate x * The optimal solution to the optimization problem satisfies x * =argmin F ( x ),in, The goal of the optimization problem is to minimize the sum of noise. Here, we assume the measurement matrix... M i and y i The coefficients of satisfy a standard normal distribution. The optimal solution to this optimization problem is... x * Position coordinates x The maximum likelihood estimate, that is, the optimal solution. x * This is the most likely coordinate location of the signal source. In this embodiment, the sensor... i Random perturbation applied to state information θ i Assume that the following conditions are met. θ (1,5) Uniformly distributed random numbers, other initial values ​​are set according to step S2 above, and iterative optimization is performed according to steps 3-5, with the global state error... . θ , θ and θ The convergence of the true state, the global cost function, and the global state error as a function of the number of iterations is illustrated, and they all converge to the optimal solution. x * To minimize global cost F ( x * The values ​​of 0 and 0 indicate that the optimization method of the present invention can converge to the optimal solution after adding perturbation. θ and θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ The changes between the first and second masked states are shown, demonstrating that adding random perturbations can mask the true value of the state, thus verifying the privacy protection of this method.

[0097] The specific embodiments described above do not constitute a limitation on the scope of protection disclosed in this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can occur depending on design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection disclosed in this invention.

Claims

1. A privacy-preserving distributed multi-agent network optimization method, characterized in that, The specific steps include: Step S1: Establish an optimization problem model for a distributed multi-agent network: Step S1-1: Establish the topology of the multi-agent network. G : G ={ V , E}； in, V It is the set of agent nodes in a multi-agent network. V ={ v 1, v 2,…, v n }, n This represents the total number of agent nodes; when two agent nodes communicate bidirectionally, these two agent nodes form a pair of neighbor nodes, where each neighbor node is an agent node. v i and neighboring intelligent agent nodes v j , v i ∈ V , v j ∈ V , i≠j The edge between each pair of neighboring nodes is ( i , j )and( j , i ); E It is the set of edges between neighboring nodes in a multi-agent network. E ={( i , j ), ( j , i )};Agent Node v i The set of neighboring intelligent agent nodes is N i , N i ={ v j |j =1,2,…, m , ( i , j )∈ E }; Step S1-2: Based on the topology of the multi-agent network G Establish a distributed consistency optimization problem; Step S2: Initialize the initial values ​​of the iteration variables for each agent node: intelligent agent node v i With neighboring intelligent agent nodes v j Initial values ​​of the state auxiliary variables : in, x i 0 For intelligent agent nodes v i The initial true state; ε i 0 For intelligent agent nodes v i Initial random disturbance; Γ i,j 0 Initially, with the edge ( i , j The corresponding multiplier auxiliary variable; θ The non-negative common penalty parameter for all agent nodes; Therefore, neighboring intelligent agent nodes v j With agent nodes v i The initial value of the state auxiliary variable is ; intelligent agent node v i With neighboring intelligent agent nodes v j The edge ( i , j The initial value of the corresponding masking multiplier is ∧. i,j 0 : in, λ i,j 0 For the edge ( i , j The corresponding initial values ​​of the real multipliers; Therefore, neighboring intelligent agent nodes v j With agent nodes v i The edge ( j , i The initial value of the corresponding masking multiplier is ∧. j,i 0 , and the edge ( j , i The corresponding initial value of the real multiplier is λ j,i 0 ; intelligent agent node v i Initial values ​​of cumulative auxiliary variables a i 0 : Therefore, intelligent agent nodes v i Neighboring intelligent agent nodes v j The initial value of the cumulative auxiliary variable is a j 0 ; Step S3: Establish agent nodes v i First state of concealment Second concealment state : in, x i k For intelligent agent nodes v i No. k The actual state at the time of the next update; ε i k For intelligent agent nodes v i No. k Random disturbances generated by the next update; k =0,1,2,…, K , K The maximum number of updates to satisfy the error condition; Therefore, intelligent agent nodes v i Neighboring intelligent agent nodes v j The first state of concealment is The second state of concealment is Intelligent agent node v i With neighboring intelligent agent nodes v j Information with added random perturbations is exchanged between them; Step S4: Establish the update law for agent nodes: No. k At iteration +1, update the agent nodes. v i The following variables: in, a i k+1 For intelligent agent nodes v i In the k The cumulative auxiliary variable at +1 update; a i k For intelligent agent nodes v i In the k The cumulative auxiliary variable during the next update; x i k+1 For intelligent agent nodes v i In the k The actual state at +1 update; ∧ i,j k In the first k During the next update, the edge ( i , j The corresponding masking multiplier; ∧ j,i k In the first k During the next update, the edge ( j , i The corresponding masking multiplier; For intelligent agent nodes v i In the k The non-increasing constant sequence generated during the next update; θ The non-negative common penalty parameter for all agent nodes; x i For intelligent agent nodes v i The estimate; f i ( x i ) is an agent node v i Cost function; | N i |for sets N i The number of elements; ∧ i,j k+1 In the first k +1 update with edge ( i , j The corresponding masking multiplier; ε i k+1 For intelligent agent nodes v i No. k +1 random perturbation generated by the update; Step S5: Based on the initial values ​​of the iterative variables of the agent nodes in Step S2, generate the first and second masking states according to Step S3, and update the iterative variables according to the update law in Step S4 until the number of updates reaches [a certain number]. K traverse all agent nodes v i Obtain all agent nodes v i status x i K , .

2. The privacy-preserving distributed multi-agent network optimization method according to claim 1, characterized in that, The specific steps of step S1-2 are as follows: Topology graph based on multi-agent network G The optimal solution to the distributed consistency optimization problem can be obtained in the following manner. x * : in, x i For intelligent agent nodes v i The estimate; x j For neighboring intelligent agent nodes v j The estimate; f i ( x i ) is an agent node v i The cost function.

3. The privacy-preserving distributed multi-agent network optimization method according to claim 1, characterized in that, Maximum number of updates K The error condition is || x i K+1 - x i K ||< э , э For error condition accuracy.

Images