Federated Edge Learning Scheduling Method and System Based on Game and Multidimensional Contracts

Abstract

The present invention discloses a federated edge learning scheduling method and system based on game theory and multi-dimensional contracts in the field of computer communication technology, including the following steps: 1) Construct a federated edge learning network involving CC, EN, and UE, and establish the utility functions of CC, EN, and UE; 2) Each EN uses historical records to count the number of UEs within its communication range, and classifies the UEs into different types according to data acquisition expenditure, model training expenditure, and model parameter transmission expenditure; 3) Each EN reports the contract package of the data volume that the UE is expected to contribute and the corresponding rewards to CC; 4) Based on the above steps, obtain the optimal contract package and game solution to implement the federated edge learning scheduling mechanism. The present invention solves the overall federated edge learning scheduling problem of CC-EN-UE.

Description

Technical Field

[0001] The present invention relates to the field of computer communication technologies, and in particular, to a federated edge learning scheduling method and system based on game theory and multi-dimensional contracts. Background Art

[0002] Federated learning is a special distributed learning method that enables multiple UEs to collaboratively train a shared parameter model while ensuring that the training data resides on the UEs. The server first distributes the global model parameters to a randomly selected subset of UEs. Then each UE parallelly optimizes and updates its local parameters on its own data. Finally, the server aggregates all the local parameters and outputs the global parameters. During the federated learning training, there is no need to transmit private data through the communication network, which protects privacy to a certain extent.

[0003] However, federated learning involves thousands of heterogeneous distributed UE devices. In this case, low communication efficiency is a key bottleneck. That is, node failures and device losses caused by communication failures will lead to low learning efficiency. In addition, UE devices with severely limited connections cannot participate in the training, which has an adverse impact on the generalization ability of the model. Moreover, the long-distance interaction between the devices and the cloud server will incur significant communication costs. Edge computing technology is a computing architecture that allows execution at the network edge. It can sink various computing tasks to the network edge. Compared with centralized cloud computing, EN is geographically closer to UE devices, and at the same time, it is more widely distributed and has a larger quantity, sharing the load of centralized cloud computing and reducing latency and learning resource consumption. The federated edge learning framework that combines federated learning and edge computing can solve the above problems, where UE parameters are first uploaded to EN for intermediate aggregation. Then, global aggregation is performed in communication with CC, reducing the global communication cost and the device loss rate.

[0004] However, in learning, various devices are selfish and need to provide their own resources to participate in learning. Without reasonable compensation and effective scheduling methods, it is impossible to schedule enough participants. Summary of the Invention

[0005] The purpose of the present invention is to outline some aspects of the embodiments of the present invention and briefly introduce some preferred embodiments. In this specification, as well as in the abstract and title of the present application, some simplifications or omissions may be made to avoid obscuring the purpose of this specification, the abstract, and the title of the invention, and such simplifications or omissions cannot be used to limit the scope of the present invention.

[0006] In view of the deficiencies in the prior art, the present invention is proposed. Therefore, the present invention provides a federated edge learning scheduling method and system based on game theory and multi-dimensional contracts to solve the problem of scheduling CC, EN, and UE to participate in federated edge learning.

[0007] To solve the above technical problems, the present invention provides the following technical solutions:

[0008] A federated edge learning scheduling method based on game theory and multi-dimensional contracts, comprising the following steps:

[0009] Step 1) Construct a federated edge learning network involving a cloud server CC, edge servers EN, and end users UE, and establish utility functions for CC, EN, and UE;

[0010] Step 2) Each EN uses historical records to count the number of UEs within its communication range, and classifies UEs into different types according to data acquisition expenditure, model training expenditure, and model parameter transmission expenditure; based on the unit data reward released by CC, EN solves optimization problem 1 to design different contract packages for different types of UEs. A certain type of contract package includes the amount of data contributed by UEs of that type and the corresponding rewards;

[0011] Step 3) Each EN reports the contract package of the expected data volume that UEs can contribute and the corresponding rewards to CC; construct a principal-agent game under complete information conditions, where EN is the agent and CC is the principal; CC solves the optimal cost through optimization problem 2 and pays it to EN, and then EN pays the cost to the selected UEs according to the contract package; the selected UEs will carry out the federated edge learning training process;

[0012] Step 4) Based on the above steps, obtain the optimal contract package and game solution to implement the federated edge learning scheduling mechanism.

[0013] As a preferred solution of the federated edge learning scheduling method based on game theory and multi-dimensional contracts of the present invention, the utility function of UE in step 1) is:

[0014]

[0015] where x m,n is the amount of data contributed by the nth UE under the mth EN, τ is the number of local model updates, σ is the number of EN model aggregations, r m,n represents the reward given by the mth EN to UE n, represents the unit expenditure of UE n for data acquisition, represents the unit expenditure of energy consumption for model training, η is the processor computing power consumed for executing one bit of data volume, s is the size of each sample data, κ m,n is the effective switching capacitance, f m,n represents the square of the processor frequency of the nth UE under the mth EN, represents the unit expenditure of energy consumption for transmitting the updated local model parameters, d is the transmission power, t maxis the total time required for model training and transmission; the meaning represented by each part of the utility function is as follows: the first part is the obtained reward, the second part is the expenditure for data acquisition, the third part is the expenditure for model training, and the fourth part is the expenditure for transmitting the updated local model parameters; simplified as:

[0016]

[0017] where assuming d and are the same; the data acquisition expenditure, model training expenditure, and model parameter transmission expenditure of the UE are unknown to the EN. Therefore, according to the types of these expenditures, the UE can be divided into different classes, namely, data acquisition expenditure, model training expenditure, and model parameter transmission expenditure types; defined as Υ m ={γ m,i : 1≤i≤I m}, Λ m ={v m,j : 1≤j≤J m}, There are a total of I m J m K m UEs in the learning expenditure class within the communication range of the m-th EN; the joint probability distribution of each learning expenditure class is The corresponding quantity is N m,i,j,k , that is The types of UEs are sorted non-decreasingly: 0 < γ m,1 ≤γ m,2 ≤...≤γ m,I , 0 < ν m,1 ≤ν m,2 ≤...≤ν m,J and The UE with data acquisition expenditure type i, model training expenditure type j, and model parameter transmission expenditure type k is represented as type-(m, i, j, k); the utility of type (m, i, j, k) UE is redefined as

[0018]

[0019] As a preferred solution of the federated edge learning scheduling method based on game and multi-dimensional contract of the present invention, the utility function of the EN in step 1) is:

[0020]

[0021] where p is the price per unit of data, ζ m is the profit per unit of satisfaction, and x m,i,j,kThe data volume collected by the UE with data collection expenditure, model training expenditure, and model parameter transmission expenditure types of i, j, and k respectively under the m-th EN, r m,i,j,k The reward provided by the m-th EN to the subordinate UEs with data collection expenditure, model training expenditure, and model parameter transmission expenditure types of i, j, and k respectively.

[0022] As a preferred solution of the federated edge learning scheduling method based on game and multi-dimensional contract described in the present invention, the utility function of the CC in step 1) is:

[0023]

[0024] Φ represents the profit obtained per unit of precision.

[0025] As a preferred solution of the federated edge learning scheduling method based on game and multi-dimensional contract described in the present invention, the construction process of optimization problem 1 in step 2) includes:

[0026] The multi-dimensional contract optimization problem 1 is expressed as:

[0027]

[0028] C2: r m，i，j，k ≥0, 1 ≤ i ≤ I, 1 ≤ j ≤ J, 1 ≤ k ≤ K,

[0029] C3: x m，i，j，k ≥0, 1 ≤ i ≤ I, 1 ≤ j ≤ J, 1 ≤ k ≤ K, (6)

[0030] Define the total expenditure of the UE of type (m, i, j, k) as

[0031]

[0032] Define the marginal expenditure α of the data volume of the UE of type (m, i, j, k) as

[0033]

[0034] Represents the degree of unwillingness of the UE of type (m, i, j, k) to participate. The UE with a larger marginal expenditure is always more unwilling to participate; reorder the types (m, i, j, k) in non-decreasing order according to the marginal expenditure of the data volume Φ m，1 (x), Φ m，2 (x),..., Φ m，h (x),..., Φ m，IJK (x) (9)

[0035] where Φ m，h (x) represents a certain type (m, i, j, k) as type Φm，h UE; Given a sorting order, the UE types are arranged in ascending order of the marginal expenditure of data volume:

[0036] α(Φ m，1 , x) ≤... α(Φ m，h , x) ≤... ≤ α(Φ m，IJK , x) (10)

[0037] For ease of representation, use the type Φ m，h (x) to represent the UE type, that is, represented as π m，h = (x m，h , r m，h ) type Φ m，h (x) UE design contract; Use C(Φ m，h , x m，h ) to represent the new sorting of expenditures, and use α(Φ m，h , x m，h ) to represent the marginal expenditure of data volume;

[0038] The optimization problem 1 is transformed into:

[0039]

[0040] s.t. C1: r m，h - C(φ m，h , x m，h ) ≥ 0,

[0041] C2: α(φ m,IJK , x) ≥.. ≥ α(φ m，h , x) ≥... ≥ α(φ m，1 , x), r m，IJK ≤... ≤ r1 ≤ 0, x m，IJK ≤... ≤ x1 ≤ 0

[0042] C3: r m，h+1 - C(φ m，h+1 , x m，h+1 ) + C(φ m，h+1 , x m，h ) ≥ r m，h ≥ r m，h+1 - C(φ m，h , x m，h+1 ) + C(φ m，h , x m，h ) i ∈ {1,..., IJK - 1},

[0043] C4: r m，i，j，k ≥ 0, x m,i，j，k ≥ 0

[0044] C5: 1 ≤ i ≤ I, 1 ≤ j ≤ J, 1 ≤ k ≤ K (11)

[0046] Among them, C1 is the individual rationality constraint IR indicating that the UE will not choose negative utility, C2 is the monotonicity of the contract, C3 is the scheduling compatibility constraint IC indicating that the UE has the maximum utility only when the contract provided by the adverse selection EN matches itself, and the constraints C4 and C5 are the limiting conditions for the rewards obtained by the UE and the amount of data collected, respectively.

[0047] As a preferred solution of the federated edge learning scheduling method based on game and multi-dimensional contract according to the present invention, the solution process of the optimization problem 1 in the step 2) includes:

[0048] Calculate the best reward obtained by the single UE from the affiliated EN as:

[0049]

[0050] Where Δ h = r m,h+1 - r m,h = C(φ m,h , x m,h+1 ) - C(φ m,h , x m,h ), h = 1,..., IJK - 1;

[0051] Transform the optimization problem 1 into:

[0052]

[0053] Where, When h = 2,..., IJK, When h = 1, b m,h = N m,1 q m,1 α(φ m,1 , x m,1 );

[0054] Solve the optimal data volume of the optimization problem 1 as:

[0055]

[0056] According to formula (11) and formula (13), the contract package between the EN and the UE is obtained.

[0057] As a preferred solution of the federated edge learning scheduling method based on game and multi-dimensional contract according to the present invention, the establishment and solution process of the optimization problem 2 in the step 3) includes:

[0058] The optimization problem 2 is expressed as:

[0059]

[0060] For CC, in order to solve for the optimal unit data reward, substitute the optimal data volume of EN into the utility function of optimization problem 2 to obtain

[0061]

[0062] Take the first - order and second - order derivatives of formula (15) to obtain the following equalities

[0063]

[0064] and

[0065]

[0066] When time, Therefore, there exists an optimal unit data price p * , let formula (17) equal to 0 to obtain the optimal unit price.

[0067] A federated edge learning scheduling system based on game and multi - dimensional contract, including a CC, multiple ENs, and multiple UEs. After multiple rounds of federated learning with the UEs, the ENs send intermediate parameters to the CC. The CC aggregates the intermediate parameters to obtain global parameters and sends them back to the ENs to start the next round of learning. Among them, the CC, ENs, and UEs are all special hardware devices, and when the special hardware devices execute the calculation program, they implement the steps of the federated edge learning scheduling method based on game and multi - dimensional contract.

[0068] The present invention solves the following technical problems: The master party CC and the slave party EN construct a principal - agent game under complete information conditions, and the EN and the UE construct a multi - dimensional contract optimization problem; the slave party EN and the UE solve the contract problem to obtain a contract package, and the master party CC uses the contract package of the slave party to backward induction to find the optimal unit price; after the solution, the CC publishes the optimal unit price to schedule the EN, and the EN uses the contract package to match and schedule the UEs to participate in learning.

[0069] Compared with the prior art, the present invention has the following beneficial effects: The present invention can solve the scheduling problem in the information asymmetry between the EN and the UE in federated edge learning, that is, when the EN only knows the total number of learning expenditure types of the UE and the probability of each learning expenditure type, a series of contracts can be provided for UEs with different learning expenditure types. The UE can only obtain benefits by providing its own resources to participate in federated edge learning, thus scheduling the participation of selfish devices; and when participating, only by selecting a contract that matches itself can the maximum utility be obtained, thus suppressing the participation of malicious devices. In addition, according to the contract package obtained by solving the contract optimization problem, a master-slave game problem under complete information conditions is constructed, which can optimize the utility of the CC on the premise of ensuring the maximum utility of the UE, thus solving the overall scheduling problem of CC-EN-UE. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained according to these drawings. Among them:

[0071] Figure 1 is a flowchart of an embodiment of the present invention.

[0072] Figure 2 is a system scenario diagram of an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0073] In order to make the above objects, features, and advantages of the present invention more obvious and understandable, the following will make a detailed description of the specific embodiments of the present invention in conjunction with the accompanying drawings of the specification.

[0074] In the following description, many specific details are set forth in order to fully understand the present invention. However, the present invention can also be implemented in other ways different from those described herein. Those skilled in the art can make similar promotions without departing from the connotation of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed below.

[0075] Secondly, the so-called "one embodiment" or "embodiment" herein refers to a specific feature, structure, or characteristic that can be included in at least one implementation manner of the present invention. The "in one embodiment" that appears in different places in this specification does not all refer to the same embodiment, nor is it a separate or alternative embodiment that mutually excludes other embodiments.

[0076] Next, the present invention will be described in detail with reference to the schematic diagrams. When describing the embodiments of the present invention in detail, for the convenience of explanation, the cross-sectional views showing the device structure will be enlarged locally in a non-general proportion, and the schematic diagrams are only examples and should not limit the scope of protection of the present invention herein. In addition, in actual production, three-dimensional spatial dimensions including length, width, and depth should be included.

[0077] See Figure 1 , a federated edge learning scheduling method based on game and multi-dimensional contracts, where CC, EN, and UE participate in federated edge learning. Among them, EN and UE obtain the reward-data volume contract package by solving Optimization Problem 2, and then CC and EN solve the principal-agent game problem under the condition of complete information by backward induction to obtain the optimal price. After the solution is completed, CC pays the optimal price to EN, and then EN pays according to the contract package to UE to schedule UE to participate in learning, constituting the basic process of the federated edge learning scheduling mechanism based on game and multi-dimensional contracts.

[0078] See Figure 2 , one CC and multiple ENs, each EN has multiple UEs under it. There are a total of I m J m K m UEs in the learning expenditure category. The joint probability distribution of each learning expenditure category is The corresponding quantity is N m,i,j,k ; CC, EN, and UE use the above-mentioned federated edge learning scheduling method based on game and multi-dimensional contracts to participate in learning together, jointly constituting a federated edge learning system.

[0079] Specifically, it includes the following steps:

[0080] Step 1) Construct a federated edge learning network participated by CC, EN, and UE, and establish the utility functions of CC, EN, and UE;

[0081] Step 2) Each EN uses historical records to count the number of UEs within its communication range, and divides the UEs into different types according to data acquisition expenditure, model training expenditure, and model parameter transmission expenditure. Based on the unit data reward released by CC, EN solves Optimization Problem 1 to design different contract packages for different types of UEs. A certain type of contract package includes the data volume contributed by the UEs of this type and the corresponding rewards;

[0082] Step 3) Each EN reports the contract package of the data volume that the UE is expected to contribute and the corresponding rewards to CC; construct a principal-agent game under the condition of complete information, with EN as the agent and CC as the principal. CC solves the optimal cost through Optimization Problem 2 and pays it to EN, and then EN pays the cost to the selected UEs according to the contract package. The selected UEs will carry out the federated edge learning training process;

[0083] Step 4) Based on the above steps, obtain the optimal contract package and game solution, and thus implement the federated edge learning scheduling mechanism;

[0084] In step 1) of this embodiment, the utility function of the UE is:

[0085]

[0086] where x m,n is the amount of data contributed by the nth UE under the mth EN, τ is the number of local model updates, σ is the number of EN model aggregations, r m,n represents the reward given by the mth EN to UEn, represents the unit expenditure of UEn data collection, represents the unit expenditure of the energy consumption of model training, η is the processor computing power consumed by executing one bit of data volume, s is the size of each sample data, κ m,n is the effective switching capacitance, f m,n represents the square of the processor frequency of the nth UE under the mth EN, represents the unit expenditure of the energy consumption for transmitting the updated local model parameters, d is the transmission power, t max is the total time required for model training and transmission. The meaning of each part of the utility function is as follows: The first part is the obtained reward, the second part is the expenditure of data collection, the third part is the expenditure of model training, and the fourth part is the expenditure of transmitting the updated local model parameters. Simplified as:

[0087]

[0088] where Assume that d and are the same. The data collection expenditure, model training expenditure, and model parameter transmission expenditure of the UE are unknown to the EN. Therefore, according to the types of these expenditures, the UE can be divided into different classes, namely, data collection expenditure, model training expenditure, and model parameter transmission expenditure types. Define the following Υ m ={γ m,i : 1≤i≤I m}, Λ m ={ν m,j : 1≤j≤J m}, Therefore, there are a total of I m J m K m UEs in the learning expenditure classes within the communication range of the mth EN. The joint probability distribution of each learning expenditure class is The corresponding quantity is N m,i,j,k , that is The types of UEs are sorted in non-decreasing order: 0 < γm,1 ≤γ m,2 ≤…≤γ m,I ,0 < v m,1 ≤v m,2 ≤...≤v m,J and Denote the UE with the data collection expenditure type of i, the model training expenditure type of j, and the model parameter transmission expenditure type of k as type-(m, i, j, k). Redefine the utility of the type (m, i, j, k) UE as

[0089]

[0090] This step solves the technical problem of how to calculate the utility of the UE in federated edge learning. Through technical design and modeling, jointly considering the data collection, model training, and communication expenditures of the UE, the scheduling mechanism is made more effective and practical for the UE.

[0091] The utility function of the EN in step 1) is as follows:

[0092]

[0093] where p is the price per unit of data, ζ m is the profit per unit of satisfaction, x m,i,j,k is the amount of data collected by the UE with the data collection expenditure type of i, the model training expenditure type of j, and the model parameter transmission expenditure type of k under the m-th EN, and r m,i,j,k is the reward provided by the m-th EN to the UE with the data collection expenditure type of i, the model training expenditure type of j, and the model parameter transmission expenditure type of k under its subordinate.

[0094] This step solves the technical problem of how to calculate the utility of the EN in federated edge learning. Through technical design, the greater the accuracy of the model parameters of the EN for the CC, the greater the utility it obtains. At the same time, the log function is used to show that when the amount of data collected by the UE increases, the income of the EN increases slowly. Therefore, the amount of data collected by scheduling the UE cannot be infinitely large and needs to be reasonable, which conforms to the law of diminishing marginal utility in reality.

[0095] The utility function of the CC in step 1) is as follows:

[0096]

[0097] Φ represents the profit obtained per unit of accuracy. This step solves the technical problem of how to calculate the utility of the CC in federated edge learning.

[0098] The construction process of optimization problem 1 in step 2) of this embodiment includes:

[0099] The multi-dimensional contract optimization problem 1 is expressed as:

[0100]

[0101] C2: r m，i，j，k ≥ 0, 1 ≤ i ≤ I, 1 ≤ j ≤ J, 1 ≤ k ≤ K,

[0102] C3: x m，i，j，k ≥ 0, 1 ≤ i ≤ I, 1 ≤ j ≤ J, 1 ≤ k ≤ K, (6)

[0103] Define the total expenditure of the type (m, i, j, k) UE as

[0104]

[0105] Define the marginal expenditure α of the data volume of the type (m, i, j, k) UE as

[0106]

[0107] Indicates the degree of unwillingness of the type (m, i, j, k) UE to participate, because the UE with a larger marginal expenditure is always more unwilling to participate. Reorder the type (m, i, j, k) in non-decreasing order according to the marginal expenditure of the data volume

[0108] Φ m，1 (x), Φ m，2 (x),..., Φ m，h (x),..., Φ m，IJK (x) (9)

[0109] where Φ m，h (x) represents a certain type (m, i, j, k) as the type Φ m，h UE. Given the sorting order, the UE types are arranged in ascending order of the marginal expenditure of the data volume:

[0110] α(Φ m，1 , x) ≤... α(Φ m，h , x) ≤... ≤ α(Φ m，IJK , x) (10)

[0111] For ease of representation, use the type Φ m，h (x) to represent the UE type, that is, represented as π m，h = (x m，h , r m，h ) type Φ m，h (x) UE-designed contract. Use C(Φ m，h , x m，h ) to represent the new sorting of the expenditure, and use α(Φ m，h , x m，h ) to represent the marginal expenditure of the data volume.

[0112] The optimization problem 1 is transformed into:

[0113]

[0114] where C1 is the individual rationality constraint IR indicating that the UE will not choose negative utility, C2 is the monotonicity of the contract, C3 is the scheduling compatibility constraint IC indicating that the UE has the maximum utility only when the contract provided by the adverse selection EN matches itself, and the constraints C4 and C5 are the limiting conditions for the rewards obtained by the UE and the amount of data collected respectively; the solution process of the optimization problem 1 includes: calculating the best reward obtained by the single UE from the affiliated EN as:

[0115]

[0116] where Δ h = r m,h+1 - r m,h = C(φ m,h , x m,h+1 ) - C(φ m,h , x m,h ), h = 1,..., IJK - 1;

[0117] Transforming the optimization problem 1 is expressed as:

[0118]

[0119] where, when h = 2,..., IJK, when h = 1, b m,h = N m,1 q m,1 α(φ m,1 , x m,1 );

[0120] The optimal amount of data for solving the optimization problem 1 is:

[0121]

[0122] According to formula (11) and formula (13), the contract package between the EN and the UE is obtained.

[0123] This step solves the problem that multiple non-convex optimizations in the original multi-dimensional contract optimization problem 1 are difficult to solve. By defining the marginal cost independent of the amount of data through the three types of learning costs of the UE, the multi-dimensional contract optimization problem is transformed into a one-dimensional contract optimization problem. Through derivation and solution, the one-dimensional contract optimization problem is finally transformed into a convex optimization problem to find the optimal amount of data when the unit price p is known, and the problem of how to calculate the reward-data volume contract package between the UE and the EN is solved.

[0124] The establishment and solution process of optimization problem 2 in step 3) includes:

[0125] Optimization problem 2 is expressed as:

[0126]

[0127] For CC, in order to solve for the optimal unit data reward, the optimal data volume of EN is substituted into the utility function of optimization problem 2 to obtain

[0128]

[0129] The first-order and second-order derivatives of formula (15) are taken to obtain the following equalities

[0130]

[0131] and

[0132]

[0133] When At this time, Therefore, there exists an optimal unit data price p * , let formula (17) be equal to 0 to obtain the optimal unit price.

[0134] This step solves the problem of calculating the optimal unit data price between CC and EN. Since the modeling is a principal-agent game under complete information conditions, CC is the principal and EN is the agent. Using backward induction, the agent EN knows the action of the principal CC, i.e., the unit price p, before making a decision. The agent EN uses the known prior information to derive the contract relationship package in the previous step, ensuring the maximization of its own utility; the principal CC uses the solution result of the agent to find its own optimal unit price p, ensuring the maximization of its own utility, and the induction method solving is completed. Finally, the principal publishes p, and the agent uses the contract relationship package to schedule the UE to participate in learning.

[0135] Next, an example of the actual application of this embodiment is given. For example, in the application in the field of education, an educational institution uses federated learning technology to collaboratively build a general learning plan model based on the data stored in the student-side mobile devices. However, due to the device heterogeneity problem caused by different devices on the student side, a UE-side - EN-side - CC federated edge learning system can be introduced to allow multiple ENs to perform partial model aggregation and then send it to CC. Thus, the student side can update the local model according to its own specialties, needs, interests, etc., and train a customized and personalized learning guidance model. Among them, after receiving the rewards and data requirements provided by the CC side, the EN side can use the scheduling method described above to schedule the UE side to participate in learning.

[0136] Importantly, it should be noted that the construction and arrangement of the present application shown in multiple different exemplary embodiments are merely illustrative. Although only a few embodiments are described in detail in this disclosure, those who refer to this disclosure should easily understand that many modifications are possible without materially departing from the novel teachings and advantages of the subject matter described in this application (e.g., changes in the dimensions, scales, structures, shapes and proportions of various elements, as well as parameter values (such as temperature, pressure, etc.), installation arrangements, use of materials, colors, orientations, etc.). For example, an element shown as integrally formed may be composed of multiple parts or elements, the position of the element may be inverted or otherwise changed, and the nature, number or position of discrete elements may be altered or changed. Accordingly, all such modifications are intended to be included within the scope of the present invention. The order or sequence of any process or method steps may be changed or reordered according to alternative embodiments. In the claims, any "means plus function" clauses are intended to cover the structures that perform the recited function herein, and not only structural equivalents but also equivalent structures. Other substitutions, modifications, changes and omissions may be made in the design, operating conditions and arrangement of the exemplary embodiments without departing from the scope of the present invention. Therefore, the present invention is not limited to specific embodiments, but extends to various modifications that still fall within the scope of the appended claims.

[0137] In addition, in order to provide a concise description of the exemplary embodiments, not all features of the actual embodiments may be described (i.e., those features that are not relevant to the currently contemplated best mode of carrying out the present invention, or those features that are not relevant to the implementation of the present invention).

[0138] It should be understood that in the development of any actual implementation, as in any engineering or design project, numerous specific implementation decisions may be made. Such development efforts may be complex and time-consuming, but for those of ordinary skill in the art who benefit from this disclosure, without undue experimentation, such development efforts will be a routine task of design, fabrication and production.

[0139] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention may be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention, and they should all be covered by the scope of the claims of the present invention.

Claims

1. A federated edge learning scheduling method based on game theory and multi-dimensional contracts, characterized in that, Including: Step 1) Construct a federated edge learning network involving a cloud server CC, edge servers EN, and end users UE, and establish the utility functions of CC, EN, and UE; Step 2) Each EN uses historical records to count the number of UEs within its communication range, and classifies the UEs into different types according to data acquisition expenditure, model training expenditure, and model parameter transmission expenditure; Based on the unit data reward issued by CC, EN solves optimization problem 1 to design different contract packages for different types of UEs. A certain type of contract package includes the amount of data contributed by UEs of that type and the corresponding reward; Step 3) Each EN reports the contract packages of the expected data volume and corresponding rewards of UEs to CC; construct a principal-agent game under complete information conditions, where EN is the agent and CC is the principal; CC solves for the optimal cost through optimization problem 2 and pays it to EN, and then EN pays the cost to the selected UEs according to the contract packages; the selected UEs will carry out the federated edge learning training process; Step 4) Based on the above steps, obtain the optimal contract packages and game solutions to implement the federated edge learning scheduling mechanism; The construction process of optimization problem 1 in step 2) includes: The multi-dimensional contract optimization problem 1 is expressed as: Define the total expenditure of type (m, i, j, k) UEs as: Define the marginal expenditure α of the data volume of type (m, i, j, k) UEs as: Indicates the degree of unwillingness of a UE of type (m, i, j, k) to participate. A UE with a larger marginal expenditure is always more unwilling to participate; the types are sorted in non-decreasing order according to the marginal expenditure of the data volume (m, i, j, k) is re-ordered Φ m,1 (x), Φ m,2 (x),..., Φ m,h (x),..., Φ m,IJK (x) (9) Among them, Φ m,h (x) represents a certain type (m, i, j, k) as type Φ m,h UE; given a sorting order, the UE types are arranged in ascending order of marginal expenditure of data volume: For ease of representation, use type Φ m,h (x) to represent the UE type, that is, represented as π m,h =(x m,h ,r m,h ) type Φ m,h (x) The contract of UE design; use C(Φ m,h ,x m,h ) to represent the new order of expenditures, use α(Φ m,h ,x m,h ) to represent the marginal expenditure of data volume; Optimization problem 1 is transformed into: Among them, C1 is the individual rationality constraint IR indicating that UEs will not choose negative utility, C2 is the monotonicity of the contract, C3 is the scheduling compatibility constraint IC indicating that UEs have the maximum utility only when they reverse-select the contract that matches themselves provided by EN, and constraints C4 and C5 are the limiting conditions for the rewards obtained by UEs and the amount of data collected respectively.

2. The federated edge learning scheduling method based on game and multi-dimensional contract according to claim 1, characterized in that: The utility function of UE in step 1) is: where x m,n is the data volume contributed by the nth UE under the mth EN, τ is the number of local model updates, σ is the number of EN model aggregations, r m,n represents the reward given by the mth EN to UEn, represents the unit expenditure for UEn data collection, represents the unit expenditure for the energy consumption of model training, η is the processor computing power consumed by the data volume of one bit, s is the size of each sample data, κ m,n is the effective switching capacitance, represents the unit expenditure for the energy consumption of transmitting the updated local model parameters, d is the transmission power, t max is the total time required for model training and transmission; the meaning represented by each part of the utility function is as follows: the first part is the obtained reward, the second part is the expenditure for data collection, the third part is the expenditure for model training, and the fourth part is the expenditure for transmitting the updated local model parameters; simplified as: Among them p is the price of unit data. Assume that p and β 3 are the same; the data collection expenditure, model training expenditure, and model parameter transmission expenditure of the UE are unknown to the EN. Therefore, according to the types of these expenditures, the UE is divided into different categories, namely, data collection expenditure, model training expenditure, and model parameter transmission expenditure types; define the following γ m ={γ m,i : 1 ≤ i ≤ I m}, Λ m ={ν m,j : 1 ≤ j ≤ J m}, There are a total of I m J m K m UEs in the learning expenditure category within the communication range of the m-th EN; the joint probability distribution of each learning expenditure category is The corresponding quantity is N m,i,j,k , that is The types of the UE are sorted in non-decreasing order: 0 < γ m,1 ≤ γ m,2 ≤... ≤ γ m,I , 0 < ν m,1 ≤ ν m,2 ≤... ≤ ν m,J and The UE with the data collection expenditure type i, model training expenditure type j, and model parameter transmission expenditure type k is represented as type (m, i, j, k); the utility function of the type (m, i, j, k) UE is redefined as 3. The federated edge learning scheduling method based on game and multi-dimensional contract according to claim 2, characterized in that: The utility function of EN in step 1) is: Among them, p is the price of unit data, ζ m is the profit of unit satisfaction, x m,i,j,k is the data volume collected by the UE of the m-th EN with the expenditure types of data collection, model training, and model parameter transmission being i, j, and k respectively, r m,i,j,k is the reward provided by the m-th EN to the UE with the expenditure types of data collection, model training, and model parameter transmission being i, j, and k respectively for its subordinates.

4. The federated edge learning scheduling method based on game and multi-dimensional contract according to claim 3, characterized in that: The utility function of CC in step 1) is: Φ represents the profit obtained per unit of precision.

5. The federated edge learning scheduling method based on game and multi-dimensional contract according to claim 4, characterized in that: The solution process of optimization problem 1 in step 2) includes: Calculate the best reward obtained by a single UE from its affiliated EN as: where Δ h = r m,h+1 - r m,h = C(φ m,h , x m,h+1 ) - C(φ m,h , x m,h ), h = 1, ..., IJK - 1; Transform the expression of optimization problem 1 as: Among them, when h = 2,..., IJK, when h = 1, b m,h = N m,1 q m,1 α(φ m,1 , x m,1 ); The optimal data volume for solving optimization problem 1 is: According to formula (11) and formula (13), the contract packages between EN and UE are obtained.

6. The federated edge learning scheduling method based on game and multi-dimensional contract according to claim 5, characterized in that: The establishment and solution process of optimization problem 2 in step 3) includes: Optimization problem 2 is expressed as: For CC, in order to solve for the optimal unit data reward, substitute the optimal data volume of EN into the utility function of optimization problem 2 to obtain Perform first-order and second-order derivatives on formula (15) to obtain the following equations and When then Therefore, there exists an optimal unit data price p * , such that setting formula (17) equal to 0 gives the optimal unit price.

7. A federated edge learning scheduling system based on game theory and multi-dimensional contracts, characterized in that: Including one CC, multiple ENs, and multiple UEs. After multiple federated learning with the UEs, the ENs send intermediate parameters to CC. CC aggregates the intermediate parameters to obtain global parameters and sends them back to EN to start the next round of learning. Among them, CC, EN, and UE are all special hardware devices, and when the special hardware devices execute the computing program, they implement the steps of the federated edge learning scheduling method based on game and multi-dimensional contract as described in any one of claims 1 to 6.

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