Machine learning programs, machine learning devices, and machine learning methods

Abstract

To improve the speed of generating solution sets for multi-objective optimization problems. [Solution] The machine learning device acquires a multi-objective optimization problem containing multiple objective functions, extracts multiple weight parameters based on a simplex constructed at points corresponding to the number of weight parameters that weight each of the multiple objective functions, and trains a machine learning model that outputs a second solution set corresponding to a given weight parameter by inputting a mapping to a first solution set corresponding to the multiple weight parameters.

Description

[Technical Field]

[0001] The present invention relates to a machine learning program, a machine learning device, and a machine learning method. [Background technology]

[0002] Constrained combinatorial optimization problems are among the most important problems in combinatorial optimization and have many practical applications. In recent years, with the advancement of information science, machine learning has been used to rapidly solve combinatorial optimization problems. The technique of pointing is developing. [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2023-059128 [Patent Document 2] Japanese Patent Publication No. 2022-188527 [Patent Document 3] U.S. Patent Application Publication No. 2022 / 0215137 [Patent Document 4] U.S. Patent Application Publication No. 2022 / 0012542 [Overview of the project] [Problems that the invention aims to solve]

[0004] However, the above techniques have difficulty solving multi-objective optimization problems that simultaneously optimize multiple cost functions and generating Pareto optimal solutions quickly. For example, the above techniques require running a solver for each weight parameter that weights the objective function, which can make generating Pareto optimal solutions time-consuming.

[0005] In one aspect, the aim is to provide machine learning programs, machine learning devices, and machine learning methods that can improve the speed of generating solution sets for multi-objective optimization problems. [Means for solving the problem]

[0006] The machine learning program is characterized by causing a computer to perform a process that involves acquiring a multi-objective optimization problem containing multiple objective functions, extracting the multiple weight parameters based on a simplex constructed of points corresponding to the number of multiple weight parameters that weight each of the multiple objective functions, and inputting a mapping to a first solution set corresponding to the multiple weight parameters to train a machine learning model that outputs a second solution set corresponding to a predetermined weight parameter. [Effects of the Invention]

[0007] According to one embodiment, the speed of generating solution sets for multi-objective optimization problems can be improved. [Brief explanation of the drawing]

[0008] [Figure 1] Figure 1 shows an example of the overall processing of the machine learning device according to the embodiment. [Figure 2] Figure 2 shows an example of the processing during training of the machine learning device according to the embodiment. [Figure 3] Figure 3 shows an example of processing when using the machine learning device according to the embodiment. [Figure 4] Figure 4 is a block diagram of a machine learning device according to an embodiment. [Figure 5] Figure 5 shows an example of the objective function storage unit of a machine learning device according to an embodiment. [Figure 6] Figure 6 shows an example of the weight parameter storage unit of a machine learning device according to an embodiment. [Figure 7] Figure 7 shows an example of the Pareto optimal solution storage unit of the machine learning device according to the embodiment. [Figure 8] Figure 8 shows an example of the machine learning model storage unit of the machine learning device according to the embodiment. [Figure 9] Figure 9 is a flowchart of the overall processing performed by the machine learning device according to the embodiment. [Figure 10] Figure 10 is a flowchart of model learning processing by the machine learning device according to the embodiment. [Figure 11] Figure 11 is a flowchart of model utilization processing by the machine learning device according to the embodiment. [Figure 12] Figure 12 is a hardware configuration diagram of the machine learning device.

Mode for Carrying Out the Invention

[0009] Hereinafter, embodiments of the machine learning program, machine learning device, and machine learning method disclosed in the present application will be described in detail based on the drawings. Note that the present invention is not limited by this embodiment. Each embodiment can be appropriately combined within a non-contradictory range.

Embodiment

[0010] <Explanation of Machine Learning Device 10> Figure 1 is a diagram showing an example of the overall processing of the machine learning device 10 according to the embodiment. The machine learning device 10 shown in Figure 1 is an example of a computer device that learns a multi-objective optimization problem OP1 and generates a Pareto front PF1 that is a solution set PS1 of the multi-objective optimization problem OP1.

[0011] As shown in Figure 1, the machine learning device 10 extracts a weight parameter WP1 of the multi-objective optimization problem OP1 from a multi-dimensional simplex WS1 (step S1). For example, the machine learning device 10 acquires an M-objective optimization problem in which the multi-objective optimization problem OP1 simultaneously optimizes M objective functions from the user U1, and extracts P weight parameters WP1 from the M-1 dimensional simplex WS1 constructed by the M weight parameters WP1.

[0012] The machine learning device 10 trains the machine learning model LM1 using a mapping to the solution set PS1 corresponding to the extracted P weight parameters WP1 (step S2). For example, the machine learning device 10 formulates the relaxation variable as a response function that is a function of the weight parameters WP1, converts the P weight parameters WP1 into an embedding vector, and minimizes the empirical loss with respect to the P weight parameters WP1. The machine learning device 10 also linearly scales the P weight parameters WP1 and the bias b1 corresponding to the weight parameters WP1, and similarly minimizes the empirical loss with respect to the P weight parameters WP1.

[0013] Figure 2 shows an example of the processing during training of the machine learning device 10 according to the embodiment. As shown in Figure 2, the machine learning device 10 extracts the weight parameters WP1 of the multi-objective optimization problem OP1 from the simplex WS1, thereby obtaining the weight parameter set WPS1 as λ={λ i The} is extracted. The machine learning device 10 also performs node embedding or linear embedding by embedding vector transformation processing and calculates the gradient LG1 of the loss function, which represents the empirical loss, by loss function gradient calculation processing. The machine learning device 10 trains the machine learning model LM1 as described above.

[0014] The machine learning device 10 generates a Pareto front PF1 as a solution set PS1 corresponding to the unknown weight parameter WP1* (step S3). For example, the machine learning device 10 inputs the unknown weight parameter WP1* into a trained machine learning model LM1 to generate a Pareto front PF1 that shows the Pareto optimal solution corresponding to the unknown weight parameter WP1*, and sends it to user U1.

[0015] Figure 3 shows an example of processing when using the machine learning device 10 according to the embodiment. As shown in Figure 3, the machine learning device 10 uses λ as the unknown weight parameter WP1* of the multi-objective optimization problem OP1. *The machine learning device 10 also performs node embedding or linear embedding by embedding vector transformation processing, and extracts the unknown weight parameter WP1* λ. * A solution set PS1 is generated as an approximate solution corresponding to the given value. The machine learning device 10 utilizes the machine learning model LM1 as described above.

[0016] <Optimization solution> Constrained combinatorial optimization problems are among the most important problems in combinatorial optimization and have many practical applications. For example, general-purpose solvers such as Ising machines use penalty methods to search for constraint-satisfying solutions, but depending on the penalty coefficient, solving can be difficult. Also, local transition algorithms like Ising machines can only search for local solutions, making it difficult to obtain a variety of solutions at once. In recent years, with the advancement of information science, technologies aimed at rapidly solving combinatorial optimization problems using machine learning have been developing.

[0017] A multiobjective optimization problem involves having M objective functions f1(x), f2(x), ..., f for any x ∈ X. M The objective is to optimize (x) simultaneously. Note that in typical multi-objective optimization problems, there is no "minimizer x" that minimizes all objective functions.

[0018] As a countermeasure to the above, we obtain a Pareto optimal solution, which is a solution set in which one of the objective functions cannot be improved without degrading one of the objective functions, i.e., the Pareto optimal solution defined by equation (1) below, and obtain a preferred solution.

[0019]

number

[0020] Furthermore, as a relaxation problem, obtaining the Pareto optimal solution can sometimes be sought as a relaxed single-objective optimization problem expressed by equation (2) below.

[0021]

number

[0022] At this time, for any i ∈ [M], f i If (x) is a convex function and X is a convex set, then it is guaranteed that a Pareto optimal solution can be obtained by solving any relaxed single-objective optimization problem expressed by equation (3) below.

[0023]

number

[0024] (Continuous Relaxation Method) The continuous relaxation method is an optimization technique that solves a problem by relaxing a discrete optimization expressed by equation (4) below into a continuous optimization expressed by equation (5) below, for parameters C that characterize the problem. Here, parameter C is the instance parameter IP1, which, for example, in the case of the knapsack problem, is a set of parameters corresponding to the price of the sweets and the capacity of the knapsack.

[0025]

number

[0026]

number

[0027] However, continuous relaxation methods can still result in a complex loss landscape. Furthermore, the solution to the continuous optimization using continuous relaxation methods may differ significantly from the original discrete optimization solution.

[0028] (Continuous Relaxation Simulated Annealing) Continuous relaxation simulated annealing is used for optimization problems where the relaxation variable p θ This is parametrically represented using a statistical model, and the loss function expressed by equations (6) and (7) below is optimized.

[0029]

Number

[0030]

Number

[0031] At this time, when the coefficient γ is negative, the relaxation variable p θ prefers a value of half-integral 1 / 2. On the other hand, when the coefficient γ is positive, the relaxation variable p θ prefers a value of binary {0, 1}.

[0032] The continuous relaxation annealing method realizes performance improvement by annealing the coefficient γ from a negative value to a positive value during learning, and can also remove the conversion from a continuous variable to a discrete variable.

[0033] <Optimization Processing of Embodiment> The above optimization solution method needs to execute a solver for each weight parameter WP1 that weights the objective function, and it may take time to generate a Pareto optimal solution. The optimization processing of the machine learning device 10 according to the embodiment generalizes the above optimization solution method by the continuous relaxation annealing method to multi-objective optimization and extends it so that the Pareto front PF1 can be obtained by one learning.

[0034] The machine learning device 10 formulates the relaxation variable p θ as a function of λ, which is the weight parameter WP1, that is, as a response function regarding λ, as represented by the following equation (8).

[0035]

Number

[0036] The machine learning device 10 uses the relaxation variable p θ(C,λ) takes C, which is an instance parameter IP1 that characterizes the multi-objective optimization problem OP1, and λ, which is the corresponding weight parameter WP1, as input, and outputs the solution of a relaxation-based single-objective optimization corresponding to λ.

[0037] When the machine learning device 10 learns the response function of equation (8) above, it defines the uniform distribution on the simplex WS1 constructed by the weight parameter WP1, λ, as UniSim(λ) and optimizes equation (9) below. Here, the simplex WS1 is the set of solutions, and in the case of a multi-objective optimization problem OP1 containing M objective functions, it is represented by a polyhedron shape with M vertices in M-1 dimensions.

[0038]

number

[0039] The machine learning device 10 can train the response function of equation (8) above in the following two ways. Below, the relaxation variable p θ We will now describe the case where (C,λ) is characterized by an L-layer GNN (Graph Neural Network) as the machine learning model LM1, as shown in equation (10) below. Note that the machine learning model LM1 is not limited to a GNN, but may also be a Transformer, MLP (Multi-Layer Perceptron), Support Vector Machine (SVM), etc.

[0040]

number

[0041] (Node embedding) The machine learning device 10 performs node embedding, which is λ-based embedding, as training for the response function of equation (10) above. For example, the machine learning device 10 extracts P points of λ according to UniSim(λ) of equation (9) above, and prepares Λ, which is a set of weight parameters WPS1, expressed by equation (11) below. In this case, the machine learning device 10 does not extract a corresponding solution from a single point on the simplex defined by UniSim(λ), but rather extracts a set of corresponding solutions PS1 from all on the simplex WS1.

[0042]

number

[0043] Furthermore, the machine learning device 10 performs position embedding on the prepared Λ, uses the transformed embedding vector as a node feature of the GNN, and performs empirical loss minimization with respect to point P.

[0044] (Linear scaling) The machine learning device 10 uses the response function of equation (10) above as training and performs linear scaling to linearly scale the weight parameters WP1 and bias b1. For example, the machine learning device 10 scales the weight parameters WP1 of each layer of the GNN so that they are expressed by equation (12) below. The machine learning device 10 also scales the bias b1 of each layer of the GNN so that they are expressed by equation (13) below.

[0045]

number

[0046]

number

[0047] Furthermore, the machine learning device 10 extracts P points of λ according to UniSim(λ) in equation (9) above, prepares Λ which is the weight parameter set WPS1 represented by equation (11) above, and performs empirical loss minimization with respect to P points, similar to the node embedding described above.

[0048] In this way, the machine learning device 10 does not need to run the solver for each weight parameter WP1 that weights the objective function, thus improving the speed of generating the solution set PS1 of the multi-objective optimization problem OP1.

[0049] <Examples of application> As an application example 1 of the embodiment, the machine learning device 10 can generate a Pareto optimal solution to a multi-objective optimization problem OP1 related to transportation planning. For example, the machine learning device 10 can generate a Pareto optimal solution to a multi-objective optimization problem OP1 that includes, as objective function 1, minimizing transportation costs (e.g., fuel costs, time, etc.), as objective function 2, minimizing carbon dioxide (CO2) emissions, and as objective function 3, minimizing delivery time. In other words, the machine learning device 10 can provide a Pareto front PF1 to a logistics company, which is user U1, for simultaneously optimizing three objectives: reducing transportation costs, reducing environmental impact (CO2 emissions), and shortening delivery time to customers.

[0050] As an application example 2 of the embodiment, the machine learning device 10 can generate a Pareto optimal solution to a multi-objective optimization problem OP1 relating to a manufacturing process. For example, the machine learning device 10 can generate a Pareto optimal solution to a multi-objective optimization problem OP1 that includes minimizing production costs as objective function 1, minimizing production time as objective function 2, and minimizing waste as objective function 3. In other words, the machine learning device 10 can provide a Pareto front PF1 to a manufacturer, which is user U1, for simultaneously optimizing three objectives: reducing manufacturing costs, shortening manufacturing time, and reducing waste.

[0051] <Functional Configuration> Figure 4 is a block diagram of a machine learning device 10 according to an embodiment. As shown in Figure 4, the machine learning device 10 has an input unit 11, an output unit 12, a communication unit 13, a storage unit 14, and a control unit 15.

[0052] The input unit 11 is a processing unit that controls the input of various types of information to the machine learning device 10, and is implemented by, for example, a mouse, keyboard, touch panel, etc.

[0053] The output unit 12 is a processing unit that controls the output of various types of information from the machine learning device 10, and is implemented by, for example, a display, a speaker, etc.

[0054] The communication unit 13 is a processing unit that controls communication with other devices, and is implemented, for example, by a communication interface.

[0055] The memory unit 14 is a processing unit that stores various data and various programs executed by the control unit 15, and is implemented by, for example, memory or a hard disk. For example, the memory unit 14 includes an objective function memory unit 14a, a weight parameter memory unit 14b, a Pareto optimal solution memory unit 14c, and a machine learning model memory unit 14d.

[0056] Figure 5 shows an example of the objective function storage unit 14a of the machine learning device 10 according to the embodiment. The objective function storage unit 14a stores multiple objective functions included in the multi-objective optimization problem OP1. The objective function storage unit 14a shown in Figure 5 stores "CF101", "CF102", "CF103", ... as objective functions included in the multi-objective optimization problem OP1 identified as "OP001".

[0057] Figure 6 shows an example of the weight parameter storage unit 14b of the machine learning device 10 according to the embodiment. The weight parameter storage unit 14b stores multiple weight parameters WP1 that weight multiple objective functions included in the multi-objective optimization problem OP1. The weight parameter storage unit 14b shown in Figure 6 stores "WP101", "WP102", "WP103", ... as weight parameters WP1 that weight the objective function included in the multi-objective optimization problem OP1 identified as "OP001".

[0058] Figure 7 shows an example of the Pareto optimal solution storage unit 14c of the machine learning device 10 according to the embodiment. The Pareto optimal solution storage unit 14c stores the Pareto optimal solutions, which are the solution set PS1 of the multi-objective optimization problem OP1. The Pareto optimal solution storage unit 14c shown in Figure 7 stores "PS101", "PS102", "PS103", ... as Pareto optimal solutions of the multi-objective optimization problem OP1, which is identified as "OP001".

[0059] Figure 8 shows an example of a machine learning model storage unit 14d of the machine learning device 10 according to the embodiment. The machine learning model storage unit 14d stores trained machine learning models LM1 used to solve the multi-objective optimization problem OP1. The machine learning model storage unit 14d shown in Figure 8 stores "LM101", "LM102", "LM103", ... as trained machine learning models LM1 used to solve the multi-objective optimization problem OP1.

[0060] The control unit 15 is a processing unit that manages the machine learning device 10 and is implemented by, for example, a processor. For example, the control unit 15 has an acquisition unit 15a, a training unit 15b, and an execution unit 15c. The acquisition unit 15a, the training unit 15b, and the execution unit 15c are implemented by electronic circuits of the processor or processes executed by the processor.

[0061] The acquisition unit 15a acquires a multi-objective optimization problem OP1 that includes multiple objective functions. For example, for any x ∈ X, the acquisition unit 15a acquires M objective functions f1(x), f2(x), ..., f MThe data for the multi-objective optimization problem OP1, which aims to simultaneously optimize (x), is obtained from user U1. Specifically, the acquisition unit 15a acquires the data for the multi-objective optimization problem OP1, which is identified as "OP001" and includes "CF101", "CF102", "CF103", ... as objective functions, and stores it in the objective function storage unit 14a.

[0062] The training unit 15b extracts multiple weight parameters WP1 based on a simplex WS1 constructed at points corresponding to the number of weight parameters WP1 that weight each of the multiple objective functions. Specifically, if there are M weight parameters WP1 that weight the M objective functions included in the multi-objective optimization problem OP1 identified as "OP001", the training unit 15b constructs a simplex WS1 represented by a polyhedron shape with M vertices in M-1 dimensions, extracts P weight parameters WP1 from arbitrary points on the simplex WS1, namely "WP101", "WP102", "WP103", ..., and stores them in the weight parameter storage unit 14b.

[0063] The training unit 15b trains a machine learning model LM1 that outputs a solution set PS1* corresponding to a given weight parameter WP1* by inputting mappings to solution sets PS1 corresponding to multiple weight parameters WP1. Specifically, the training unit 15b refers to "WP101", "WP102", "WP103", ... as P weight parameters WP1 stored by the weight parameter storage unit 14b, and trains the model by inputting mappings to solution sets PS1 corresponding to the P weight parameters WP1 into "LM101", which is the machine learning model LM1 stored by the machine learning model storage unit 14d.

[0064] The machine learning model LM1 performs a response function with respect to instance parameter IP1, which characterizes the multi-objective optimization problem OP1, and weight parameter WP1, which corresponds to instance parameter IP1, as relaxation variables. The machine learning model LM1 also linearly scales weight parameter WP1 and bias b1, which corresponds to weight parameter WP1, as part of its response function. Furthermore, the machine learning model LM1 transforms weight parameter WP1 into an embedding vector and minimizes the empirical loss as part of its response function.

[0065] The execution unit 15c inputs predetermined weight parameters WP1* into the trained machine learning model ML1 and generates a solution set PS1*. Specifically, the execution unit 15c inputs "WP101*" as an unknown weight parameter WP1* into "LM101", a trained machine learning model LM1 stored by the machine learning model storage unit 14d, and obtains the Pareto optimal solution "PS101", which is the output solution set PS1*. The execution unit 15c also generates a Pareto front PF1 that includes the solution set PS1*.

[0066] <Specific processing flow> Figures 9 to 11 illustrate an example of the specific processing flow performed by the machine learning device 10. Figure 9 is a flowchart of the overall processing by the machine learning device 10 according to the embodiment. Figure 10 is a flowchart of the model learning process by the machine learning device 10 according to the embodiment. Figure 11 is a flowchart of the model utilization process by the machine learning device 10 according to the embodiment.

[0067] Using Figure 9, an example of the overall processing by the machine learning device 10 according to the embodiment will be explained. The machine learning device 10 performs model training (step S101). For example, the machine learning device 10 trains a machine learning model LM1 that outputs a solution set PS1 of the multi-objective optimization problem OP1 by performing the processes described in steps S201 to S205. The machine learning device 10 then performs model utilization processing (step S102) and terminates the process. For example, the machine learning device 10 generates a Pareto front PF1 that includes a solution set PS1* corresponding to an arbitrary weight parameter WP1* by performing the processes described in steps S301 to S303.

[0068] An example of model learning processing by the machine learning device 10 according to the embodiment will be explained using Figure 10. The machine learning device 10 performs model initialization processing (step S201). For example, the training unit 15b of the machine learning device 10 sets the model parameters of the machine learning model LM1 to predetermined initial values. The machine learning device 10 performs weight parameter embedding processing (step S202). For example, the training unit 15b of the machine learning device 10 converts the weight parameters WP1 of P points extracted from the simplex WS1 of the multi-objective optimization problem OP1 into embedding vectors. The machine learning device 10 performs learning execution processing (step S203). For example, the training unit 15b of the machine learning device 10 uses the converted embedding vectors as node features of the machine learning model LM1 and minimizes the empirical loss for the P weight parameters WP1. The machine learning device 10 performs model update processing (step S204). For example, the training unit 15b of the machine learning device 10 calculates the gradient LG1 of the loss function and updates the model parameters using the calculated gradient LG1 of the loss function. At this time, if the training unit 15b of the machine learning device 10 satisfies the convergence condition, for example, when the loss function no longer decreases to a certain extent (step S205: Yes), it terminates the model learning process. On the other hand, if the training unit 15b of the machine learning device 10 does not satisfy the convergence condition (step S205: No), it returns to the process in step S203.

[0069] An example of model utilization processing by the machine learning device 10 according to the embodiment will be explained using Figure 11. The machine learning device 10 performs weight parameter embedding processing (step S301). For example, the execution unit 15c of the machine learning device 10 converts the unknown weight parameter WP1* specified by user U1 into an embedding vector. The machine learning device 10 performs model inference processing (step S302). For example, the execution unit 15c of the machine learning device 10 inputs the converted embedding vector into the machine learning model LM1 and obtains the solution set PS1*, which is the output inference result. The machine learning device 10 performs thresholding processing (step S303) and terminates the model utilization processing. For example, the execution unit 15c of the machine learning device 10 sets a threshold for each value output by the machine learning model LM1, binarizes it, and converts continuous values ​​into discrete values.

[0070] <Effects> The machine learning device 10 acquires a multi-objective optimization problem OP1 containing multiple objective functions, extracts multiple weight parameters WP1 based on a simplex WS1 constructed at points corresponding to the number of weight parameters WP1 that weight each of the multiple objective functions, and trains a machine learning model LM1 that outputs a solution set PS1* corresponding to a given weight parameter WP1* by inputting a mapping to the solution set PS1 corresponding to the multiple weight parameters WP1. In this way, the machine learning device 10 can improve the speed of generating the solution set PS1 of the multi-objective optimization problem OP1.

[0071] The machine learning model LM1 executes a response function with respect to instance parameter IP1, which characterizes the multi-objective optimization problem OP1, and weight parameter WP1, which corresponds to instance parameter IP1, as relaxation variables. This allows the machine learning device 10 to improve the speed of generating the solution set PS1 of the multi-objective optimization problem OP1 by generalizing the optimization solution method using continuous relaxation simulated annealing to multi-objective optimization.

[0072] The machine learning model LM1 linearly scales the weight parameter WP1 and the bias b1 corresponding to the weight parameter WP1 as its response function. This allows the machine learning device 10 to improve the rate at which it generates the solution set PS1 of the multi-objective optimization problem OP1 by performing machine learning with linear scaling applied.

[0073] The machine learning model LM1 converts the weight parameter WP1 into an embedding vector as a response function and minimizes the empirical loss. This allows the machine learning device 10 to improve the speed of generating the solution set PS1 of the multi-objective optimization problem OP1 by performing machine learning that embeds the weight parameter WP1 extracted from the simplex WS1.

[0074] The machine learning device 10 inputs predetermined weight parameters WP1* into the trained machine learning model LM1 and generates a solution set PS1*. This allows the machine learning device 10 to improve the speed of generating the solution set PS1* for the multi-objective optimization problem OP1 by generating a solution set PS1* corresponding to unknown weight parameters WP1* in a single training session.

[0075] The machine learning device 10 generates a Pareto front containing the solution set PS1*. This allows the machine learning device 10 to improve the speed of generating the solution set PS1 for the multi-objective optimization problem OP1 by generating a Pareto front PF1 corresponding to the unknown weight parameter WP1* in a single training run.

[0076] (system) Unless otherwise specified, the processing procedures, control procedures, specific names, and various data and parameters shown in the above documents and drawings may be changed at will.

[0077] Furthermore, the specific forms of distribution and integration of the components of each device are not limited to those shown in the diagram. In other words, all or part of the components may be functionally or physically distributed or integrated in any unit depending on various loads and usage conditions. Moreover, all or any part of the processing functions of each device may be implemented by a CPU (Central Processing Unit) and a program that is analyzed and executed by the CPU, or by hardware using wired logic.

[0078] Furthermore, each processing function performed by each device may be implemented, in whole or in part, by a CPU and a program executed for analysis by that CPU, or by hardware using wired logic.

[0079] (Hardware) Figure 12 is a hardware configuration diagram of the machine learning device. As shown in Figure 12, the machine learning device 10 includes a communication device 10a, an HDD (Hard Disk Drive) 10b, memory 10c, and a processor 10d. Furthermore, the components shown in Figure 12 are interconnected by a bus or the like.

[0080] The communication device 10a is a network interface card or the like, and communicates with other devices. The HDD 10b stores programs and databases that operate the functions shown in Figure 4.

[0081] The processor 10d operates a process that performs the functions described in Figure 4 by reading a program that performs the same processing as each processing unit shown in Figure 4 from the HDD 10b or the like and loading it into memory 10c. For example, the above process performs the same functions as each processing unit of the machine learning device 10. Specifically, the processor 10d reads a program that has the same functions as the acquisition unit 15a, training unit 15b, execution unit 15c, etc. from the HDD 10b or the like. Then, the processor 10d executes a process that performs the same processing as the acquisition unit 15a, training unit 15b, execution unit 15c, etc.

[0082] Thus, the machine learning device 10 operates as a machine learning device that executes an information processing method by reading and executing a program. Furthermore, the machine learning device 10 can also achieve the same functionality as the embodiment described above by reading the program from a recording medium using a media reader and executing the read program. Note that the program in this embodiment is not limited to being executed by the machine learning device 10. For example, the embodiment may also be applied to cases where another computer or server executes the program, or where these devices collaborate to execute the program.

[0083] This program may be distributed via a network such as the Internet. Alternatively, this program may be recorded on a computer-readable recording medium such as a hard disk, flexible disk (FD), CD-ROM, MO (Magneto-Optical disk), or DVD (Digital Versatile Disc), and executed by being read from the recording medium by a computer. [Explanation of symbols]

[0084] 10 Machine Learning Devices 10a Communication device 10b HDD 10c memory 10d processor 11 Input section 12 Output section 13 Communications Department 14 Storage section 14a Objective function storage unit 14b Weight parameter storage unit 14c Pareto optimal solution memory unit 14d Machine Learning Model Memory Unit 15 Control Unit 15a Acquisition part 15b Training Department 15c Execution Unit

Claims

1. On the computer, We obtain a multi-objective optimization problem that includes multiple objective functions, Based on a simplex constructed at points corresponding to the number of weight parameters that weight each of the aforementioned multiple objective functions, the aforementioned multiple weight parameters are extracted. A machine learning model is trained to output a second solution set corresponding to a predetermined weight parameter by inputting a mapping to a first solution set corresponding to the aforementioned multiple weight parameters. A machine learning program characterized by executing a process.

2. The aforementioned machine learning model, As relaxation variables, an instance parameter that represents the characteristics of the multi-objective optimization problem, and a response function with respect to the weight parameters corresponding to the instance parameter are executed. The machine learning program according to feature 1.

3. The aforementioned machine learning model, The response function is one in which the weight parameters and the bias corresponding to the weight parameters are linearly scaled. The machine learning program according to feature 2.

4. The aforementioned machine learning model, The response function is obtained by converting the weight parameters into an embedding vector and minimizing the empirical loss. The machine learning program according to claim 2 or 3, characterized by the above.

5. On the computer, The predetermined weight parameters are input to the trained machine learning model to generate the second solution set. The machine learning program according to claim 1, characterized by executing a process.

6. A Pareto front is generated that includes the second set of solutions. The machine learning program according to feature 5.

7. An acquisition unit that acquires a multi-objective optimization problem containing multiple objective functions, Based on a simplex constructed at points corresponding to the number of weight parameters that weight each of the aforementioned multiple objective functions, the aforementioned multiple weight parameters are extracted. A training unit that trains a machine learning model that outputs a second solution set corresponding to a predetermined weight parameter by inputting a mapping to a first solution set corresponding to the aforementioned plurality of weight parameters, A machine learning device characterized by having the following features.

8. Computers We obtain a multi-objective optimization problem that includes multiple objective functions, Based on a simplex constructed at points corresponding to the number of weight parameters that weight each of the aforementioned multiple objective functions, the aforementioned multiple weight parameters are extracted. A machine learning model is trained to output a second solution set corresponding to a predetermined weight parameter by inputting a mapping to a first solution set corresponding to the aforementioned multiple weight parameters. A machine learning method characterized by performing a process.

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