Arithmetic program, arithmetic method, and information processing device

Abstract

To provide an arithmetic program, an arithmetic method, and an information processing device capable of reducing the number of times of sampling.SOLUTION: An arithmetic program causes a computer to repeatedly execute processes of: generating a plurality of training data sets from a training data group; creating a plurality of Ising models by creating the Ising models for each of the plurality of training data sets; creating a combined Ising model by combining the plurality of Ising models according to the average and the deviation of the coefficients of the plurality of Ising models; searching for a recommended point for the combined Ising model; and adding the recommended point and the evaluation value of the recommended point to the training data group.SELECTED DRAWING: Figure 7

Description

[Technical field]

[0001] The present invention relates to a computing program, a computing method, and an information processing device. [Background technology]

[0002] Techniques for performing optimization using models have been disclosed (see, for example, Patent Documents 1 to 3). [Prior art documents] [Patent documents]

[0003] [Patent Document 1] International Publication No. 2021-059604 [Patent Document 2] Special Publication No. 2021-504836 [Patent Document 3] Patent Publication No. 2021-149160 Summary of the Invention [Problem to be solved by the invention]

[0004] For example, the technique of optimizing by sampling using a QUBO format Ising model is a method of sequentially sampling recommendation points on the model, so there is a risk that the sampling area may be limited. As a result, there is a risk that the number of samplings may be large.

[0005] In one aspect, an object of the present invention is to provide a calculation program, a calculation method, and an information processing device that can reduce the number of sampling operations. [Means for solving the problem]

[0006] In one aspect, the computation program causes a computer to repeatedly execute the following processes: generating a plurality of training data sets from a training data group; creating a plurality of Ising models by creating an Ising model for each of the plurality of training data sets; creating a composite Ising model by combining the plurality of Ising models according to an average and deviation of coefficients of the plurality of Ising models; searching for recommendation points for the composite Ising model; and adding the recommendation points and an evaluation value of the recommendation points to the training data group. Effect of the Invention

[0007] The number of sampling times can be reduced. [Brief description of the drawings]

[0008] [Figure 1] FIG. 1 illustrates a solution search in QUBO format. [Diagram 2] (a) is an example of structure and property learning data, and (b) is an example of FMDA output. [Diagram 3] 1 is a flowchart showing the execution procedure of a sampling technique using a QUBO format model. [Figure 4] FIG. 2A is a block diagram illustrating an example of an overall configuration of an information processing device, and FIG. 2B is a block diagram illustrating an example of a hardware configuration of the information processing device. [Diagram 5] 11 is a flowchart illustrating an example of an operation of the information processing device. [Figure 6] 13 is a flowchart showing details of step S13. [Figure 7] FIG. [Figure 8] 1A is a diagram illustrating an optimization problem for a magnetic shield, FIG. 1B is a diagram illustrating an arrangement of Gaussian basis functions, and FIG. 1C is a diagram illustrating magnetic flux lines generated from a coil. [Figure 9] FIG. 1 illustrates a positive and negative configuration. [Figure 10]FIG. 13 is a diagram illustrating a shape function. [Figure 11] FIG. 13 is a diagram showing a simulation result. [Figure 12] FIG. 13 is a diagram showing a simulation result. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0009] Binary variable sampling technology is used as a technique for searching for a good solution with a high evaluation value from a large number of combinations and sequences. Examples of binary variable sampling technology include sampling technology that performs random sampling and sampling technology that uses the Ising model in the QUBO format.

[0010] Although the random sampling technique allows easy sampling, it has the drawback that sampling efficiency is low and a large number of samplings must be performed to obtain a good solution with high accuracy.

[0011] An example of a sampling technique that uses a QUBO-format model is FMQA (Factorization Machine with Quantum Annealing). FMQA is a method that combines QA (Quantum Annealing) and FM (Machine Learning). FMQA creates a QUBO-format FM model from training data, finds a good answer through QA, analyzes the evaluation value of the good answer with a solver, adds the result to the training data, and performs interactive sampling. Another sampling technique that uses a QUBO-format model is FMDA technology. FMDA replaces the QA part of FMQA with DA (Digital Annealer).

[0012] Here, the QUBO format stands for Quadratic Unconstrained Binary Optimization, which is a format that allows binary optimization without quadratic constraints. The QUBO format can be expressed, for example, as in the following formula. Note that x i= 0 or 1 (i = 1, ..., N). ij x i and x j is the coupling coefficient. i x i is the bias coefficient. The first term on the right hand side is a quadratic term and represents the interaction. The second term on the right hand side is a linear term and represents the bias action. The third term on the right hand side is a constant term. In the QUBO format, a good solution x is searched for to minimize E(x), which represents the energy, according to the following formula, as illustrated in Figure 1.

number

[0013] Here, we will provide an overview of FMDA as an example of a sampling technique that uses a QUBO format Ising model. Figure 2(a) is a diagram illustrating learning data of structure and characteristics. The characteristics expressed by the y value are the objective function value. Data expressed by the n-dimensional vector of x is binary-valued structure data. The data in Figure 2(a) is input into FMDA. Figure 2(b) is an example of FMDA output (recommendation points). The recommendation points are evaluated by analyzing them with a solver.

[0014] Figure 3 is a flowchart showing the execution procedure of the sampling technique using the Ising model in the QUBO format. As illustrated in Figure 3, first, a group of learning data is generated by randomly generating learning data (initial points) (step S1). The number of learning data to be generated is determined by the user's settings.

[0015] Next, a solver is used to calculate an evaluation value of the initial point (step S2). The evaluation value is an index for determining whether the initial point and the recommendation point (described later) are good or not. Through the above steps, an initial learning data group consisting of a set of the initial point and the evaluation value is generated.

[0016] Next, an Ising model in QUBO format is created by generating an FM from the training data group (step S3). Since the FM is in QUBO format, generating an FM is equivalent to generating an Ising model in QUBO format. Other machine learning models can also be used as long as they can generate an Ising model in QUBO format.

[0017] Next, the created Ising model in QUBO format is optimized using DA to generate a good solution (DA recommendation point) that provides the best evaluation value (step S4).

[0018] Next, the evaluation value of the DA recommendation point is calculated using a solver (step S5).

[0019] Next, the evaluation result (a set of recommendation points and evaluation values) is added as learning data to the learning data group (step S6).

[0020] Next, it is determined whether the number of iterations has reached an upper limit (step S7). If the determination in step S7 is "No", execution is resumed from step S3. Thereby, steps S3 to S6 are repeated until a termination condition is satisfied. If the determination in step S7 is "Yes", execution of the flowchart ends. Note that, as the termination condition, a condition such as a case where the amount of change in the objective function is less than a threshold for a certain period of time can be used.

[0021] The above procedure updates the training data set, enabling the optimal solution to be obtained.

[0022] In addition, although FMDA has been explained in Fig. 3, the DA part of FMDA may be replaced with QA, and other methods may be used as long as the Ising machine can solve QUBO. In addition to using an Ising machine dedicated to solving QUBO, the Ising model may be solved using software.

[0023] The sampling technique using the QUBO format model is a method of sequentially sampling recommendation points on the Ising model, so there is a risk that the sampling area may be limited. In addition, with the sampling technique using the QUBO format Ising model, the sampling performance depends on the learning data set for generating the Ising model. In addition, since FM is a second-order Ising model, there is a possibility that the problem cannot be fully expressed. For the above reasons, in order to increase the search accuracy of the optimal solution, the number of samplings will increase.

[0024] In the following embodiment, an example in which the number of sampling times can be reduced will be described. EXAMPLES

[0025] Fig. 4(a) is a block diagram illustrating an example of the overall configuration of an information processing device 100. As illustrated in Fig. 4(a), the information processing device 100 includes a storage unit 10, an initial point generation unit 20, an evaluation unit 30, an FMDA execution unit 40, a learning data update unit 50, an output unit 60, and the like.

[0026] Fig. 4(b) is a block diagram illustrating an example of a hardware configuration of the information processing device 100. As illustrated in Fig. 4(b), the information processing device 100 includes a CPU 101, a RAM 102, a storage device 103, an input device 104, a display device 105, and the like.

[0027] The CPU (Central Processing Unit) 101 is a central processing unit. The CPU 101 includes one or more cores. The RAM (Random Access Memory) 102 is a volatile memory that temporarily stores a program executed by the CPU 101, data processed by the CPU 101, and the like. The storage device 103 is a non-volatile storage device. For example, a ROM (Read Only Memory), a solid state drive (SSD) such as a flash memory, or a hard disk driven by a hard disk drive can be used as the storage device 103. The storage device 103 stores a calculation program. The input device 104 is an input device such as a keyboard or a mouse. The display device 105 is a display device such as an LCD (Liquid Crystal Display). The CPU 101 executes the calculation program to realize a storage unit 10, an initial point generation unit 20, an evaluation unit 30, an FMDA execution unit 40, a learning data update unit 50, an output unit 60, and the like. In addition, the storage unit 10, the initial point generation unit 20, the evaluation unit 30, the FMDA execution unit 40, the learning data update unit 50, the output unit 60, and the like may be implemented using hardware such as dedicated circuits.

[0028] Fig. 5 is a flowchart showing an example of the operation of the information processing device 100. As illustrated in Fig. 5, the initial point generating unit 20 generates a learning data group by randomly generating initial points of learning data (step S11). The number of learning data to be generated is determined by a user setting. In addition, the initial points of the learning data may be set by the user.

[0029] Next, the evaluation unit 30 uses a solver to calculate an evaluation value for each initial point (step S12). An initial learning data group, which is a set of the initial points obtained in step S11 and the evaluation values ​​calculated in step S12, is stored in the storage unit 10.

[0030] Next, the FMDA executing unit 40 generates a DA recommendation point by using the learning data group stored in the storage unit 10 (step S13).

[0031] Next, the evaluation unit 30 uses a solver to calculate an evaluation value of the recommendation point (step S14).

[0032] Next, the learning data update unit 50 adds the evaluation result (a set of recommendation points and evaluation value) to the learning data group as learning data (step S15).

[0033] Next, the FMDA execution unit 40 judges whether the number of iterations has reached an upper limit (step S16). The number of times step S16 is executed may be set as the number of iterations. The upper limit of the number of iterations is preset by the user.

[0034] If the determination in step S16 is "No", the process is executed again from step S13. If the determination in step S16 is "Yes", the execution of the flow chart ends.

[0035] The output unit 60 outputs the result of the processing in Fig. 5. The output result is displayed, for example, by the display device 105. For example, the output unit 60 may output the contents of the learning data group, or may output learning data with a high evaluation value from the learning data group as a good answer.

[0036] 6 is a flowchart showing the details of step S13. As shown in FIG. 6, the FMDA execution unit 40 calculates the search degree α and the maximum search degree α max and the maximum value of the search degree α are set to the set value (step S21). max is determined in advance by a user or the like.

[0037] Next, the FMDA execution unit 40 selects N d N pieces of training data are extracted as a training data set (step S22). d is the number of pickup data items that is determined in advance by the user, etc. d is a number smaller than the number of pieces of training data included in the training data group.

[0038] Next, the FMDA execution unit 40 generates an FM from the learning data set extracted in step S22 and converts it into a QUBO to generate an Ising model (step S23). Since the FM is in the QUBO format, generating an FM is equivalent to generating an Ising model in the QUBO format. Other machine learning models can also be used as long as they can generate an Ising model in the QUBO format.

[0039] Next, the FMDA execution unit 40 determines whether the number of times the Ising model in the QUBO format is generated is the QUBO generation number N S It is determined whether or not the number of the inputs reaches the predetermined number (step S24). If it is determined "No" in step S24, the process is executed again from step S22.

[0040] Steps S22 to S24 are repeatedly executed to obtain N S Each Ising model is generated. Note that at least some of the learning data sets extracted each time step S22 is executed are different. For example, if data No. 1 to No. 10 are extracted the first time and data No. 15 to No. 24 are extracted the second time, different data sets will be included, although some of them will overlap. Alternatively, all of the learning data included in each learning data set may be different for each learning data set. For example, if data No. 1 to No. 10 are extracted the first time and data No. 11 to No. 20 are extracted the second time, all of the learning data will be different.

[0041] In addition, when the number of learning data included in the learning data group is small, it is preferable to overlap some of the learning data sets when generating each learning data set. For example, data No. 1 to No. 5 are the first learning data set, No. 2 to No. 6 are the second learning data set, No. 3 to No. 7 are the third learning data set, etc. In this case, even if the number of initial points is small, multiple types of learning data sets can be generated.

[0042] If the answer is "Yes" in step S24, the FMDA execution unit 40 calculates the coefficient of determination R2 A synthetic QUBO is generated from the Ising model whose coefficients are equal to or greater than the threshold δ according to the average and deviation of the coefficients (step S25).

[0043] By repeating step S23 above to generate each Ising model, E(x) in the QUBO format described in Figure 1 is obtained. For each E(x), ij , b i , const. is obtained. For each E(x), W ij The average value of W ij _ave and b i The average of b i Let _ave be the mean of const. and const._ave be the mean of const. For each E(x), W ij The standard deviation of W ij Let _σ and b i The standard deviation of b i Let const._σ be the standard deviation of const., and const._σ be the standard deviation of const.. As an example, in the QUBO format E(x) described in Figure 1, ij (W ij _ave-α×W ij _σ), b i (b i _ave-α×b i _σ) and replace const. with (const._ave-α×const._σ). This gives us a composite QUBO.

[0044] In this way, by using the average of the coefficients of each E(x), it becomes possible to search for an area with a good objective function value. Furthermore, since it is possible to search for areas with large deviations, it becomes possible to search for areas with high uncertainty that have not yet been explored. The larger the search degree α, the more importance is attached to deviations, making it possible to actively search for areas with high uncertainty. Setting the search degree α to 0 makes it possible to actively search for areas with a good objective function value.

[0045] Coefficient of determination R 2is an index of model accuracy, and the closer it is to 1, the better the accuracy of searching for a good solution with a high evaluation value. Although a synthetic QUBO may be generated regardless of the coefficient of determination, it is possible to generate a highly accurate synthetic QUBO by excluding Ising models whose coefficient of determination is less than the threshold δ.

[0046] Coefficient of determination R 2 can be calculated, for example, by the following formula:

number

number

number

[0047] Next, the FMDA execution unit 40 generates DA recommendation points for the number of DA setting recommendations by optimizing the composite QUBO generated in step S25 by DA (step S26). The number of DA setting recommendations is set in advance by the user. The DA recommendation points are good solutions (recommendation points) with the best evaluation value. Alternatively, the DA recommendation points are good solutions (recommendation points) with evaluation values ​​equal to or greater than a threshold value. Alternatively, the DA recommendation points are good solutions (recommendation points) with evaluation values ​​in the top predetermined order.

[0048] Next, the FMDA execution unit 40 determines whether the recommendation point obtained in step S26 is a point that has already been searched (step S27). For example, it determines whether the recommendation point obtained in step S26 is included in the learning data group stored in the storage unit 10.

[0049] If the result of the determination in step S27 is “Yes”, the FMDA execution unit 40 sets the maximum value of the search degree as α max = α max +Δα (step S28).

[0050] Next, the FMDA executing unit 40 randomly generates a value between 0 and αmax, and updates the search degree α to the generated value (step S29). After that, the process is executed again from step S25.

[0051] If the determination in step S27 is "No", the execution of the flowchart ends.

[0052] FIG. 7 is a diagram summarizing this embodiment. As illustrated in FIG. 7, an initial point of the learning data is generated. From this group of learning data, a specified number of learning data are extracted as multiple types of learning data sets. Next, for each learning data set, an FM model is generated, QUBOized, and an Ising model is generated. According to the average and deviation of the coefficients in the QUBO format, Ising models with model accuracy equal to or greater than a threshold are synthesized, and a synthesized QUBO is generated.

[0053] The composite QUBO is used to generate recommendation points through DA optimization. If the recommendation points have already been searched for, the search degree α is changed, a new composite QUBO is generated, and a recommendation point is generated through DA optimization. If the recommendation points have not been searched for, the recommendation points are analyzed using a solver, and the analysis results of the recommendation points are added to the training data. The same process is then repeated with the updated training data.

[0054] According to this embodiment, in order to generate a plurality of Ising models, the coefficients (W ij , b i , const.) can be calculated. When synthesizing multiple Ising models, by considering not only the average of the coefficients but also the deviation, it becomes possible to search for areas with high uncertainty. Specifically, by synthesizing Ising models using (average - α × deviation), it becomes possible to search not only areas with good objective function values, but also areas with high uncertainty where the deviation is large and which have not yet been explored. This makes it possible to prevent the model from falling into a local solution, and as a result, the number of sampling times can be reduced.

[0055] When synthesizing multiple Ising models, the accuracy of the synthesized QUBO can be improved by excluding Ising models whose accuracy is below a threshold. By including overlapping learning data in at least two sets of multiple training datasets, multiple Ising models can be generated even when the number of training data such as initial points is small. If the recommendation point searched for by DA has already been searched, the search degree α is changed and the synthesized QUBO is regenerated, making it possible to search unexplored areas.

[0056] In the above, the search degree α is updated as in step S29, but it may be gradually updated using an interval value between 0 and αmax. Alternatively, the search degree α may be updated according to the number of times step S13 is repeated.

[0057] (Simulation results) Hereinafter, a description will be given of the results of a simulation in which a hypothetical problem was set and the computational processing according to the above embodiment was performed. FIG. 8(a) is a diagram illustrating an optimization problem of a magnetic shield. FIG. 8(a) is a diagram illustrating a magnetic shield analysis model, and illustrating a coil, a design area of ​​a magnetic body, and a target area. The target area is an area where it is desired to prevent the influence of magnetic flux. The design area of ​​the magnetic body is an area for placing the magnetic body. FIG. 8(b) is a diagram illustrating the placement of Gaussian basis functions. As illustrated in FIG. 8(b), 96 magnetic bodies can be placed in the design area of ​​the magnetic body. FIG. 8(c) is a diagram illustrating magnetic flux lines generated from a coil.

[0058] The table in FIG. 9 is a diagram illustrating positive and negative placements. s1 to s96 indicate 96 positive placement locations. "0" in s1 to s96 indicates that no magnetic material is placed, and "1" indicates that a magnetic material is placed. z1 to z96 indicate 96 negative placement locations. "0" in z1 to z96 indicates that no magnetic material is placed, and "1" indicates that a magnetic material is placed.

[0059] This placement problem can be expressed as a shape function y as follows: i ,z i ∈{0,1}, and w i ∈{-1,0,1}. In this way, the optimization problem of the magnetic shield is viewed as a placement problem of positive and negative Gaussian basis functions.

number

[0060] The distribution of shape function y is shown in the upper diagram of Figure 10. From this result, it becomes possible to determine material information from the magnitude of shape function y, as shown in the lower diagram of Figure 10. In the lower diagram of Figure 10, if the shape function y is 0 or more, material is present, and if the shape function y is less than 0, material is not present.

[0061] The purpose of optimizing the magnetic shield shape is to determine the average magnetic flux density B ave T and the magnetic area S mag Specifically, it is the minimization of the following equation. Note that E 1 is the value of B when the design domain is entirely air. ave T It is one tenth of E 2 is the S when the design domain is entirely magnetic. mag It is.

number

[0062] For this optimization problem, sampling was performed using two methods: the FMDA method and the method of this embodiment. The common settings were the number of initial points to be 96. The number of iterations was 192, and the threshold δ was 0.85. The number of pickup data N d is set to 400, and the number of QUBOs generated is N S was set to 10. The weight of the objective function β 1 , β 2 In addition, the search degree α was set to 0.5, and the change amount Δα of the search degree α was set to 0.1.

[0063] 11 and 12 are diagrams showing the results. FIG. 11 shows the best value found in the search. The vertical axis represents the energy E in the QUBO format. Therefore, the smaller the value on the vertical axis, the better the result. The number of CAE analyses on the horizontal axis represents the number of iterations. The lower diagram in FIG. 11 is an enlarged diagram in which the vertical axis of the upper diagram in FIG. 11 has been scaled. As shown in FIG. 11 and FIG. 12, it can be seen that the method of this embodiment can sample more efficiently than the FMDA method.

[0064] In the above example, the FMDA execution unit 40 and the learning data update unit 50 are an example of an execution unit that repeatedly executes the following processes: generating a plurality of learning data sets from a learning data group, creating a plurality of Ising models by creating an Ising model for each of the plurality of learning data sets, creating a composite Ising model by synthesizing the plurality of Ising models according to the average and deviation of the coefficients of the plurality of Ising models, searching for recommendation points for the composite Ising model, and adding the recommendation points and the evaluation values ​​of the recommendation points to the learning data group.

[0065] Although the embodiments of the present invention have been described in detail above, the present invention is not limited to such specific embodiments, and various modifications and variations are possible within the scope of the gist of the present invention described in the claims. (Appendix 1) On the computer, generating a plurality of training data sets from the training data group; A process of creating a plurality of Ising models by creating an Ising model for each of the plurality of learning data sets; A process of generating a composite Ising model by synthesizing the plurality of Ising models according to the average and deviation of the coefficients of the plurality of Ising models; A process of searching for a recommendation point for the synthetic Ising model; and adding the recommendation points and evaluation values ​​of the recommendation points to the learning data group. (Appendix 2) 2. The arithmetic program according to claim 1, wherein, when synthesizing the plurality of Ising models, an Ising model having an accuracy less than a threshold is excluded. (Appendix 3) 2. The computational program according to claim 1, wherein at least two of the plurality of training data sets include training data that overlap with each other. (Appendix 4) The arithmetic program according to claim 1, characterized in that, when the searched-for recommendation point is already included in the learning data group, when the plurality of Ising models used to search for the recommendation point are synthesized, a reflection degree of the deviation is changed to re-create the synthesized Ising model, and a recommendation point is searched for in the recreated synthesized Ising model. (Appendix 5) The calculation program according to claim 1, wherein the coefficient is at least one of a coupling coefficient, a bias coefficient, and a constant term of the Ising model. (Appendix 6) The computer generating a plurality of training data sets from the training data group; A process of creating a plurality of Ising models by creating an Ising model for each of the plurality of learning data sets; A process of generating a composite Ising model by synthesizing the plurality of Ising models according to the average and deviation of the coefficients of the plurality of Ising models; A process of searching for a recommendation point for the synthetic Ising model; and repeatedly executing a process of adding the recommendation points and evaluation values ​​of the recommendation points to the learning data group. (Appendix 7) 7. The method according to claim 6, wherein, when synthesizing the plurality of Ising models, an Ising model having an accuracy less than a threshold is excluded. (Appendix 8) 7. The method of claim 6, wherein at least two of the plurality of training data sets include training data that overlap with each other. (Appendix 9) The calculation method according to claim 6, characterized in that, when the searched recommendation point is already included in the learning data group, when the plurality of Ising models used to search for the recommendation point are synthesized, a reflection degree of the deviation is changed to regenerate the synthesized Ising model, and a recommendation point is searched for using the recreated synthesized Ising model. (Appendix 10) The calculation method according to claim 6, wherein the coefficient is at least one of a coupling coefficient, a bias coefficient, and a constant term of the Ising model. (Appendix 11) an execution unit that repeatedly executes a process of generating a plurality of learning data sets from a learning data group, creating a plurality of Ising models by creating an Ising model for each of the plurality of learning data sets, creating a composite Ising model by synthesizing the plurality of Ising models according to an average and a deviation of coefficients of the plurality of Ising models, searching for recommendation points for the composite Ising model, and adding the recommendation points and an evaluation value of the recommendation points to the learning data group. (Appendix 12) The information processing device according to claim 11, wherein the execution unit excludes an Ising model whose accuracy is less than a threshold when synthesizing the multiple Ising models. (Appendix 13) The information processing device according to claim 11, wherein at least two of the plurality of training data sets include training data that overlap with each other. (Appendix 14) The information processing device according to claim 11, wherein when the searched recommendation point is already included in the learning data group, the execution unit recreates the synthesized Ising model by changing a reflection degree of the deviation when synthesizing the plurality of Ising models used to search for the recommendation point, and searches for the recommendation point for the recreated synthesized Ising model. (Appendix 15) The information processing device according to claim 11, wherein the coefficient is at least one of a coupling coefficient, a bias coefficient, and a constant term of the Ising model. [Explanation of symbols]

[0066] 10 Storage area 20 Initial point generation section 30 Evaluation Section 40 FMDA Executive Division 50 Learning data update unit 60 Output section 100 Information processing device 101 CPU 102 RAM 103 Storage device 104 Input Devices 105 Display device

Claims

1. On the computer, generating a plurality of training data sets from the training data group; A process of creating a plurality of Ising models by creating an Ising model for each of the plurality of learning data sets; A process of generating a composite Ising model by synthesizing the plurality of Ising models according to the average and deviation of the coefficients of the plurality of Ising models; A process of searching for a recommendation point for the synthetic Ising model; and adding the recommendation points and evaluation values ​​of the recommendation points to the learning data group.

2. 2. The computing program according to claim 1, wherein, when the plurality of Ising models are synthesized, an Ising model having an accuracy less than a threshold value is excluded.

3. 2. The computing program according to claim 1, wherein at least two of the plurality of training data sets include training data that overlap with each other.

4. 2. The arithmetic program according to claim 1, wherein, when the searched-for recommendation point is already included in the learning data group, when the plurality of Ising models used to search for the recommendation point are synthesized, a reflection degree of the deviation is changed to re-create the synthetic Ising model, and the recommendation point is searched for in the recreated synthetic Ising model.

5. 2. The computing program according to claim 1, wherein the coefficient is at least one of a coupling coefficient, a bias coefficient, and a constant term of the Ising model.

6. The computer generating a plurality of training data sets from the training data group; A process of creating a plurality of Ising models by creating an Ising model for each of the plurality of learning data sets; A process of generating a composite Ising model by synthesizing the plurality of Ising models according to the average and deviation of the coefficients of the plurality of Ising models; A process of searching for a recommendation point for the synthetic Ising model; and repeatedly executing a process of adding the recommendation points and evaluation values ​​of the recommendation points to the learning data group.

7. an execution unit that repeatedly executes a process of generating a plurality of learning data sets from a learning data group, creating a plurality of Ising models by creating an Ising model for each of the plurality of learning data sets, creating a composite Ising model by synthesizing the plurality of Ising models according to an average and a deviation of coefficients of the plurality of Ising models, searching for recommendation points for the composite Ising model, and adding the recommendation points and an evaluation value of the recommendation points to the learning data group.

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