Parameter optimization device, method and system

Abstract

The present invention relates to a parameter optimization device, method and system. The problem to be solved by the present invention is to provide a parameter optimization device, method and system that can efficiently search for optimal parameter values. The parameter optimization device has a storage unit, a search space determination unit, a first acquisition unit and a parameter search unit. The storage unit stores a plurality of data sets including a first parameter value of a first dimension and an observation value of an objective function corresponding to the first parameter value. The search space determination unit determines a search space of a second dimension smaller than the first dimension that includes a predetermined first parameter value. The first acquisition unit acquires one or more data sets having a first parameter value included in a predetermined distance from the search space or a data set having a second parameter value corresponding to the data set based on the plurality of data sets. The parameter search unit uses a proxy model of the objective function based on the acquired one or more data sets to search in the search space for the first parameter value or the second parameter value that can optimize the objective function.

Description

[0001] This application is based on Japanese Patent Application No. 2020-185291 (filing date: November 5, 2020) and claims priority from the aforementioned application. The present application incorporates the entire contents of the aforementioned application by reference. Technical Field

[0002] Embodiments of the present invention relate to a parameter optimization device, method and system. Background Art

[0003] In society, there are various devices, and these devices are composed of various parts. These devices and parts are designed, manufactured, and used.

[0004] During the design phase, equipment and components are sometimes designed to have characteristics that meet specifications. In this case, by changing the parameters that can be adjusted during design to various values, simulations, experiments, and questionnaires are performed to obtain the characteristics when designed according to these parameter values, and the parameter values ​​that meet the specifications for the characteristics are obtained. Here, the characteristics are, for example, the performance of equipment and components, the manufacturing cost, and the customer satisfaction. The better the performance of the equipment and components, the more preferred it is, the lower the manufacturing cost, the more preferred it is, and the higher the customer satisfaction, the more preferred it is. In the case where the value of the characteristic is as large as possible, it is required to find the parameter value that maximizes the characteristic with less time and effort. In the case where the value of the characteristic is as small as possible, it is required to find the parameter value that minimizes the characteristic with less time and effort.

[0005] The process of finding the parameter value that maximizes or minimizes the characteristic is called parameter optimization. The characteristic that changes according to the parameter value is called the objective function. Simulation, experiment, and questionnaire survey are means for observing the value of the objective function.

[0006] Parameter optimization is sometimes used in the manufacturing stage, for example, to find parameter values ​​that maximize the yield rate during manufacturing or to find parameter values ​​that minimize the failure rate after shipment.

[0007] Parameter optimization is sometimes used in the utilization stage. For example, when the user makes initial settings, parameter values ​​are sometimes obtained so that the device or component at the user's disposal can exhibit performance that matches the user's usage environment.

[0008] There are many cases where there are multiple parameters. When D represents the number of parameters to be adjusted, multiple parameters can be expressed by a D-dimensional vector. The parameters that can be expressed by a D-dimensional vector are called D-dimensional parameters, and the values ​​of the D-dimensional parameters are called D-dimensional parameter values. The space for searching for the optimal D-dimensional parameter value is the D-dimensional space. The larger D is, the wider the search space is, so it is difficult to optimize.

[0009] As a parameter optimization method for searching for a D-dimensional parameter value that maximizes or minimizes an objective function in a D-dimensional space (D≥2), a technique of non-patent document 1 is known. In this technique, the search space is limited to a 1-dimensional space in the D-dimensional space, and the Bayesian optimization is repeatedly performed while switching the 1-dimensional search space to search for parameter values. This makes the search for D-dimensional parameters more efficient.

[0010] Prior art literature

[0011] Patent Literature

[0012] Patent Document 1: Japanese Patent Application Publication No. 2020-27370

[0013] Non-patent literature

[0014] Non-patent document 1: J.Kirschner, M.Mutny, N.Hiller, R.Ischebeck, and A.Krause, "Adaptive and safe Bayesian optimization in high dimensions via one-dimensional subspaces," in Proceedings of the 36th International Conference onMachine Learning, vol.97, pp.3429-3438, PMLR, 2019. Summary of the invention

[0015] In the Bayesian optimization method used in the non-patent document 1, the calculation of the inverse matrix is ​​required, and the amount of calculation increases according to the number of iterations of the parameter search. Although simulation, experiment, questionnaire survey and other methods take a long time to observe the value of the objective function, the amount of calculation sometimes becomes a non-negligible length when the number of iterations of the parameter search increases.

[0016] The problem to be solved by the present invention is to provide a parameter optimization device, method and system capable of efficiently searching for optimal parameter values.

[0017] The parameter optimization device of the embodiment has a storage unit, a search space determination unit, a first acquisition unit, and a parameter search unit. The storage unit stores a plurality of data sets including a first parameter value of a first dimension and an observed value of an objective function corresponding to the first parameter value. The search space determination unit determines a search space of a second dimension smaller than the first dimension including a predetermined first parameter value. The first acquisition unit acquires one or more data sets having a first parameter value included in a predetermined distance from the search space or a data set having a second parameter value corresponding to the data set based on the plurality of data sets. The parameter search unit searches for a first parameter value or a second parameter value that can optimize the objective function in the search space using a proxy model of the objective function based on the acquired one or more data sets. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a diagram showing a functional configuration example of the parameter optimization system according to the first embodiment.

[0019] Figure 2 FIG. 1 is a diagram showing an example of a data set stored in the data storage unit.

[0020] Figure 3 is a diagram showing an example of a one-dimensional search space in a two-dimensional parameter space.

[0021] Figure 4 2 is a diagram showing the concept of a data set near a one-dimensional search space in a two-dimensional parameter space.

[0022] Figure 5 This is a diagram showing an example of a method of transforming a 20-dimensional dataset into a 1-dimensional dataset.

[0023] Figure 6 This is a diagram showing an example of a method of converting a 1-dimensional parameter value into a 20-dimensional parameter value.

[0024] Figure 7 This is a flowchart showing an example of the processing operation of the parameter optimization system according to the first embodiment.

[0025] Figure 8 is a diagram showing an example of a one-dimensional affine subspace.

[0026] Fig. 9 It is a diagram showing a functional configuration example of a parameter optimization system according to the second embodiment.

[0027] Fig.10 This is a flowchart showing an example of the processing operation of the parameter optimization system according to the second embodiment.

[0028] Fig.11 This is a diagram showing an example of a dimension acquisition screen.

[0029] Fig.12 : is a figure which shows an example of the distance type input screen.

[0030] Fig.13 : is a figure which shows an example of the threshold value input screen.

[0031] Fig.14 It is a diagram showing a hardware configuration example of a parameter optimization device.

[0032] Explanation of symbols

[0033] 1: parameter optimization system; 2A, 2B: parameter optimization device; 3: observation value output device; 11: data storage unit; 12: search space determination unit; 13: data acquisition unit; 14: parameter search unit; 15: data generation unit; 16: optimal parameter value acquisition unit; 17: dimension acquisition unit; 18: distance acquisition unit; 19: threshold acquisition unit; 20: display unit; 21: external data acquisition unit. DETAILED DESCRIPTION

[0034] The terms used in this embodiment are defined. D represents the number of parameters to be adjusted. D parameters can be expressed by a D-dimensional vector. A parameter that can be expressed by a D-dimensional vector is called a D-dimensional parameter, and the value of a D-dimensional parameter is called a D-dimensional parameter value. x represents the D-dimensional parameter value. f(·) represents the optimized objective function, and y represents the observed value of the objective function. x represents the D-dimensional parameter value. r Denotes the parameter value of the r dimension. Let D>r.

[0035] When it is desired to find the D-dimensional parameter value that maximizes the value of the objective function, the sign of the objective function can be inverted to rewrite it as an equivalent minimization problem. Therefore, the following describes an example of finding the D-dimensional parameter value that minimizes the value of the objective function f(·), and the description of the maximization problem is omitted.

[0036] The following describes the parameter optimization device, method, and system of the present embodiment with reference to the accompanying drawings. In the following embodiments, the characteristic structure and operation of the parameter optimization device are mainly described, but the parameter optimization device may have structures and operations omitted in the following description.

[0037] (First embodiment)

[0038] Figure 1 1 is a diagram showing an example of a functional configuration of a parameter optimization system 1 according to a first embodiment. Figure 1As shown, the parameter optimization system 1 is a computer system having a parameter optimization device 2A and an observation value output device 3. The parameter optimization device 2A and the observation value output device 3 are connected to each other via wired or wireless communication. The parameter optimization device 2A is a computer that searches for parameter values ​​that may optimize the objective function based on the observation values ​​from the observation value output device 3 and the parameter values ​​corresponding to the observation values. The observation value output device 3 is a computer that performs simulation, experiment or questionnaire survey based on the parameter values ​​and observes the value of the objective function, in other words, outputs the observation value of the objective function. The parameter optimization system 1 repeats the search for parameter values ​​that may optimize the objective function by the parameter optimization device 2A and the output of the observation value of the objective function by the observation value output device 3 corresponding to the searched parameter value.

[0039] like Figure 1 As shown, the parameter optimization device 2A includes, for example, a data storage unit 11 , a search space determination unit 12 , a data acquisition unit 13 , a parameter search unit 14 , a data generation unit 15 , and an optimal parameter value acquisition unit 16 .

[0040] The data storage unit 11 stores, for example, a set of D-dimensional parameter values ​​and the observed values ​​of the objective function corresponding to the D-dimensional parameter values ​​as data. The data of the set of D-dimensional parameter values ​​and the observed values ​​is called a data set. In the data storage unit 11, more than one data set is stored. The observed value of the objective function is calculated by the observed value output device 3 based on the D-dimensional parameter value.

[0041] The data storage unit 11 stores N0 data sets {(x n ,y n )|n=0, 1,...,N0-1}. x n Indicates the nth D-dimensional parameter value. n Represents x n The observed value of the objective function f. That is, y n =f(x n )+ε n Here, ε n Represents the observed value y n The number of data sets N0 may increase because the data sets generated by the data generating unit 15 are stored in the data storage unit 11 .

[0042] Observation value y nIt is observed based on simulation, experiment, questionnaire, etc. performed by the observation value output device 3. In the experiment, simulation, questionnaire, etc., characteristic values ​​for more than one item can be obtained. When the number of items is one, the characteristic value obtained is a scalar, so the characteristic value is used as the observation value of the objective function. When there are multiple items of characteristic values ​​obtained by experiments, simulations, questionnaires, etc., the obtained characteristic values ​​are expressed as vectors. The value obtained by converting the characteristic value expressed by a vector into a scalar is used as the observation value of the objective function. As a conversion to a scalar, for example, a linear weighted sum method is used.

[0043] Figure 2 FIG. 1 is a diagram showing an example of a data set stored in the data storage unit 11 . Figure 2 is an example of a dataset with D = 20. The 20-dimensional parameter has 20 variables x (0) 、x (1) , …, x (19) , each variable has a unique value. Each variable can be a design parameter of a filter or device, or a setting parameter of a manufacturing device. The value of each variable can also be a continuous value, a discrete value, or a category variable. The variable of the observed value of the objective function calculated based on the 20-dimensional parameter value is set to y. Figure 2 Each row of is a data set having 20-dimensional parameter values ​​and observation values ​​of the objective function corresponding to the 20-dimensional parameter values.

[0044] The search space determination unit 12 obtains the D-dimensional parameter value x that minimizes the observed value of the objective function from the data set stored in the data storage unit 11. exp , select r-dimensional parameters smaller than D-dimensional from D-dimensional parameters, and determine the r-dimensional search space containing the acquired D-dimensional parameter value. If there is no data set stored in the data storage unit 11, the D-dimensional parameter value x can be randomly set. exp , or it can be borrowed from past adjustment results. The search space is an affine subspace. The value of the dimension r can be a predetermined value or a randomly determined value.

[0045] Figure 3 is a diagram showing an example of a 1-dimensional search space in a 2-dimensional parameter space. That is, Figure 3 This is an example of the case where D=2 and r=1. Figure 3 The 2D parameter space shown is a space defined by the coordinate axis x0 and the coordinate axis x1. The contour map 50 represents the 2D target function in the 2D parameter space. The center 51 of the contour map 50 corresponds to the minimum value of the target function. The 4 points represent 4 2D parameter values. Among these 2D parameter values, the 2D parameter value with the minimum observed value of the target function is marked as x. exp . The 2D parameter value x expis the reference point of the 1-dimensional search space 52. When determining the 1-dimensional search space 52, it is necessary to select the 1-dimensional focus. Figure 3 In the example, x0 is selected as the one dimension of interest. The search space determination unit 12 includes the two-dimensional parameter value x exp The one-dimensional space along x0 is determined as the one-dimensional search space 52. By selecting the dimension in this way, the optimization problem of high-dimensional parameters can be localized into the optimization problem of low-dimensional parameters and solved.

[0046] The data acquisition unit 13 acquires a data set having a D-dimensional parameter value contained in a predetermined distance from the search space acquired by the search space determination unit 12 based on a plurality of data sets stored in the data storage unit 11. A data set having a D-dimensional parameter value contained in a predetermined distance from the search space is referred to as a data set near the search space. The distance between the search space and the D-dimensional parameter value can be arbitrarily selected from Euclidean distance, Manhattan distance, cosine distance, and Mahalanobis distance. The cosine distance is obtained by subtracting cosine similarity from 1. The cosine distance does not satisfy the mathematical axiom of distance, but can be used as a scale for measuring the distance from the search space. In addition, the data set acquired by the data acquisition unit 13 can be either a set of D-dimensional parameter values ​​and observation values ​​or a set of r-dimensional parameter values ​​and observation values.

[0047] Figure 4 is a diagram showing the concept of a data set near a 1-dimensional search space in a 2-dimensional parameter space. That is, Figure 4 This is an example of a case where D = 2 and r = 1. The 2D parameter value near the 1D search space refers to the 2D parameter value whose predetermined distance from the 1D search space 52 is less than the threshold value d. In other words, the 2D parameter value x contained in the space 53 whose distance from the 1D search space 52 is less than the threshold value d is obtained. exp and the 2D parameter value x oth . The 2D parameter value x oth is included in space 53, but not in one-dimensional search space 52. In the case of d=0, the two-dimensional parameter value near the one-dimensional search space means the two-dimensional parameter value on the one-dimensional search space 51. Figure 4 Among the four points in the 1D search space 51, the 2D parameter value is only x exp When d = 0, the 2D parameter value x oth The data acquisition unit 13 cannot acquire it.

[0048] The data acquisition unit 13 may select a data set near the search space from a plurality of data sets stored in the data storage unit 11, or may generate a data set based on a plurality of data sets stored in the data storage unit 11. The data acquisition unit 13 may also transform a data set having a D-dimensional parameter value near the search space acquired from the data storage unit 11 into a data set of r-dimensional parameter values ​​and observation values ​​of the objective function corresponding to the r-dimensional parameter values. In addition, a D-dimensional parameter value or an r-dimensional parameter value near the search space may be randomly generated, and a data set may be produced based on the parameter value.

[0049] Figure 5 is a diagram showing an example of a method for transforming a 20-dimensional dataset into a 1-dimensional dataset. That is, Figure 5 This is an example of the case where D=20 and r=1. Figure 5 The one-dimensional parameter selected by the search space determination unit 12 is x (2) For example, Figure 5 The left side of is a 20-dimensional data set near the 1-dimensional search space acquired from the data storage unit 11. The transformation of the 20-dimensional data set to a 1-dimensional data set is performed, for example, by converting the 1-dimensional parameter x selected by the search space determination unit 12 to (2) The value of and the observed value y of the objective function are set as a set to digitize.

[0050] The parameter search unit 14 uses a proxy model of the objective function based on one or more data sets acquired by the data acquisition unit 13 to determine a D-dimensional parameter value x that can optimize the objective function within the search space determined by the search space determination unit 12. next Or the r-dimensional parameter value x r next Specifically, the parameter search unit 14 generates a proxy model of the objective function based on the acquired data set, and searches for a D-dimensional parameter value or an r-dimensional parameter in the r-dimensional search space that optimizes the proxy model as a D-dimensional parameter value x that can optimize the objective function. next Or the r-dimensional parameter value x r next When the parameter value of the data set acquired from the data acquisition unit 13 is D-dimensional, the D-dimensional parameter value x is searched. next On the other hand, when the parameter value of the data set acquired from the data acquisition unit 13 is r-dimensional, the r-dimensional parameter value x is searched. r next . Bayesian optimization or the like may be used to search for parameter values.

[0051] The data generation unit 15 generates a data including the D-dimensional parameter value x found by the parameter search unit 14. next Or the r-dimensional parameter value x r nextThe corresponding observed value y of the objective function next And the D-dimensional parameter value x next Or the r-dimensional parameter value x r next of the dataset.

[0052] Specifically, the data generation unit 15 searches for the D-dimensional parameter value x by the parameter search unit 14. next In the case of next The observed value output device 3 performs simulation, experiment, and questionnaire survey to obtain the D-dimensional parameter value x. next Output observation value y next The data generation unit 15 obtains the observed value y from the observed value output device 3 next , generates a D-dimensional parameter value x next and the observed value y next The data generation unit 15 stores the data set in the data storage unit 11. The data generation unit 15 searches for the dimension parameter value x by the parameter search unit 14r. r next In the case of r next Transformed into D-dimensional parameter value x next .

[0053] Figure 6 is a diagram showing an example of a method for transforming a 1-dimensional parameter value into a 20-dimensional parameter value. That is, Figure 6 This is an example of the case where D=20 and r=1. Figure 6 The one-dimensional parameter selected by the search space determination unit 12 is the one-dimensional parameter value x of the third element. (2) An example of the case. Figure 6 So the 1-dimensional parameter value x 1 next Embedded into 20-dimensional parameter value x exp The 1-dimensional parameter value x of the third element in (2) , thus transforming into a 20-dimensional parameter value x exp .

[0054] Then, the data generation unit 15 converts the transformed D-dimensional parameter value x next The observed value output device 3 performs simulation, experiment, and questionnaire survey to obtain the D-dimensional parameter value x. next Output observation value y next The data generation unit 15 obtains the observed value y from the observed value output device 3 next , generates a D-dimensional parameter value x next and the observed value y next The data set is stored in the data storage unit 11.

[0055] The optimal parameter value acquisition unit 16 selects the D-dimensional parameter value corresponding to the smallest observation value among the plurality of data sets stored in the data storage unit 11 as the optimal parameter value x best .

[0056] Next, refer to Figure 7 , the processing operation of the parameter optimization system 1 having the parameter optimization device 2A according to the first embodiment is described. Figure 7 This is a flowchart showing an example of the processing operation of the parameter optimization system 1 according to the first embodiment.

[0057] like Figure 7 As shown, first, the search space determination unit 12 determines the parameter value x as the reference point of the search space. exp Initial parameter values ​​are set (step SA1). The initial parameter values ​​may be randomly selected or may be used from past adjustment results.

[0058] When step SA1 is performed, the search space determination unit 12 selects an r-dimensional parameter that is smaller than D-dimensional (step SA2). In addition, if there is a data set stored in the data storage unit 11, the search space determination unit 12 obtains the D-dimensional parameter value x that minimizes the observed value of the objective function. exp If there is no stored data set, the parameter value x set in step SA1 is obtained. exp The selection of the r-dimensional parameters may be, for example, pre-dividing the D-dimensional parameters into groups including a plurality of r-dimensional parameters, selecting one group from the plurality of groups, or randomly selecting. Each time a predetermined number of iterations of the loop related to the second condition described later are repeated, a group may be selected in order from the plurality of groups. For example, x0 to x4 may be set as the first group, x5 to x9 may be set as the second group, and x1 to x2 may be set as the third group. 10 to x 14 Set it as group 3, and set x 15 to x 19 The fourth group is set, and the first group, the second group, the third group, and the fourth group are selected in order for each iteration of the loop related to the second condition. Alternatively, the r-dimensional parameters may be randomly selected from the D-dimensional parameters without grouping.

[0059] When step SA2 is performed, the search space determination unit 12 includes the D-dimensional parameter value x obtained in step SA2. exp The r-dimensional affine subspace corresponding to the r-dimensional parameter selected in step SA2 is determined as the search space (step SA3). Specifically, the search space determination unit 12 determines the value of the parameter x exp Here, let A represent the r-dimensional affine subspace. A is represented by A=x exp + U = {xexp +u|u∈U}. exp is the position vector of A. U is the r-dimensional linear subspace associated with A. The r-dimensional affine subspace can be changed for each iteration of the loop related to the second condition.

[0060] Figure 8 is a diagram showing an example of a one-dimensional affine subspace 61. That is, Figure 8 This is an example of the case where D=2 and r=1. Figure 8 The example shows a one-dimensional affine subspace 61 set in a two-dimensional space with x0 and x1 as coordinate axes. A one-dimensional linear subspace 62 is set to accompany the one-dimensional affine subspace 61. The one-dimensional linear subspace 62 passes through the origin of the two-dimensional coordinate space. The one-dimensional affine subspace 61 can be exp The one-dimensional linear subspace 62 is changed according to the number of iterations of the loop related to the second condition within the range. For example, the one-dimensional affine subspace 61 is changed in a manner parallel to each coordinate axis of the two-dimensional space according to the number of iterations of the loop related to the second condition. Figure 8 In the case of the example, the one-dimensional affine subspace 61 before the change is parallel to the x0 axis corresponding to the one-dimensional x0 selected in step SA2, but in the case of repeating the loop related to the second condition, it can also be changed in a manner parallel to the x1 axis corresponding to the one-dimensional x1 selected in step SA2. In this way, the one-dimensional linear subspace 62 attached to the one-dimensional affine subspace 61 can also be changed alternately to the x0 axis and the x1 axis every time the loop related to the second condition is repeated. The search space determination unit 12 sets the one-dimensional affine subspace 61 after the change as the one-dimensional search space.

[0061] When D>r≥2 and the dimension of the affine subspace is 2 or more, for each iteration of the loop related to the second condition, the r-dimensional linear subspace attached to the r-dimensional affine subspace may be set so that it includes any r coordinate axes among the D coordinate axes that define the D-dimensional space. exp When it is not a zero vector, the r-dimensional affine partial space is parallel to the r coordinate axes.

[0062] When step SA3 is performed, the data acquisition unit 13 acquires a data set that is within a predetermined distance (threshold) from the r-dimensional search space (step SA4). Specifically, the data acquisition unit 13 selects a data set having a D-dimensional parameter value (D-dimensional parameter value near the search space) contained within a predetermined distance from the r-dimensional search space from among the multiple data sets contained in the data storage unit 11 and acquires it. Specifically, the data acquisition unit 13 calculates the distance between the D-dimensional parameter value and the r-dimensional search space for each of the N0 data sets, and determines the D-dimensional parameter value whose calculated distance is less than the predetermined distance. A data set containing the determined D-dimensional parameter value and the observation value corresponding to the D-dimensional parameter value is acquired from the data storage unit 11. Here, the data acquisition unit 13 may also acquire the r-dimensional parameter value from the determined D-dimensional parameter value. In this case, the data acquisition unit 13 may also store the data set related to the determined D-dimensional parameter value as Figure 6 The transformation is shown as r-dimensional parameter values ​​and data sets related to the r-dimensional parameter values. The threshold value of the distance does not need to be a fixed value, and can also be set to be variable. The threshold value of the distance can also be changed each time in the cycle related to the steps SA11 and SA12 described later. It can also be changed according to the number of repetitions of the cycle. It can also be that the more the number of repetitions, the smaller the threshold value is set.

[0063] N represents the number of data sets acquired by the data acquisition unit 13. n ,y n )|n=0,1,…,N-1} represents N data sets. The number N0 of data sets stored in the data storage unit 11 increases by repeating the loop related to the first condition and the loop related to the second condition, so the value of the number N changes according to the repetition of the loop related to the first condition and the loop related to the second condition.

[0064] When step SA4 is performed, the data acquisition unit 13 determines whether one or more data sets have been acquired from the data storage unit 11 in step SA4 (step SA5 ).

[0065] When it is determined in step SA5 that more than one data set is obtained (step SA5: Yes), the parameter search unit 14 generates a proxy model of the objective function based on the more than one data set (step SA6). As described above, in step SA6, the parameter search unit 14 models the objective function by Gaussian process regression as an example. When the parameter value of the data set obtained in step SA4 is a D-dimensional parameter value, the objective function is modeled as a function of the D-dimensional parameter. When the parameter value of the data set obtained in step SA4 is an r-dimensional parameter value, the objective function is modeled as a function of the r-dimensional parameter.

[0066] When step SA6 is performed, the parameter search unit 14 uses the surrogate model to search for a D-dimensional parameter value x that is likely to minimize the observed value of the objective function in the r-dimensional search space. next Or the r-dimensional parameter value x r next (Step SA7) When the target function is modeled as a function of a D-dimensional parameter, the D-dimensional parameter value x is searched. next , when the objective function is modeled as a function of r-dimensional parameters, search for the r-dimensional parameter value x r next .

[0067] Here, step SA6 and step SA7 are described in detail. In generating the proxy model of the objective function, Gaussian process regression may be used, or other proxy models such as TPE (Tree-structured Parzen Estimator) and random forest regression may be used.

[0068] In the case of Bayesian optimization, Gaussian process regression as a function of D-dimensional parameters can be used. In this case, the parameter search unit 14 calculates the N data sets {(x n ,y n )|n=0,1,…,N-1}, as a proxy model of the objective function, a Gaussian process regression model is generated. Next, the parameter search unit 14 uses the Gaussian process regression model to calculate the probability that the Gaussian process regression model corresponds to an arbitrary D-dimensional parameter value x ＊ The corresponding observed value y of the objective function ＊ The mean value m(x ＊ ) and standard deviation σ(x ＊ ). The parameter search unit 14 calculates the average value m(x ＊ ) and standard deviation σ(x ＊ )Calculate the function a(x ＊ ). The parameter search unit 14 will obtain the function a(x ＊ )The maximum D-dimensional parameter value x next The D-dimensional parameter value x is determined by limiting the search space to r dimensions. next The D-dimensional parameter value is determined to have a high probability of minimizing the observed value of the objective function.

[0069] When the parameter value acquired from the data acquisition unit 13 is r-dimensional, when the Gaussian process regression model is used, it is possible to calculate the relationship between the parameter value x and any r-dimensional parameter value x. r ＊ The corresponding observed value y of the objective function ＊ The mean m of the predicted distribution r (x r＊ ) and standard deviation σ r (x r ＊ ). Then, find the average value m in the r-dimensional search space. r (x r ＊ ) and standard deviation σ r (x r ＊ ) Calculate the obtained function a r (x r ＊ )The largest r-dimensional parameter value x r next , the r-dimensional parameter value x r next The r-dimensional parameter value is set to have a high probability of minimizing the observed value of the objective function. When compared with the formula in the case where the parameter value obtained from the data acquisition unit 13 is D-dimensional, there is a difference between having and not having the superscript r. As a formula in the case of r-dimensional, the superscript r can be added to the formula in the case of D-dimensional, so in the following, the description of the case where the parameter value is r-dimensional may be partially omitted.

[0070] The acquisition function can be, for example, PI (Probability of Improvement) or EI (Expected Improvement). Alternatively, UCB (Upper Confidential Bound), TS (Thompson Sampling), ES (Entropy Search), or MI (Mutual Information) can be used. In addition, the D-dimensional parameter value x that maximizes the acquisition function can be obtained. next Methods for maximizing the function are known, such as full search, random search, grid search, Newton's method, L-BFGS, DIRECT, CMA-ES, multi-start local search, etc. The method for maximizing the function is not limited to these, and any method can be used.

[0071] Here, Gaussian process regression is described in detail. The N data sets acquired by the data acquisition unit 13 are set to {(x n ,y n )|n=0,1,…,N-1}. In Gaussian process regression, it is assumed that the vector {x n |n=0,1,…,N-1} corresponding to the observed value of the objective function {y n |n=0,1,…,N-1} follows the Gaussian distribution Norm(m,K+s 2I). m is the mean vector of N dimensions. The i-th component of m is modeled according to the mean function m0(x i ) to calculate. K represents all the input parameter values ​​x n The N×N matrix of covariance between K and (x i , x j ) components according to the kernel function k(x i , x j ) is calculated. The kernel function can also be, for example, a Gaussian kernel, a Matern kernel, or a linear kernel. s is the standard deviation of the noise component when observing the target function f(·). I is an N×N unit matrix. In addition, regarding m0, there are many cases where the data is properly processed and treated as a 0 vector. Therefore, in the following, it is assumed that the Gaussian distribution Norm(0, K+s 2 I) is modeled and explained.

[0072] When using a Gaussian process regression model to predict with any D-dimensional parameter value x ＊ The corresponding observed value y of the objective function ＊ In the case of a distribution of ＊ The mean value m(x ＊ ) According to m(x ＊ )=k(x ＊ , x 0:N－1 ) T (K+s 2 I) -1 y 0:N－1 Calculate, disperse σ 2 (x ＊ ) According to σ 2 (x ＊ )=k(x ＊ , x ＊ )-k(x ＊ , x 0:N－1 ) T (K+s 2 I) -1 k(x ＊ , x 0:N－1 ) calculation. It is known that in the observed value y ＊ K+s used in the calculation of the predictive distribution 2 The inverse matrix of I (K+s 2 I) -1 is an inverse matrix of N rows and N columns, and its order of computation is О(N 3 ). When the parameter value is r-dimensional, the order of the calculation amount is О(N 3On the other hand, when all the N0 data sets stored in the data storage unit 11 are used instead of the N data sets acquired by the data acquisition unit 13, the order of the amount of calculation of the corresponding inverse matrix is ​​О(N0 3 ).

[0073] As in the data acquisition unit 13 of the present embodiment, by selecting N data sets used in Gaussian process regression from the N0 data sets stored in the data storage unit 11, the number of data sets used for Gaussian process regression can be reduced to reduce K+s 2 The inverse matrix of I (K+s 2 I) -1 Thus, K+s can be solved. 2 The inverse matrix of I (K+s 2 I) -1 In addition, using a data set near the r-dimensional search space as a guideline for selecting a data set will prevent the deterioration of the search efficiency. In other words, through this embodiment, it is possible to simultaneously achieve the reduction of the amount of calculation and the suppression of the deterioration of the search efficiency.

[0074] When TPE is used instead of Gaussian process regression, in step SA2, the search space determination unit 12 sets r = 1. In step SA6, the parameter search unit 14 divides the data set into two groups, a group whose observed values ​​of the objective function are smaller than the threshold and a group whose observed values ​​are greater than the threshold, according to a predetermined threshold, and calculates the r-dimensional parameter values ​​x of the two groups by kernel density estimation. r The distribution of the group whose observed value of the objective function is smaller than the threshold is set to l(x r ), the distribution of the group whose observed value of the objective function is larger than the threshold is set to g(x r ). Distribution l(x r ) and distribution (x r ) corresponds to the surrogate model of the objective function.

[0075] Next, in step SA7, the parameter search unit 14 sets g(x r ) / l(x r )The smallest r-dimensional parameter value x r next The r-dimensional parameter value with the highest probability of minimizing the observed value of the objective function is determined. Even when TPE is used, the dataset used is limited to the dataset near the search space, so g(x r ) / l(x r ) etc. Prevent the degradation of search efficiency. Therefore, according to this embodiment, it is possible to simultaneously achieve the reduction of the amount of calculation and the suppression of the degradation of search efficiency.

[0076] When it is determined in step SA5 that at least one data set has not been acquired (step SA5: No), the data acquisition unit 13 acquires the D-dimensional parameter value x next (Step SA8 ). In step SA8 , the data acquisition unit 13 uses the D-dimensional parameter value x as the observation value for calculating the objective function. next For example, to obtain the D-dimensional parameter value x set in step SA2 exp The data acquisition unit 13 may also randomly generate a D-dimensional parameter value x from the r-dimensional search space. next In addition, the data acquisition unit 13 can also obtain the D-dimensional parameter value x next The same method is used to obtain the r-dimensional parameter value x r next .

[0077] When step SA7 or SA8 is performed, the observed value output device 3 outputs the D-dimensional parameter value x according to the D-dimensional parameter value x searched or acquired in step SA7 or SA8. next Output the observed value of the objective function (step SA9). Specifically, first, the data generation unit 15 outputs the D-dimensional parameter value x that is searched or acquired in step SA7 or SA8. next The data generation unit 15 notifies the observed value output device 3. When the r-dimensional parameter value x is searched or acquired in step SA7 or SA8, r next In the case of r next Transformed into D-dimensional parameter value x next , notifies the observed value output device 3. The observed value output device 3 uses the D-dimensional parameter value x next To perform simulations, experiments, or questionnaires, etc., the output is related to the D-dimensional parameter value x next The observed value of the corresponding objective function.

[0078] For example, the observation value output device 3 includes a simulator, an experimental device, and a transformation device. The simulator, the experimental device, and the transformation device are implemented by a computer. The simulator and the experimental device are based on the D-dimensional parameter value x next Conduct simulation, experiment or questionnaire survey, or obtain the results of simulation, experiment or questionnaire survey outside the observation value output device 3, and output the D-dimensional parameter value x next The conversion device obtains characteristic values ​​from the simulator and the experimental device, and converts the obtained characteristic values ​​into scalars. The characteristic values ​​converted into scalars are used as the D-dimensional parameter value x next The observed value y of the objective function next And it is sent to the data generation unit 15.

[0079] Furthermore, the simulator, the experimental device, and the conversion device may be realized by a single computer. In addition, any one of the simulator, the experimental device, and the conversion device may be embedded in the parameter optimization device 2A, for example, included in the data generation unit 15 .

[0080] When step SA9 is performed, the data storage unit 11 stores the D-dimensional parameter value x that is searched or acquired in step SA7 or SA8. next The data set of the observation values ​​outputted in step SA9 is stored in the data storage unit 11 (step SA10). Specifically, first, the data generation unit 15 stores the D-dimensional parameter value x searched or acquired in step SA7 or SA8. next The observed value y output in step SA9 next Combine to generate a data set (x next ,y next Then, the data storage unit 11 stores the generated data set (x next ,y next ).

[0081] When step SA10 is performed, the data acquisition unit 13 determines whether the first condition is satisfied (step SA11). The first condition stipulates the number of times the parameter search is repeated in the r-dimensional search space determined by the search space determination unit 12. Therefore, during this repetition, the r-dimensional search space does not change. Satisfying the first condition means, for example, that the number of times exceeds a predetermined number of times, the elapsed time exceeds a predetermined time, or the improvement in the observed value of the objective function is lower than a predetermined value. Alternatively, it can be a combination of these conditions.

[0082] If it is determined that the first condition is not satisfied (step SA11: No), the data acquisition unit 13 performs the processing of step SA4 on the same r-dimensional search space. Then, steps SA5 to SA11 are performed. Until it is determined that the first condition is satisfied in step SA11, the processing of steps SA4 to SA11 by the data storage unit 11, the data acquisition unit 13, the parameter search unit 14, and the data generation unit 15 is repeated, and the D-dimensional parameter value x is repeatedly performed on the same r-dimensional search space. next Search or obtain and include the D-dimensional parameter value x next and the observed value y next The dataset (x next ,y next ) is generated and stored. The series of processing from step SA4 to step SA11 can be executed in parallel by multiple tasks or can be executed serially. In this case, a data storage unit 11 is provided in each task, and multiple data sets (x next,y next ).

[0083] Then, when it is determined in step SA11 that the first condition is satisfied (step SA11: yes), the search space determination unit 12 determines whether the second condition is satisfied (step SA12). The second condition specifies the number of determinations of the r-dimensional search space based on the search space determination unit 12. The value of r can be a predetermined value or a randomly determined value. Satisfying the second condition means, for example, that the number of times exceeds a predetermined number of times, that the elapsed time exceeds a predetermined time, or that the improvement in the observed value of the objective function is less than a predetermined value. Alternatively, it can be a combination of these conditions.

[0084] If it is determined that the second condition is not satisfied (step SA12: No), the search space determination unit 12 selects a different r-dimensional parameter from the D-dimensional parameters (step SA2). In addition, the search space determination unit 12 obtains the D-dimensional parameter value x that minimizes the observed value of the objective function from the data set stored in the data storage unit 11. exp . The selection of the r-dimensional parameter can be done by selecting one in order from a plurality of groups when the D-dimensional parameter is pre-divided into a plurality of r-dimensional parameter groups as described above, or it can be randomly selected. In addition, the r-dimensional parameter can be randomly selected from the D-dimensional parameters. The value of r can also be randomly set within a range less than D. Thereafter, steps SA3 to SA12 are performed. Until it is determined in step SA12 that the second condition is satisfied, the processing of steps SA2 to SA12 of the data storage unit 11, the search space determination unit 12, the data acquisition unit 13, the parameter search unit 14, and the data generation unit 15 is repeated, while changing the r-dimensional parameter, that is, while changing the r-dimensional search space, the D-dimensional parameter value x is repeatedly performed. next Search or obtain and include the D-dimensional parameter value x next and the observed value y next The dataset (x next ,y next ) is generated and stored. The series of processing from step SA2 to step SA12 can be executed in parallel by multiple tasks or can be executed serially. In this case, a data storage unit 11 is provided in each task, and multiple data sets (x next ,y next ).

[0085] Furthermore, when a series of processes from step SA4 to step SA11 are executed in parallel or serially by a plurality of tasks, after determining that the first condition is satisfied and before performing the process of step SA2, the data generation unit 15 may acquire the D-dimensional parameter value that minimizes the observed value of the objective function from a plurality of data sets stored in the data storage unit 11 of each task. The acquired D-dimensional parameter value and the data set of the observed value corresponding to the D-dimensional parameter value are stored in the data storage unit 11 of each task.

[0086] Then, when it is determined in step SA12 that the second condition is satisfied (step SA12: Yes), the optimal parameter value acquisition unit 16 acquires the optimal parameter value x that minimizes the observed value of the objective function from the data set stored in the data storage unit 11. best (Step SA13). Optimal parameter value x best is output to an external device. In the case of the manufacturing stage, the optimal parameter value x best For example, it means the parameter value that maximizes the yield rate during manufacturing, and the parameter value that minimizes the failure rate after shipment. In the case of the utilization stage, the optimal parameter value x best For example, it means the parameter value that enables the device or component at the user's disposal to achieve the performance that suits the user's usage environment. best It can also be used for various purposes in an external device at the output destination. best It may also be stored in the data storage unit 11 or displayed on a display device.

[0087] In addition, when the series of processing from step SA2 to step SA12 is executed in parallel or serially by a plurality of tasks, after determining that the second condition is satisfied, the optimal parameter value acquisition unit 16 may acquire the optimal parameter value x that minimizes the observed value of the objective function from among the plurality of data sets stored in the data storage unit 11 of each task. best .

[0088] Based on the above, the processing operation of the parameter optimization system 1 according to the first embodiment is completed.

[0089] As described above, according to the first embodiment, the data set used in the calculation of the proxy model is limited to the data set near the search space, so the amount of calculation of the proxy model can be reduced compared to the past. In addition, as the data set used in the calculation of the proxy model, a data set with a relatively short distance from the search space is used, thereby preventing the parameter value x from being too large. next That is, it is possible to simultaneously reduce the amount of calculation and suppress the degradation of search efficiency. The optimal parameter value x best The search efficiency, in other words, the efficiency of parameter optimization is improved.

[0090] (Second embodiment)

[0091] Next, a parameter optimization system 1 and a parameter optimization device 2B according to a second embodiment will be described. In the following description, components having substantially the same functions as those of the first embodiment are denoted by the same reference numerals, and repeated description will be given only when necessary.

[0092] Fig. 9 1 is a diagram showing an example of a functional configuration of a parameter optimization system 1 according to a second embodiment. Fig. 9 As shown, the parameter optimization system 1 of the second embodiment includes a parameter optimization device 2B and an observation value output device 3 .

[0093] The parameter optimization device 2B has a data storage unit 11, a search space determination unit 12, a data acquisition unit 13, a parameter search unit 14, a data generation unit 15, an optimal parameter value acquisition unit 16, a dimension acquisition unit 17, a distance acquisition unit 18, a threshold acquisition unit 19, a display unit 20 and an external data acquisition unit 21.

[0094] The dimension acquisition unit 17 acquires the dimension r input by the user via an input device, etc. For example, the dimension acquisition unit 17 acquires the dimension r input to a GUI (Graphical User Interface) screen (hereinafter referred to as dimension input screen) displayed on the display unit 20 for inputting the dimension r.

[0095] The distance acquisition unit 18 acquires the type of distance input by the user via an input device, etc. For example, the distance acquisition unit 18 acquires the type of distance input into a GUI screen for inputting the type of distance displayed on the display unit 20 (hereinafter referred to as a distance type input screen).

[0096] The threshold acquisition unit 19 acquires a threshold for the distance from the r-dimensional search space input by the user via an input device, etc. For example, the threshold acquisition unit 19 acquires a threshold input to a GUI screen for inputting a threshold displayed on the display unit 20 (hereinafter referred to as a threshold input screen).

[0097] The display unit 20 displays a dimension input screen, a distance type input screen, a threshold input screen, etc. on a display device. The display device may be realized by, for example, a display or a projector.

[0098] The external data acquisition unit 21 acquires a plurality of data sets from a device external to the parameter optimization device 1B.

[0099] Next, refer to Fig.10 , the processing operation of the parameter optimization system 1 having the parameter optimization device 2B according to the second embodiment is described. Fig.10This is a flowchart showing an example of the processing operation of the parameter optimization system 1 according to the second embodiment.

[0100] like Fig.10 As shown, the dimension acquisition unit 17, the distance acquisition unit 18 and / or the threshold acquisition unit 19 acquire various setting values ​​according to the instruction from the user via the input device (step SB1). The setting value is a general term for the dimension r, the type of distance and the threshold.

[0101] In step SB1, dimension acquisition unit 17 receives an instruction regarding the dimension from the user and supplies it to search space determination unit 12 and display unit 20. For example, dimension acquisition unit 17 receives an input instruction regarding the dimension from the user on a dimension acquisition screen displayed on display unit 20.

[0102] Fig.11 FIG. 1 is a diagram showing an example of the dimension acquisition screen I1. Fig.11 As shown, the dimension acquisition screen I1 displays a message urging the input of the dimension r, such as "Please input the dimension r of the search space", a display bar I11 for the dimension r, and up and down buttons I12. The display bar I11 displays the numerical value of the dimension r specified by the user. The up and down buttons I12 are pressed by the user via the input device to increase or decrease the numerical value of the dimension r. When the up and down buttons I12 are pressed, the display unit 20 increases or decreases the numerical value of the dimension r displayed in the display bar I11 by a predetermined value. The numerical value displayed on the display unit 20 is accepted by the dimension acquisition unit 17 as an input instruction of the dimension.

[0103] also, Fig.11 The dimension acquisition screen I1 shown is an example and can be modified in various ways. For example, a text box for the user to directly input the numerical value of the dimension r via an input device may be displayed on the dimension acquisition screen I1. The user inputs the numerical value representing the dimension in the text box, and an indication of the dimension accepted by the dimension acquisition unit 17 is output. In the present embodiment, it is assumed that r is an integer value greater than 1 and less than D, so the dimension acquisition unit 17 may also limit the input value so that a numerical value less than 1 or greater than D or a decimal cannot be input. In addition, the dimension acquisition unit 17 may also display an error on the display unit 20 when a numerical value less than 1 or greater than D or a decimal is input.

[0104] The user is not required to input the dimension. If there is no input instruction of the dimension from the user, the dimension acquisition unit 17 supplies the default value of the dimension to the search space determination unit 12 and the display unit 20. The default value may be set to "1", for example. The default value may also be displayed in a text box.

[0105] In step SB1, distance acquisition unit 18 receives an instruction regarding the type of distance from the user and supplies it to search space determination unit 12 and display unit 20. For example, distance acquisition unit 18 receives an input instruction regarding the type of distance from the user on a distance type input screen displayed on display unit 20.

[0106] Fig.12 FIG. 1 is a diagram showing an example of the distance type input screen I2. Fig.12 As shown, on the distance type input screen 12, a message urging input of the distance type such as "Please select the distance type", a candidate display column 121 for the distance type, and a selection button 122 are displayed. In the candidate display column 121, for example, Euclidean distance, Manhattan distance, cosine distance, Mahalanobis distance, etc. are displayed. The selection button 122 is provided corresponding to each of the plurality of candidates displayed in the candidate display column 121. When the user presses the selection button 122 via an input device such as a mouse, the corresponding distance type is accepted by the distance acquisition unit 18 as an input instruction of the distance type.

[0107] also, Fig.12 The distance type input screen I2 shown is an example and can be modified in various ways. For example, a text box for the user to directly input the type of distance via an input device may be displayed on the distance type input screen I2. The user inputs a character string representing the type of distance in the text box, thereby outputting an indication of the type of distance accepted by the distance acquisition unit 18.

[0108] The input indication of the type of distance by the user is not necessary. In the absence of the input indication of the type of distance by the user, the distance acquisition unit 18 supplies the default value of the type of distance to the data acquisition unit 13 and the display unit 20. The default value can be set to Euclidean distance, for example. However, the default value can also be set to Manhattan distance, cosine distance, or Mahalanobis distance. There are cases where the units, scales, and domains of the parameters of the D types are different, and where the Mahalanobis distance is effective. Regarding the distance scale of the kernel function used in Gaussian process regression, Manhattan distance, cosine distance, or Mahalanobis distance can be used instead of Euclidean distance.

[0109] In step SB1, the threshold acquisition unit 19 receives an instruction about the threshold from the user and supplies it to the data acquisition unit 13 and the display unit 20. The threshold acquired by the threshold acquisition unit 19 is a threshold for the distance from the search space. For example, the threshold acquisition unit 19 receives an input instruction of the threshold from the user on the threshold input screen displayed on the display unit 20.

[0110] Fig.13 1 is a diagram showing an example of a threshold value input screen I3. Fig.13As shown, on the threshold input screen I3, a message urging the input of the threshold such as "Please input the threshold for the distance from the search space", a threshold display bar I31, and up and down buttons I32 are displayed. The display bar I31 displays the numerical value of the threshold d specified by the user. The up and down buttons I32 are pressed by the user via the input device to increase or decrease the numerical value of the threshold d. By pressing the up and down buttons I32, the display unit 20 increases or decreases the numerical value of the threshold d displayed in the display bar I31 by a predetermined value. The numerical value displayed on the display unit 20 is accepted by the dimension acquisition unit 17 as an input instruction of the threshold d.

[0111] also, Fig.13 The threshold input screen I3 shown is an example and can be modified in various ways. For example, a text box for the user to directly input the numerical value of the threshold d via an input device can also be displayed on the threshold input screen I3. The user enters the numerical value representing the threshold d in the text box, and an indication of the threshold d accepted by the threshold acquisition unit 19 is output. The threshold d envisioned in this embodiment is a decimal greater than 0.0, so the threshold acquisition unit 19 can also limit the input value so that a negative value cannot be input. In addition, the threshold acquisition unit 19 can also display an error on the display unit 20 when a negative value is input.

[0112] The input indication of the threshold value by the user is not necessary. In the absence of an input indication of the threshold value from the user, the threshold acquisition unit 19 supplies the default value of the threshold value to the search space determination unit 12 and the display unit 20. The default value can be set to "0.0" or any positive value, for example. The default value can also be displayed in a text box. In the absence of an input indication of the threshold value from the user, the threshold value maintains the default value without being set to a fixed value, and can also be changed automatically. The threshold value can also be changed each time in the loop related to steps SB10, SB11, and SB12 described later. It can also be changed according to the number of repetitions of the loop. The more repetitions there are, the smaller the threshold value can be set.

[0113] When step SB1 is performed, the external data acquisition unit 21 acquires N0 data sets {(x n ,y n )|n=0, 1, . . . , N0-1} (step SB2 ). In this way, the results of past simulations, experiments, questionnaire surveys, etc. are acquired. The acquired N0 data sets are stored in the data storage unit 11 .

[0114] After step SB2 is performed, the search space determination unit 12 sets the parameter value x exp (Step SB3). Parameter value x exp It is set to the D-dimensional parameter value corresponding to the smallest observation value among the N0 data sets stored in the data storage unit 11 .

[0115] After step SB3 is performed, the search space determination unit 12 selects an r-dimensional parameter smaller than the D dimension (step SB4). Step SB4 is substantially the same as step SA3. The dimension r is the dimension acquired by the dimension acquisition unit 17 in step SB1.

[0116] When step SB4 is performed, the data acquisition unit 13 acquires a data set within a predetermined distance from the r-dimensional search space (step SB5). Step SB5 is substantially the same as step SA4. In addition, the type of distance uses the type of distance acquired by the distance acquisition unit 18 in step SB1. The threshold value uses the threshold value acquired by the threshold value acquisition unit 19 in step SB1. n ,y n )|n=0, 1, ..., N-1} represents the acquired N data sets. The value of N changes in accordance with the repetition of the loop related to the first condition.

[0117] After step SB5 is performed, the parameter search unit 14 generates a proxy model of the target function based on one or more data sets (step SB6). Step SB6 is substantially the same as step SA6.

[0118] When step SB6 is performed, the parameter search unit 14 searches the r-dimensional search space using the surrogate model and determines a parameter value x that is likely to minimize the observed value of the objective function. next (Step SB7 ) Step SB7 is substantially the same as step SA7 .

[0119] When step SB7 is performed, the observed value output device 3 outputs the D-dimensional parameter value x determined in step SB7. next Output the observed value y of the objective function next (Step SB8 ) Step SB8 is substantially the same as step SA9 .

[0120] When step SB8 is performed, the data storage unit 11 stores the D-dimensional parameter value x determined in step SB7. next and the observed value y output in step SB8 next The dataset (x next ,y next ) is stored in the data storage unit 11 (step SB9). Step SB9 is substantially the same as step SA10.

[0121] When step SB9 is performed, the data acquisition unit 13 determines whether the first condition is satisfied (step SB10 ). The first condition related to the second embodiment is defined as the number of repetitions of the loop related to the first condition reaching a predetermined number of times.

[0122] If it is determined that the first condition is not satisfied (step SB10: No), steps SB5 to SB10 are performed. Until it is determined that the first condition is satisfied in step SB10, the processing of steps SB5 to SB10 of the data storage unit 11, the data acquisition unit 13, the parameter search unit 14, and the data generation unit 15 is repeated, and the D-dimensional parameter value x is repeatedly searched for the same r-dimensional search space. next Search or obtain and include the D-dimensional parameter value x next and the observed value y next The dataset (x next ,y next ) is generated.

[0123] Then, when it is determined in step SB10 that the first condition is satisfied (step SB10: Yes), the search space determination unit 12 determines whether the second condition is satisfied (step SB11). The second condition related to the second embodiment is defined as the number of iterations of the loop related to the second condition reaching a predetermined number of times.

[0124] If it is determined that the second condition is not satisfied (step SB11: No), steps SB3 to SB11 are performed. The processing of steps SB3 to SB11 of the data storage unit 11, the search space determination unit 12, the data acquisition unit 13, the parameter search unit 14, and the data generation unit 15 is repeated until it is determined that the second condition is satisfied in step SB11. Thus, the D-dimensional parameter value x of the specified search space is changed. exp and the r-dimensional search space containing the parameter value, while repeatedly performing the D-dimensional parameter value x next Search or obtain and include the D-dimensional parameter value x next and the observed value y next The dataset (x next ,y next ) is generated.

[0125] When it is determined in step SB11 that the second condition is satisfied (step SB11: Yes), the search space determination unit 12 determines whether the third condition is satisfied (step SB12). The third condition is, for example, a condition for the number of repetitions of steps SB3 to SB12. Specifically, it is specified that the number of repetitions reaches a predetermined number. The predetermined number is set to an integer greater than 1.

[0126] If it is determined that the third condition is not satisfied (step SB12: No), steps SB3 to SB12 are performed. The processing of steps SB3 to SB12 of the data storage unit 11, the search space determination unit 12, the data acquisition unit 13, the parameter search unit 14, and the data generation unit 15 is repeated until it is determined that the third condition is satisfied in step SB12. Thus, the D-dimensional parameter value x of the specified search space is changed. exp and the r-dimensional search space containing the parameter value, while repeatedly performing the D-dimensional parameter value x next Search or obtain and include the D-dimensional parameter value x next and the observed value y next The dataset (x next ,y next ) is generated.

[0127] Then, when it is determined in step SB12 that the third condition is satisfied (step SB12: Yes), the optimal parameter value acquisition unit 16 acquires the optimal parameter value x that minimizes the observed value of the objective function from the data set stored in the data storage unit 11. best (Step SB13). Optimal parameter value x best Output to an external device.

[0128] Based on the above, the processing operation of the parameter optimization system 1 according to the second embodiment is completed.

[0129] As described above, according to the second embodiment, as in the first embodiment, the data set used in the calculation of the proxy model is limited to the data set near the search space, so the amount of calculation of the proxy model can be reduced compared to the past. In addition, the data set used in the calculation of the proxy model is used to make use of the data set that is relatively close to the search space, thereby preventing the parameter value x from being too large. next That is, it is possible to simultaneously reduce the amount of calculation and suppress the degradation of search efficiency. The optimal parameter value x best The search efficiency, in other words, the efficiency of parameter optimization is improved.

[0130] Furthermore, according to the second embodiment, setting items such as the dimension, the type of distance, and the threshold value can be set according to the user's instruction using a GUI, etc. Therefore, parameter optimization can be performed efficiently using the user's knowledge.

[0131] (Variation Example)

[0132] Hereinafter, some modified examples of the first embodiment and / or the second embodiment will be described. In the following description, components having substantially the same functions as those of the present embodiment are denoted by the same reference numerals, and repeated description will be given only when necessary.

[0133] (Variant 1)

[0134] In the above embodiment, the data acquisition unit 13 acquires a data set near the search space from the database stored in the data storage unit 11. The data acquisition unit 13 of the modification 1 randomly generates D-dimensional parameter values ​​near the search space. The generated D-dimensional parameter values ​​are supplied to the data generation unit 15. R represents the number of randomly generated D-dimensional parameter values. Here, R is an integer greater than 1. rand,i |i=0, 1, ..., R-1} represents the generated R random D-dimensional parameter values.

[0135] The data generation unit 15 converts the D-dimensional parameter value {x rand,i |i=0, 1, …, R-1} is sent to the observation value output device 3.

[0136] Next, for example, a simulator and an experimental device as an example of a component of the observation value output device 3 are used to calculate the R D-dimensional parameter values ​​{x rand,i |i=0,1,…,R-1} respectively implement simulation, experiment or questionnaire survey, about {x rand,i |i=0,1,…,R-1}, outputs characteristic values ​​for one or more items. A conversion device, which is an example of a component of the observation value output device 3, obtains one or more characteristic values ​​and converts them into scalars. The characteristic values ​​converted into scalars are used as the D-dimensional parameter value {x rand,i |i=0,1,…,R-1}corresponding to the observed value of the objective function {y rand,i |i=0,1,…,R-1} and output. rand,i |i=0, 1, . . . , R−1} is sent to the data generating unit 15 .

[0137] The data generation unit 15 converts the data set {(x rand,i ,y rand,i )|i=0, 1, ..., R-1} is supplied to the data storage unit 11, and the data storage unit 11 stores the data set {(x rand,i ,y rand,i )|i=0,1,…,R-1}.

[0138] Finally, the data acquisition unit 13 acquires a data set having a D-dimensional parameter value whose distance to the search space is equal to or smaller than a threshold value as an element from the data stored in the data storage unit 11 .

[0139] In the N data sets obtained in this way {(x n ,y n )|n=0,1,…,N-1}, including {(x rand,i ,y rand,i)|i=0,1,…,R-1}. That is, in addition to acquiring a data set having a D-dimensional parameter value whose distance to the search space is less than a threshold value as an element from the data stored in the data storage unit 11, the data acquisition unit 13 may randomly generate a D-dimensional parameter value whose distance to the search space is less than the threshold value, and acquire a data set including the D-dimensional parameter value and the observation value of the objective function corresponding to the D-dimensional parameter value.

[0140] Thus, Gaussian process regression is not required, and D-dimensional parameter values ​​whose distance to the search space is less than or equal to the threshold value can be simply added. Since Gaussian process regression is not required, calculation of the inverse matrix is ​​also not required.

[0141] (Variant 2)

[0142] Regarding the second embodiment, the timing at which the dimension acquisition unit 17 , the distance acquisition unit 18 , and the threshold acquisition unit 19 operate may be different from the timing at step SB1 .

[0143] The dimension r acquired by the dimension acquisition unit 17 is used in the search space determination unit 12. That is, the dimension acquisition unit 17 may operate before the search space determination unit 12 operates.

[0144] The type of distance acquired by the distance acquisition unit 18 is used by the data acquisition unit 13. That is, the distance acquisition unit 18 may be operated before the data acquisition unit 13 is operated.

[0145] The threshold value acquired by the threshold value acquisition unit 19 is used in the data acquisition unit 13. That is, the threshold value acquisition unit 19 may be operated before the data acquisition unit 13 is operated.

[0146] For each iteration of the loop related to the first condition, the second condition, and the third condition, the dimension acquisition unit 17, the distance acquisition unit 18, and the threshold acquisition unit 19 may be operated at a timing at which the dimension, the type of distance, and the threshold can be changed.

[0147] Thereby, it is possible to accept instructions from the user at various timings, and to change the dimension, the type of distance, and the threshold at various timings.

[0148] (Variant 3)

[0149] In the description of the first and second embodiments above, Figure 3 , 4 , 5, 6, and 8 show that the r-dimensional affine partial space set as the search space is passed through x expAn example of controlling the 1-dimensional affine subspace of the D-dimensional space in a manner parallel to different coordinate axes of the D-dimensional space according to the number of repetitions of the loop related to the second condition and / or the third condition. In this example, r is limited to 1, and the r-dimensional linear subspace attached to the r-dimensional affine subspace is controlled so as to include an arbitrary coordinate axis. However, the control method of the r-dimensional affine subspace set as the search space is not limited to this.

[0150] The r-dimensional affine partial space as the search space is determined according to the dimension r and the r-dimensional linear partial space attached to the r-dimensional affine partial space. Therefore, the r-dimensional affine partial space set as the search space can be controlled by controlling r and the r-dimensional linear partial space. In this variant, r is not limited to 1, and r can also be changed in the range of integers greater than 1 in the loop related to the second condition and the third condition. r can be changed in the loop related to the second condition and the third condition according to the rules corresponding to the predetermined order and the number of repetitions, or it can be changed randomly. In addition, the r-dimensional linear partial space attached to the r-dimensional affine partial space is not limited to containing arbitrary coordinate axes, and it can also be changed in the loop related to the second condition and the third condition. The r-dimensional linear partial space can be changed in the loop related to the second condition and the third condition according to the rules corresponding to the predetermined order and the number of repetitions, or it can be changed randomly.

[0151] For example, when r is set to 1 at a certain time point, the r(=1)-dimensional affine subspace can be controlled to be a straight line, and when r is set to 2 at another time point, the r(=2)-dimensional affine subspace can be controlled to be a plane. When r is 1, as long as the r(=1)-dimensional linear subspace attached to the r(=1)-dimensional affine subspace is set so as not to include any coordinate axis, the r(=1)-dimensional affine subspace can be controlled to pass through x. exp When r is 1, the r(=1)-dimensional linear subspace attached to the r(=1)-dimensional affine subspace can be controlled to pass through x. exp When r is 2, the r(=2)-dimensional linear subspace attached to the r(=2)-dimensional affine subspace can be controlled to pass through x. exp When r is 2, the r(=2)-dimensional linear subspace attached to the r(=2)-dimensional affine subspace can be controlled to pass through x. expWhen r is 2, the r(=2)-dimensional linear subspace attached to the r(=2)-dimensional affine subspace can be controlled to pass through x. exp A plane parallel to these two coordinate axes.

[0152] In addition, when the r-dimensional linear subspace attached to the r-dimensional affine subspace does not include r coordinate axes, the search space determination unit 12 does not determine the r-dimensional affine subspace by selecting an r-dimensional parameter smaller than D dimensions in step SA3 or step SB4, but determines it as described above. If the r-dimensional affine subspace as the search space is determined, then in step SA4 or step SB5, the data acquisition unit 13 calculates the projection length of the D-dimensional parameter value to the r-dimensional affine subspace as the distance between the D-dimensional parameter value and the r-dimensional affine subspace.

[0153] (Variant 4)

[0154] The D-dimensional parameter value can also be normalized or denormalized by the parameter optimization devices 2A and 2B.

[0155] There are many cases where the units, scales, and domains of the D types of parameters to be adjusted are different. Therefore, the parameter values ​​can also be normalized by the parameter optimization devices 2A and 2B so that the domain is, for example, 0 to 1, or the normalized parameters can be inversely normalized in order to restore the original domain. Normalization can be performed by a normalization unit, and inverse normalization can be performed by an inverse normalization unit. In the case of normalization, the normalization unit can be set in the parameter optimization devices 2A and 2B, and in the case of inverse normalization, the inverse normalization unit can be set in the parameter optimization devices 2A and 2B. As a result, it is easy to simultaneously process D types of parameters with different units, scales, and domains.

[0156] In addition, normalization and / or inverse normalization may be performed outside the parameter optimization devices 2A, 2B such as the observation value output device 3 or other devices.

[0157] (Variant 5)

[0158] The second condition of the first embodiment and the third condition of the second embodiment may also be changed to a condition of whether the absolute value (improvement amount) of the difference between the observed value of the objective function corresponding to the optimal parameter value obtained by the optimal parameter value acquisition unit 16 through the current iterative process and the observed value of the objective function corresponding to the optimal parameter value obtained through the iterative process just before is less than a predetermined threshold value. The observed value of the objective function corresponding to the optimal parameter value may be obtained by acquiring the value stored in the data storage unit 11.

[0159] This allows the process to be terminated at a timing when the amount of improvement in the optimal parameter value based on the iterative process becomes small. Therefore, the optimal parameter value can be efficiently searched.

[0160] (Variant 6)

[0161] In this embodiment, in order to optimize the D-dimensional parameter value, the search space is set to the r-dimensional affine subspace. Any D-dimensional parameter value belonging to the r-dimensional affine subspace can be expressed by an r-dimensional vector, and the r-dimensional vector can be inversely transformed into the original D-dimensional vector without degradation. When the threshold value of the distance is 0, the D-dimensional parameter value acquired by the data acquisition unit 13 belongs to the r-dimensional affine subspace. Therefore, when the threshold value is 0, the parameter search unit 15 of the modification example 6 performs the following processing as steps SA6 and SA7 and steps SB6 and SB7.

[0162] The parameter search unit 15 of the modification example 6 takes the D-dimensional parameter value x belonging to the r-dimensional affine subspace as n (n=0, 1, ..., N-1) is transformed into r-dimensional parameter value x r n (n=0, 1, ..., N-1). According to N data sets {(x r n ,y n )|n=0,1,…,N-1} to generate a Gaussian process regression model. Next, the Gaussian process regression model is used to calculate the value of the arbitrary r-dimensional parameter x r The value of the objective function h(x r ) average m r (x r ) and standard deviation σ r (x r Here, the objective function h(·) is about the r-dimensional parameter value x after all D-dimensional parameter values ​​x belonging to the r-dimensional affine subspace are transformed into r-dimensional vectors. r Satisfy h(x r )=f(x). Use m r (x r ) and σ r (x r ), find the value of the r-dimensional parameter x r The related acquisition function a r (x r )The largest x r As a method of obtaining a function or maximizing a function, any method may be used. r The result of the transformation to the D-dimensional parameter value is set to x next The x next belongs to the r-dimensional affine partial space, i.e., the search space. nextSupplied to the data generating unit 15.

[0163] As a result, the dimension of the parameters processed in the Gaussian process regression is reduced from D to r. In addition, the dimension of the parameters of the kernel function used in the Gaussian process regression and the dimension of the parameters processed in the acquisition function are also reduced from D to r. This can reduce the amount of calculation. In addition, when the threshold of the distance is a positive value, the D-dimensional parameter value obtained by the data acquisition unit 13 does not belong to the r-dimensional affine partial space, but the distance is below the threshold and is not far. Therefore, the D-dimensional parameter value obtained by the data acquisition unit 13 can also be projected to the r-dimensional affine partial space and processed in the same way as when the threshold is 0. Although there is degradation during the inverse transformation, the degradation error is not large, so the same effect as when the threshold is 0 can be obtained.

[0164] (Variant 7)

[0165] In the first and second embodiments, the parameter optimization devices 2A and 2B and the observation value output device 3 are different computers. The observation value output device 3 of Modification 7 is embedded in the parameter optimization devices 2A and 2B. Thus, the parameters can be automatically optimized by a single device.

[0166] (Variant 8)

[0167] The respective examples of the first embodiment, the second embodiment, Modification 1, Modification 2, Modification 3, Modification 4, Modification 5, Modification 6, and Modification 7 can be arbitrarily combined.

[0168] (Hardware Structure)

[0169] Fig.14 2A and 2B are diagrams showing an example of the hardware configuration of the parameter optimization devices 2A and 2B. Fig.14 As shown, the parameter optimization devices 2A and 2B include a processing circuit 91, a main storage device 92, an auxiliary storage device 93, a display device 94, an input device 95, and a communication device 96. The processing circuit 91, the main storage device 92, the auxiliary storage device 93, the display device 94, the input device 95, and the communication device 96 are connected via a bus.

[0170] The processing circuit 91 executes the parameter optimization program read from the auxiliary storage device 93 to the main storage device 92, and functions as a search space determination unit 12, a data acquisition unit 13, a parameter search unit 14, a data generation unit 15, an optimal parameter value acquisition unit 16, a dimension acquisition unit 17, a distance acquisition unit 18, a threshold acquisition unit 19, and an external data acquisition unit 21. The main storage device 92 is a memory such as a RAM (Random Access Memory). The auxiliary storage device 13 is a HDD (Hard Disk Drive), an SSD (Solid State Drive), a memory card, etc. The main storage device 92 and the auxiliary storage device 93 function as a data storage unit 11.

[0171] The display device 94 displays various display information. The display device 94 is, for example, a display, a projector, etc. The display device 94 functions as the display unit 20.

[0172] The input device 95 is an interface for operating the computer. The input device 95 is, for example, a keyboard, a mouse, etc. The display device 94 and the input device 95 may also be formed by a touch panel. The communication device 96 is an interface for communicating with other devices such as the observation value output device 3.

[0173] The program executed by the computer is recorded in an installable or executable file on a computer-readable storage medium such as a CD-ROM, memory card, CD-R, or DVD (Digital Versatile Disc) and provided as a computer program product.

[0174] The program executed by the computer may be stored in a computer connected to a network such as the Internet and provided by downloading it via the network. Alternatively, the program executed by the computer may be provided via a network such as the Internet without downloading it.

[0175] It is also possible to configure such that a program executed by a computer is provided by pre-compilation in a ROM or the like. The program executed by a computer is a module structure including a function block that can be realized by a program in the functional structure (function block) of the parameter optimization device 2A, 2B. Each function block is read out from a storage medium by the processing circuit 91 as actual hardware and executed, so that each function block is loaded into the main storage device 92. That is, each function block is generated on the main storage device 92.

[0176] Instead of implementing part or all of the above functional blocks by software, they may be implemented by hardware such as IC (Integrated Circuit). When multiple processors are used to implement each function, each processor may implement one function or two or more functions of each function.

[0177] The operation mode of the computer realizing the parameter optimization devices 2A and 2B may be any mode. For example, the parameter optimization devices 2A and 2B may be realized by one computer. In addition, for example, the parameter optimization devices 2A and 2B may be operated as a cloud system on the network.

[0178] (P.S.)

[0179] As described above, the parameter optimization devices 2A and 2B include a data storage unit 11, a search space determination unit 12, a data acquisition unit 13, and a parameter search unit 14. The data storage unit 11 stores a plurality of data sets including D-dimensional parameter values ​​of the first dimension D and observation values ​​of the objective function corresponding to the D-dimensional parameter values. The search space determination unit 12 determines an r-dimensional search space smaller than the D dimension including a predetermined D-dimensional parameter value. The data acquisition unit 13 acquires one or more data sets having D-dimensional parameter values ​​included in a predetermined distance d from the r-dimensional search space or a data set having r-dimensional parameter values ​​corresponding to the data set based on the plurality of data sets. The parameter search unit 14 uses a proxy model of the objective function based on the acquired one or more data sets to search for a D-dimensional parameter value or an r-dimensional parameter value that can optimize the objective function in the r-dimensional search space.

[0180] In the case of the first embodiment, the predetermined D-dimensional parameter value is the default value or random value set in step SA1 in the first loop, and after the second loop, it is the D-dimensional parameter value corresponding to the minimum observed value among the multiple data sets stored in the data storage unit 11 acquired in step SA2. In the case of the second embodiment, it is the D-dimensional parameter value corresponding to the minimum observed value among the multiple data sets stored in the data storage unit 11 set in step SB3.

[0181] According to the above configuration, in the search for the D-dimensional parameter value that can optimize the objective function, not all the data sets of the data storage unit 11 are used, but the data set having the D-dimensional parameter value included in the distance d from the r-dimensional search space or the data set having the r-dimensional parameter value corresponding to the data set is used, thereby reducing the amount of calculation related to the search compared to the case where the data acquisition unit 13 is not provided. In addition, by using the data set close to the r-dimensional search space as described above, the deterioration of the search efficiency associated with the reduction in the number of data sets can be suppressed. That is, according to this embodiment, the reduction of the amount of calculation and the suppression of the deterioration of the search efficiency can be achieved at the same time.

[0182] As described above, according to the present embodiment, it is possible to efficiently search for optimal parameters.

[0183] Several embodiments of the present invention are described, but these embodiments are presented as examples and are not intended to limit the scope of the invention. These new embodiments can be implemented in various other ways, and various omissions, substitutions, and changes can be made without departing from the gist of the invention. These embodiments and their variations are included in the scope and gist of the invention, and are included in the invention described in the patent claims and the scope equivalent thereto.

Claims

1. A parameter optimization device, comprising: a storage unit storing a plurality of data sets including first parameter values ​​of a first dimension and observation values ​​of an objective function corresponding to the first parameter values; A search space determination unit determines a search space having a second dimension smaller than the first dimension and including a predetermined first parameter value; A first acquisition unit acquires, based on the plurality of data sets, one or more data sets having a first parameter value included within a predetermined distance from the search space or one or more data sets having a second parameter value of the second dimension corresponding to the data set; A parameter search unit searches for a first parameter value or a second parameter value that can optimize the objective function in the search space using a proxy model of the objective function based on the one or more acquired data sets.

2. The parameter optimization device according to claim 1, wherein: The parameter optimization device further includes a generating unit, which generates a data set including an observed value of the objective function corresponding to the searched first parameter value or an observed value of the objective function corresponding to the first parameter value corresponding to the searched second parameter value and the searched first parameter value or second parameter value. The storage unit stores the generated data set.

3. The parameter optimization device according to claim 2, wherein: The search space determination unit determines whether a first condition is satisfied after the data set is generated by the generation unit. When it is determined that the first condition is not satisfied, the processing by the storage unit, the search space determination unit, the first acquisition unit, the parameter search unit, and the generation unit is repeated.

4. The parameter optimization device according to claim 3, wherein: During the iterative processing performed by the search space determination unit, the first acquisition unit, the parameter search unit and the generation unit, the search space determination unit obtains the first parameter value with the minimum or maximum observed value of the objective function from the multiple data sets stored in the storage unit when the second condition is satisfied, selects other second parameters of the second dimension, and determines the search space of the second dimension for searching the selected second parameter in a manner including the acquired first parameter value.

5. The parameter optimization device according to claim 4, wherein: The search space determination unit selects a second parameter belonging to one group from among the second parameter values ​​of the second dimension divided into a plurality of groups, or randomly selects the second parameter of the second dimension from among the first parameters of the first dimension, for each of the iterative processes.

6. The parameter optimization device according to claim 4, wherein: The search space determination unit sets the second dimensional affine subspace including the predetermined first parameter value as the search space, For each of the iterative processes, at least one of the second dimension or the linear subspace attached to the affine subspace is changed, thereby changing the affine subspace of the second dimension.

7. The parameter optimization device according to claim 4, wherein: The parameter search unit repeatedly searches the same search space to search for the first parameter value or the second parameter value when the second condition is not satisfied.

8. The parameter optimization device according to claim 4, wherein: The repetitive processing is executed in parallel or serially as a plurality of tasks. The storage unit includes a plurality of task storage units corresponding to the plurality of tasks, respectively. Each of the plurality of task storage units stores a first parameter value and an observation value corresponding to the first parameter value for each task. Each of the plurality of task storage units stores the first parameter value corresponding to the minimum or maximum observation value among the first parameter values ​​stored in the plurality of task storage units when the second condition is satisfied.

9. The parameter optimization device according to claim 3, wherein: The parameter optimization device further includes a second acquisition unit that acquires a first parameter value having a maximum or minimum observation value from among the data sets stored in the storage unit when the first condition is satisfied.

10. The parameter optimization device according to claim 9, wherein: The iterative processing performed by the storage unit, the search space determination unit, the first acquisition unit, the parameter search unit, and the generation unit is executed in parallel or serially as a plurality of tasks, The storage unit includes a plurality of task storage units corresponding to the plurality of tasks, respectively. Each of the plurality of task storage units stores a first parameter value and an observation value corresponding to the first parameter value for each task. The second acquisition unit acquires the first parameter value corresponding to the minimum or maximum observation value among the first parameter values ​​stored in the plurality of task storage units when the first condition is satisfied.

11. The parameter optimization device according to claim 1, wherein: The first acquisition unit calculates the distance between the first parameter value and the search space for each of the multiple data sets, and acquires the first parameter value whose distance is below a threshold or the second parameter value of the second dimension corresponding to the first parameter value as the one or more first parameter values ​​or second parameter values.

12. The parameter optimization device according to claim 11, wherein: The threshold value is a positive value.

13. The parameter optimization device according to claim 11, wherein: The threshold is zero.

14. The parameter optimization device according to claim 3, wherein: The first acquisition unit calculates the distance between the first parameter value and the search space for each of the plurality of data sets, and acquires the first parameter value whose distance is less than a threshold value or the second parameter value of the second dimension corresponding to the first parameter value as the one or more first parameter values ​​or second parameter values. The threshold value varies depending on the number of times the search space determination unit, the first acquisition unit, the parameter search unit, and the generation unit iterate.

15. The parameter optimization device according to claim 11 or 14, wherein: The parameter optimization device further includes a display unit that displays a GUI screen for selecting the threshold value in accordance with an instruction from a user.

16. The parameter optimization device according to claim 1, wherein: The distance is Euclidean distance, Manhattan distance, cosine distance or Mahalanobis distance.

17. The parameter optimization device according to claim 16, wherein: The parameter optimization device further includes a display unit that displays a GUI screen for selecting the type of the distance in accordance with an instruction from a user.

18. The parameter optimization device according to claim 1, wherein: The first acquisition unit randomly generates the one or more first parameter values ​​or second parameter values ​​whose distance to the search space is included in the predetermined distance, by extracting the one or more first parameter values ​​or second parameter values ​​based on the plurality of data sets or based on the search space of the second dimension.

19. The parameter optimization device according to claim 18, wherein: The parameter optimization device further includes a generating unit that generates a data set including the observed values ​​of the objective function corresponding to the one or more first parameter values ​​or the observed values ​​of the objective function corresponding to the first parameter values ​​corresponding to the one or more second parameter values ​​and the one or more first parameter values ​​or the second parameter values. The storage unit stores the generated data set.

20. The parameter optimization device according to claim 1, wherein: The parameter optimization device further includes a display unit that displays a GUI screen for selecting the second dimension in accordance with an instruction from a user.

21. The parameter optimization device according to claim 1, wherein: The parameter search unit generates the proxy model based on the acquired one or more data sets, and searches for a first parameter value or a second parameter value in the search space for optimizing the proxy model as the first parameter value or the second parameter value that can optimize the objective function.

22. The parameter optimization device according to claim 1, wherein: The predetermined first parameter value is any one of a default value, a random value, and a first parameter value corresponding to a minimum or maximum observed value among the first parameter values ​​stored in the storage unit.

23. A parameter optimization method having: determining a search space of a second dimension smaller than the first dimension that includes a predetermined first parameter value of the first dimension, Based on a plurality of data sets including first parameter values ​​of the first dimension and observation values ​​of the objective function corresponding to the first parameter values, one or more data sets including first parameter values ​​included within a predetermined distance from the search space or one or more data sets including second parameter values ​​of the second dimension corresponding to the data sets are obtained. Using a proxy model of the objective function based on the acquired one or more data sets, a first parameter value or a second parameter value that can optimize the objective function is searched in the search space.

24. A parameter optimization system having: a storage unit storing a plurality of data sets including first parameter values ​​of a first dimension and observation values ​​of an objective function corresponding to the first parameter values; A search space determination unit determines a search space having a second dimension smaller than the first dimension and including a predetermined first parameter value; A first acquisition unit acquires, based on the plurality of data sets, one or more data sets having a first parameter value included within a predetermined distance from the search space or one or more data sets having a second parameter value of the second dimension corresponding to the data set; A parameter search unit, using a proxy model of the objective function based on the acquired one or more data sets, searches in the search space for a first parameter value or a second parameter value that can optimize the objective function; a calculation unit that calculates an observed value of the objective function corresponding to the searched first parameter value or an observed value of the objective function corresponding to the first parameter value corresponding to the searched second parameter value; as well as The generating unit generates a data set including the searched first parameter value or the first parameter value corresponding to the second parameter value and the calculated observation value.

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