Information processing device, information processing method, and program

Abstract

To efficiently perform processing of obtaining a setting value of a parameter.SOLUTION: An information processing apparatus includes a processing unit. The processing unit estimates a first estimation value and a first estimation error of a constraint function value based on the constraint function value which is an output of a constraint function when one or more first setting values for one or more parameters are input. The processing unit calculates a robust satisfaction probability representing a probability that a second setting value satisfies a robust constraint to be satisfied by the constraint function value when a plurality of third setting values that modify one or more second setting values within a neighborhood range with respect to the second setting values for parameters based on the first estimation value and the first estimation error are input.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] An embodiment of the present invention relates to an information processing device, an information processing method, and a program. [Background technology]

[0002] Simulation-based optimization is used to consider improvement guidelines in a variety of fields. For example, in a manufacturing system that produces products, optimization is used to determine the setting values ​​of design parameters that satisfy the conditions for the objective function value (output of the objective function), which corresponds to the evaluation value of the product.

[0003] In optimization, in addition to the objective function value satisfying the conditions, there are cases where the constraint function value (the output of the constraint function) is required to always satisfy the conditions. One possible means of realizing this is to perform multiple simulations to determine whether the setting value for one parameter satisfies the constraints. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Publication No. 2022-041070 Summary of the Invention [Problem to be solved by the invention]

[0005] However, with the above-mentioned function, it is necessary to perform multiple simulations for each parameter, and therefore, when a large number of parameters are involved, it takes a long time to process the parameter setting values.

[0006] An object of the present invention is to provide an information processing device, an information processing method, and a program that can efficiently execute processing for determining parameter setting values. [Means for solving the problem]

[0007] According to an embodiment, an information processing apparatus includes a processing unit. The processing unit estimates a first estimate value and a first estimation error of a constraint function value based on a constraint function value that is an output of the constraint function when one or more first setting values ​​for one or more parameters are input. The processing unit calculates, based on the first estimate value and the first estimation error, a robust satisfaction probability that represents a probability that one or more second setting values ​​for the parameter will satisfy a robust constraint that the constraint function value must satisfy when multiple third setting values ​​obtained by changing the second setting value within a neighborhood range based on the second setting value for the parameter are input. [Brief explanation of the drawings]

[0008] [Figure 1] FIG. 1 is a block diagram of an information processing system according to an embodiment. [Figure 2] FIG. 10 is a diagram showing an example of data relating to a setting range. [Figure 3] FIG. 10 is a diagram showing an example of data relating to a neighborhood range. [Figure 4] FIG. 10 is a diagram showing an example of a dataset. [Figure 5] 10 is a flowchart of a determination process according to an embodiment. [Figure 6] FIG. 10 is a diagram showing an example of a display screen that displays an estimated robust fulfillment probability. [Figure 7] FIG. 10 is a diagram showing an example of a display screen that displays an estimated optimal value and a robust satisfying probability. [Figure 8] FIG. 1 is a hardware configuration diagram of an information processing apparatus according to an embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0009] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Preferred embodiments of an information processing apparatus according to the present invention will be described in detail below with reference to the accompanying drawings.

[0010] As a technique for determining parameter setting values ​​with a small number of trials, for example, Bayesian optimization, which can efficiently adjust parameter setting values, is known. In the following embodiment, parameter setting values ​​are estimated using Bayesian optimization.

[0011] The optimization according to this embodiment can be applied, for example, to determining optimal setting values ​​for parameters (design parameters) used in manufacturing products in order to improve productivity, yield, and reliability in a manufacturing system that manufactures products such as semiconductors.

[0012] In a manufacturing system, for example, processing time, dimensions, resistance, voltage, and charge are used as design parameters. The objective function is a function that uses these design parameters to determine the evaluation values ​​of the product (quality characteristics, defect rate, etc.). The constraint function is a function that indicates the constraints on these design parameters.

[0013] The applicable system is not limited to such manufacturing systems, but may be any system, such as the process of finding the optimal values ​​of parameters used in a power plant or the optimal values ​​of hyperparameters used in machine learning.

[0014] Setting values ​​estimated by optimization, including Bayesian optimization, may deviate from the optimal setting values ​​of parameters used in an actual system due to various factors. Even in such cases, it is required to minimize the impact. For example, even if the estimated setting values ​​deviate slightly from the optimal setting values, it is desirable to minimize the impact on the objective function values ​​and the constraint function values. Note that a slightly deviated setting value is a setting value that falls within a predetermined neighborhood range from a reference setting value.

[0015] Hereinafter, a constraint that indicates that the constraint function value always satisfies the condition even if the parameter setting value deviates slightly from the optimal setting value is referred to as a robust constraint. In this embodiment, even if the estimated setting value deviates slightly from the optimal setting value, the setting value is estimated not only to minimize the effect on the objective function value but also to satisfy the robust constraint.

[0016] Furthermore, in this embodiment, it is possible to determine whether the robustness constraints are satisfied without performing multiple simulations, for example, and therefore the process of determining the parameter setting values ​​can be executed more efficiently.

[0017] 1 is a block diagram showing an example of an information processing system 10 according to this embodiment. The information processing system 10 includes an information processing device 100 and an evaluation device 200. The information processing device 100 includes a storage unit 101, a reception unit 102, a judgment unit (optimum value determination unit) 103, an estimation unit 104, a calculation unit 105, a recommendation value determination unit 106, and an output control unit 107.

[0018] The information processing device 100 recommends setting values ​​for parameters used in a simulation or experiment. For example, in a simulation, a simulation model having parameters is used, and values ​​to be set for the parameters of the simulation model, i.e., setting values, are recommended. Also, for example, the amount of sample used in an experiment may be considered a parameter and a value for that amount may be recommended. Note that, hereinafter, unless otherwise specified, the term "experiment" includes simulation.

[0019] The evaluation device 200 evaluates the results of an experiment based on the recommended setting values ​​and generates information related to the evaluation. The information includes an objective function value (evaluation value) and a constraint function value (constraint value). The evaluation device 200 may perform a simulation based on the recommended setting values ​​and generate information related to the evaluation of the simulation. Alternatively, a user may perform an experiment based on the recommended setting values ​​and input the experimental results to the evaluation device 200, which then generates information related to the evaluation of the experiment.

[0020] Furthermore, the information processing device 100 acquires information on the evaluation of the results of an experiment based on the recommended setting values ​​from the evaluation device 200, and re-recommends setting values ​​based on the information. In other words, the information processing device 100 recommends setting values ​​to be used in the next experiment. By repeating the recommendation of setting values ​​in this manner, optimal setting values ​​are found. In other words, optimal values ​​of parameters are estimated. Hereinafter, the optimal setting values ​​will be referred to as optimal values.

[0021] In this embodiment, the optimal value is a value that is deemed optimal by the information processing device 100, and it does not matter whether it is actually optimal. Furthermore, multiple values ​​may be determined to be optimal values. That is, multiple values ​​may be output as optimal values. Furthermore, the number of parameters (also referred to as the number of model items or number of dimensions) for which the optimal value is to be calculated may be one or multiple.

[0022] 1, the information processing device 100 outputs recommended setting values ​​to the outside and acquires information on the results of the experiment from the outside. However, the information processing device 100 may also include a simulator that executes the experiment. In other words, the information processing device 100 may also function as a simulator.

[0023] Here, the optimization problem (robust constrained black-box optimization problem) handled in this embodiment will be described. In this embodiment, a set X⊂R D Consider the above objective function f(x) and constraint function c(x). D is the number of parameters (number of model items, number of dimensions). The objective function value obtained as a result of simulation (or experiment) at a certain parameter setting value x∈X is f(x), and the constraint function value is c(x).

[0024] A typical constrained black-box optimization problem that does not consider robust constraints is a problem of finding parameter settings such that the constraint function values ​​satisfy predetermined conditions (conditions on the constraint function values) and the objective function values ​​satisfy predetermined conditions (conditions on the objective function values).

[0025] The constraint function value condition indicates, for example, that the constraint function value is equal to or less than a threshold value, equal to or greater than a threshold value, or equal to or greater than threshold 1 and equal to or less than threshold 2.

[0026] When a smaller objective function value indicates a better evaluation, the condition for the objective function value indicates, for example, that the objective function value is smaller than other set values ​​(e.g., the objective function value is minimum). When a larger objective function value indicates a better evaluation, the condition for the objective function value indicates, for example, that the objective function value is smaller than other set values ​​(e.g., the objective function value is maximum).

[0027] In the following, an example will be described in which a smaller objective function value indicates a better evaluation. If a larger objective function value indicates a better evaluation, for example, an objective function value smaller than other set values ​​(minimum objective function value) can be replaced with an objective function value larger than other set values ​​(maximum objective function value).

[0028] When the constraint function value condition indicates that the constraint function value is equal to or less than a threshold value 0, and the objective function value condition indicates that the objective function value is minimum, the constrained black-box optimization problem is expressed by the following equation (1).

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[0029] As described above, when adjusting a system in operation or manufacturing a product using settings that are considered optimal, various factors may cause the settings to deviate slightly from the optimal settings. Even in such cases, the constraint function value is required to be equal to or less than the threshold value.

[0030] In this embodiment, a robust constraint is considered in which c(x+δ) always satisfies the condition of the constraint function value (less than or equal to a threshold, more than or equal to a threshold, or more than or equal to threshold 1 and less than or equal to threshold 2, etc.) even if the parameter setting value fluctuates by δ. δ is defined as δ∈Δ(x)(⊂R D ) is a value that satisfies Δ(x). Δ(x) corresponds to the neighborhood range.

[0031] Robust constraint value c* Let (x) be the maximum or minimum value of c(x+δ) when the parameter setting varies by δ∈Δ(x). In the case of the maximum value, the robust constraint value c * (x) is expressed, for example, by the following formula (2).

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[0032] The robustly constrained black-box optimization problem addressed in this embodiment is a problem where the robust constraint value c * The problem is to find parameter settings such that (x) satisfies a predetermined condition (condition on the constraint function value) and the objective function value satisfies a predetermined condition (condition on the objective function value). A robust constrained black-box optimization problem is expressed, for example, by the following equation (3).

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[0033] Next, the internal configuration of the information processing device 100 will be described. Note that the components shown in FIG. 1 are those for performing a process of determining the next recommended setting value, and other components are omitted. Furthermore, each component may be subdivided or consolidated. For example, the storage unit 101 may be divided into multiple storage units (storage media) depending on the files to be saved, etc. Furthermore, components other than the storage unit 101 may be considered as calculation units. Furthermore, the processing results of each component may be sent to the component that will perform the next process, or may be stored in the storage unit 101. In the latter case, the component that will perform the next process may access the storage unit 101 to obtain the processing results.

[0034] The storage unit 101 stores data used in processing by the information processing device 100. The data includes at least data indicating a set range, data indicating a neighborhood range, and a data set. Note that the storage unit 101 may store data other than these. For example, the storage unit 101 may store processing results of each component of the information processing device 100.

[0035] The setting range means the range within which the set value can be taken. In other words, the setting range means the range of values that can be set for a parameter, and it becomes the search range when searching for the recommended set value. The setting range is input, for example, by a user or the like and stored in the storage unit 101 in advance.

[0036] FIG. 2 is a diagram showing an example of data related to the setting range. As shown in FIG. 2, for example, there are 10 parameters from X1 to X 10 up to. For each of these parameters, a lower limit value and an upper limit value are determined. The setting range is the range from the lower limit value to the upper limit value. For example, the setting range of parameter X1 is the range from 10 to 100.

[0037] Note that the method of representing the setting range is not particularly limited. For example, matrix A and vector B may be stored, and W that satisfies AW + B <0 may be set as the setting range. Or, vector A and real number R may be stored, and W that satisfies |W - A| <R may be set as the setting range. Here, |W - A| represents the magnitude of the vector "W - A". In addition, various inequality parameters may be stored, and W that satisfies the inequality may be set as the setting range.

[0038] The neighborhood range is a range based on the recommended set value and applied to the recommended set value, and indicates the range of values considered to be in the vicinity of the set value. Whether the set value is robust is determined using this neighborhood range.

[0039] FIG. 3 is a diagram showing an example of data related to the neighborhood range. As shown in FIG. 3, for each parameter, a neighborhood range is obtained according to the set value of the parameter. Note that the method of representing the neighborhood range may be the same as or different from the setting range.

[0040] "Additive" in the "Type" section means that when the lower neighborhood limit of the set value x of a parameter X is L and the upper neighborhood limit is U, the neighborhood range is the range equal to or greater than x+L and equal to or less than x+U. For example, for parameter X1, the lower neighborhood limit is -5 and the upper neighborhood limit is +5. Therefore, when the set value of parameter X1 is 35, the neighborhood range of parameter X1 is the range equal to or greater than 30 (=35-5) and equal to or less than 40 (=35+5).

[0041] Additionally, "Multiplicative" in the "Type" section indicates that when the lower neighborhood limit of the set value x of a parameter X is L% and the upper neighborhood limit is U%, the neighborhood range is greater than or equal to x × (100 + L) / 100 and less than or equal to x × (100 + U) / 100. For example, for parameter X2, the lower neighborhood limit is -10% and the upper neighborhood limit is +10%. Therefore, when the set value of parameter X2 is 2, the neighborhood range of parameter X2 is greater than or equal to 1.8 (= 2 × (100 - 10) / 100) and less than or equal to 2.2 (= 2 × (100 + 10) / 100).

[0042] For example, if the "type" is only one of "additive" and "multiplicative," only the neighborhood lower limit and neighborhood upper limit for each parameter may be indicated in the neighborhood range data.

[0043] The neighborhood range is input by, for example, a user and stored in advance in the storage unit 101. For example, the neighborhood range may be an acceptable range when a product specification value deviates from an optimal value due to product variation or the like. Alternatively, the neighborhood range may be set based on data on recommended setting values ​​and preselected setting values. For example, the minimum value of the difference between each recommended setting value and each preselected setting value may be set as the "additive" neighborhood lower limit, and the maximum value may be set as the "additive" neighborhood upper limit. Alternatively, the "multiplicative" neighborhood lower limit may be set as the minimum value of each quotient calculated by division using the preselected setting value and the recommended setting value minus 1, and the "multiplicative" neighborhood upper limit may be set as the maximum value of each quotient minus 1.

[0044] The dataset is data that associates setting values ​​with objective function values ​​and constraint function values ​​related to the results of experiments using the setting values. As described above, the objective function values ​​and constraint function values ​​are values ​​obtained by evaluating the results of experiments based on the recommended setting values. The objective function values ​​and constraint function values ​​included in the dataset are received, for example, from the evaluation device 200.

[0045] 4 is a diagram showing an example of a data set. In the example of FIG. 4, X1 to X 10 There are ten parameters up to and including, and each row of the table shows the set values ​​of the ten parameters and the corresponding objective function values ​​and constraint function values.

[0046] The dataset is updated every time a setting value is determined by the recommended value determination unit 106, and the determined setting value is additionally registered in the dataset. In addition, the dataset is updated every time an objective function value and a constraint function value corresponding to a setting value recommended from the outside via the reception unit 102 are acquired, and the objective function value and the constraint function value are registered in the dataset in association with the setting value.

[0047] Note that test data may be registered in advance in the dataset, i.e., values ​​that have not been obtained by actually conducting experiments may be included in the dataset.

[0048] An experiment may use one or more parameters. When there are multiple parameters, each parameter is independent and has its own individual value. Furthermore, the set value of each parameter may be any of continuous values, discrete values, and logical values ​​(categorical variables). In other words, the type of parameter is not particularly limited. For example, it may be a physical parameter such as temperature or pressure. It may also be an experimental parameter such as processing time or processing conditions.

[0049] Also, parameters X1 to X 10One objective function value and one constraint function value may correspond to one set of parameters, or multiple objective function values ​​and multiple constraint function values ​​may correspond to one set of parameters. Also, when there are multiple objective function values ​​for multiple parameters, an overall objective function value and constraint function value may be calculated based on these objective function values.

[0050] The data set may include output data from which the objective function values ​​and constraint function values ​​can be calculated, instead of the objective function values ​​and constraint function values. The output data is, for example, data output from the evaluation device 200. Like the parameters, the output data may also be composed of multiple items, each of which may have its own individual value. For example, the output data may be detection data from various sensors used in the experiment, or physical characteristic values ​​and measurement values ​​of the experiment or simulation results.

[0051] The storage unit 101 can be configured from any commonly used storage medium such as a flash memory, a memory card, a RAM (Random Access Memory), an HDD (Hard Disk Drive), and an optical disk.

[0052] Returning to FIG. 1 , the receiving unit 102 receives input of information necessary for processing by the information processing device 100 from an external device. For example, the receiving unit 102 receives information such as an objective function value and a constraint function value corresponding to a recommended setting value (first setting value). This information is registered in a dataset as described above. The receiving unit 102 may also receive information such as a setting range, a neighborhood range, and a termination condition for determining whether the determining unit 103 should determine an optimal value.

[0053] The determination unit 103 determines whether to continue recommending setting values ​​based on a predetermined termination condition. When the determination unit 103 stops recommending setting values, it determines an optimal value based on the setting values ​​that have been recommended up to that point. The termination condition may be, for example, that the number of times the experiment has been performed or the elapsed time exceeds a threshold. When such a termination condition is satisfied, the determination unit 103 may terminate the recommendation of setting values ​​and select an optimal value from the setting values ​​that have been recommended up to that point. Details of the method for determining the optimal value will be described later.

[0054] If the termination condition is not satisfied, processing for recommending setting values ​​is executed by the estimation unit 104, calculation unit 105, and recommendation value determination unit 106. The processing of these components will be described below.

[0055] The estimation unit 104 calculates data {x i ,y i}(1≦i≦n-1), the estimated value μ of the objective function value f n (x) (an example of the second estimate) and the estimation error σ f n (x) (an example of the second estimation error) is calculated. If the parameter setting value of the i-th experiment is x i and is a D-dimensional vector. i The objective function value of the experiment result is y i For example, the estimator 104 may calculate the objective function values ​​stored in the data set and the estimated value μ f n Calculate the sum of squares of the error between (x) and μ so that the calculated sum of squares is minimized. f n The parameters of (x) are estimated using a regression method, such as linear regression, Lasso regression, elastic net regression, random forest regression, Gaussian process regression, or neural network regression.

[0056] For example, when using Gaussian process regression, the estimated value of the objective function μ f n (x) is expressed by the following equation (4).

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[0057] For any D-dimensional vector x, the estimated value μ of the objective function value is calculated using equation (4). f n (x) is calculated. The mean vector of the objective function value is m. The mean vector m is the vector whose ith element is m i =μ0(x i ) is an n-1-dimensional vector. y is a vector whose i-th element is y i Also, K is an n-1-dimensional vector whose i-th row and j-th column components are K i,j =k(x i ,x j ) is a (n-1) × (n-1) matrix, where μ0(x i ) is an arbitrary function, and k(x i ,x j ) is an arbitrary kernel function. The kernel function may be, for example, an exponential square kernel, a matrix kernel, or a linear kernel. Note that k(x) is the kernel function whose ith element is k. i (x)=k(x,x i ) and σ 2 is an arbitrary constant. Also, I represents the identity matrix and T represents the transpose.

[0058] In addition, the estimated error σ of the objective function value f n (x) is expressed by the following equation (5).

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[0059] Similarly, the estimation unit 104 calculates data {x i ,c i}(1≦i≦n-1), the estimated value of the constraint function μ c n (x) (an example of the first estimate) and the estimation error σ c nFor example, the estimation unit 104 calculates the estimated value μ of the constraint function value by using equation (4) in which y is replaced with c. c n (x). The estimation unit 104 also calculates the estimation error σ of the constraint function value by using equation (5). c n Calculate (x).

[0060] The calculation unit 105 calculates a robust satisfaction probability that indicates the probability that each parameter satisfies the robust constraint, based on the estimated value and estimation error of the constraint function value.

[0061] As described above, the robust constraint means that the constraint function value c(x+δ) always satisfies the constraint function value condition even if the parameter setting value (second setting value) fluctuates by δ within the neighborhood range (Δ(x)). When δ takes multiple values, x+δ corresponds to multiple setting values ​​(third setting values) obtained by changing the setting value within the neighborhood range. The robust constraint can be interpreted as a constraint that the constraint function value c(x+δ) must satisfy when the setting value x+δ is input.

[0062] For example, the calculation unit 105 first calculates a relational expression of a constraint satisfaction probability, which is the probability that each parameter and the constraint function value satisfy a condition (for example, a threshold or less or a threshold or more), based on the estimated value and estimation error of the constraint function value. When the condition of the constraint function value is a threshold value 0 or less, the constraint satisfaction probability PF n (x) is calculated, for example, by the following equation (6): where Φ is the cumulative distribution function of the standard normal distribution.

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[0063] The reason why the constraint satisfaction probability is expressed by equation (6) is explained below. In the case of Gaussian process regression, c(x) can be estimated to follow a normal distribution with mean μ(x) and standard deviation σ(x). In this case, if Z = (c(x) - μ(x)) / σ(x), Z follows a standard normal distribution. Furthermore, the probability that c(x) is below the threshold 0 is equal to the probability that Z is below -μ(x) / σ(x).

[0064] On the other hand, the cumulative distribution function Φ(a) of the standard normal distribution represents the probability that the variable Z is equal to or less than a. Therefore, the probability that Z is equal to or less than -μ(x) / σ(x) is Φ(-μ(x) / σ(x)). In other words, the probability that c(x) is equal to or less than the threshold value 0 can be calculated by Φ(-μ(x) / σ(x)), as shown in equation (6).

[0065] Next, for a setting value x (second setting value) of each parameter, the calculation unit 105 calculates multiple setting values ​​x+δ (third setting values) that are included within a neighborhood range based on the setting value x. The calculation unit 105 may randomly sample multiple setting values ​​within the neighborhood range. The calculation unit 105 may calculate the multiple setting values ​​x+δ by using δ as 0 and the set of endpoints of Δ(x), or by using δ as a value randomly sampled from the set of endpoints of 0 and Δ(x).

[0066] The calculation unit 105 calculates a constraint satisfaction probability for each of the plurality of setting values ​​using equation (6). The calculation unit 105 calculates a robust satisfaction probability using the plurality of constraint satisfaction probabilities calculated for each of the plurality of setting values. For example, the calculation unit 105 calculates the product of the plurality of constraint satisfaction probabilities calculated for the plurality of setting values ​​as the robust satisfaction probability RobustPFn(x) using the following equation (7):

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[0067] The recommended value determination unit 106 determines the next recommended setting value, in other words, the setting value to be used in the next experiment, from within the setting range based on the robust fulfillment probability and the estimated value and estimation error of the objective function value. Hereinafter, the recommended setting value may be referred to as the recommended value.

[0068] For example, the recommended value determination unit 106 may detect a setting value within the setting range that has a robust fulfillment probability equal to or greater than a predetermined threshold (probability threshold) and that reduces the objective function value based on a relational expression between the setting value and the objective function value, and determine the setting value as the setting value to be recommended next (recommended value). That is, the recommended value determination unit 106 may search for a setting value within the setting range that is estimated to reduce the objective function value compared to the previous setting value, and adopt the setting value as the setting value (recommended value) to be used in the next experiment. For example, the recommended value determination unit 106 can find a value that reduces the objective function value using various optimization methods such as exhaustive search, random search, grid search, gradient search, L-BFGS, DIRECT, CMA-ES, and multi-start local search.

[0069] Alternatively, the recommendation value determination unit 106 may determine the recommendation value based on the product of an acquisition function (first acquisition function) and a robust fulfillment probability. The acquisition function is a function calculated based on an estimated value and an estimation error of the objective function value. For example, the recommendation value determination unit 106 determines the recommendation value using a robust acquisition function (second acquisition function, details of which will be described later) that is a function based on the product of the acquisition function and the robust fulfillment probability.

[0070] For example, the recommendation value determination unit 106 may recommend a setting value that optimizes the output of the robust acquisition function. If a larger output value of the acquisition function (acquisition function value) indicates a better evaluation, the recommendation value determination unit 106 recommends a setting value that maximizes the robust acquisition function. If a smaller acquisition function value indicates a better evaluation, the recommendation value determination unit 106 recommends a setting value that minimizes the robust acquisition function. Note that the following description will be given taking as an example a case where a larger acquisition function indicates a better evaluation.

[0071] The acquisition function may be, for example, PI (Probability of Improvement) or EI (Expected Improvement), or UCB (Upper Confidence Bound), Thompson Sampling (TS), Entropy Search (ES), or Mutual Information (MI).

[0072] For example, when the expected improvement is used as the acquisition function, the recommendation value determination unit 106 first calculates μ f n (x) and PF n (x) and the current objective function value μ f n Set value x to minimize (x) + n is calculated using the following equation (8).

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[0073] Furthermore, the recommendation value determination unit 106 + n , μ f n (x), σ f n Based on (x), the expected improvement EI n (x) is calculated using the following formula (9).

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[0074] φ is the probability density function of the standard normal distribution. Zn is expressed by the following equation (10).

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[0075] The recommendation value determination unit 106 calculates the robust acquisition function RobustEICn(x) as the product of EIn(x) and RobustPFn(x) using the following equation (11).

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[0076] Then, the recommendation value determination unit 106 determines the setting value x that maximizes the robust acquisition function. ~ n is calculated using the following equation (12).

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[0077] For example, the recommendation value determination unit 106 may use the calculated setting value x ~ n The recommendation value determination unit 106 may not recommend the determined recommendation value as is, but may instead select or search for multiple setting values ​​(hereinafter referred to as neighboring setting values) from a neighborhood range of the determined recommendation value and recommend them in order as new recommendation values.

[0078] For example, the recommended value determination unit 106 may randomly select multiple setting values ​​(hereinafter referred to as neighboring setting values) from a neighboring range of the determined setting value, and output the selected multiple setting values ​​in order as recommended values.

[0079] The recommended value determination unit 106 may search again for a nearby setting value within the neighborhood of the determined setting value that maximizes the estimated value of the objective function value and the acquisition function based on the estimation error, and determine the nearby setting value as the recommended value.

[0080] The recommendation value determination unit 106 determines the setting value x ~ n Fixing Δ(x ~ n ) Constraint satisfaction probability PF for variation δ in n (x ~ n +δ) n is calculated using the following formula (13), and the recommended value is x n =x ~ n +δ n It may also be possible to use the following.

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[0081] The recommended value determination unit 106 may search again for a nearby setting value within the neighborhood of the determined setting value that maximizes the estimation error of the objective function value or the estimation error of the constraint function value, and determine the nearby setting value as the recommended value.

[0082] Up until now, it has been assumed that a dataset exists. However, for example, when a user conducts an experiment for the first time, there may be a situation where test data is not registered in the dataset. Even in such a situation, the user may wish to use the setting value recommended by the information processing device 100. In such a case, the information processing device 100 cannot determine the recommended value using the above method. Therefore, the recommended value may be a predetermined value (initial value of the setting value), or the recommended value may be determined according to a predetermined rule. The rule may be, for example, a rule for determining the setting value using random numbers, Latin squares, or Sobol sequences. In other words, the initially recommended setting value (initial value) may be a predetermined value or a value determined according to a predetermined rule (a rule using random numbers, Latin squares, or Sobol sequences).

[0083] As described above, when the termination condition is satisfied, the determining unit 103 determines the optimum value from the setting values ​​recommended up to that point. The method for determining the optimum value by the determining unit 103 will be described below.

[0084] The determining unit 103 determines, from among the recommendation values ​​output so far, a recommendation value whose robust satisfaction probability is equal to or greater than a threshold and whose objective function value is smaller or larger than the other recommendation values, as the optimum value.

[0085] For example, the determination unit 103 determines, as the optimal value, the setting value at which the objective function value stored in the storage unit 101 is optimal (minimum or maximum). The determination unit 103 may determine, among the setting values ​​recommended so far, the setting value at which the estimated value of the constraint function value is equal to or less than a threshold and the objective function value or the estimated value of the objective function value is smallest, as the optimal value. Furthermore, the determination unit 103 may determine, among the setting values ​​stored in the storage unit 101 at which the robust acquisition function is largest, the setting value at which the estimated value of the constraint function value is equal to or less than a threshold and the objective function value or the estimated value of the objective function value is smallest, as the optimal value.

[0086] Furthermore, the determining unit 103 may determine, as the optimal value, a parameter that has a robust fulfillment probability equal to or greater than a predetermined threshold (threshold value of probability value) and that minimizes the estimated value of the objective function value, among the setting values ​​that maximize the robust acquisition function stored in the storage unit 101. That is, the determining unit 103 determines, according to the following equation (14), the parameter x that minimizes the estimated value of the objective function value. + n+1 may be determined as the optimum value.

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[0087] The output control unit 107 outputs the processing results of each component. For example, the output control unit 107 outputs recommended setting values ​​and optimal values. The output control unit 107 may also receive an instruction via the receiving unit 102 and output data stored in the storage unit 101, such as a data set.

[0088] The output format of the output control unit 107 is not particularly limited and may be, for example, a table or an image. For example, the output control unit 107 may generate and output a graph based on data such as a data set.

[0089] If the information processing device 100 includes a simulator, the simulator sets the recommended setting values ​​to the parameters of the model, executes a simulation, and calculates an objective function value based on the simulation result. The calculation formula for the objective function value is determined in advance.

[0090] The information processing device 100 may be configured to include a processing unit that integrates at least some of the functions of the reception unit 102, the judgment unit 103, the estimation unit 104, the calculation unit 105, the recommendation value determination unit 106, and the output control unit 107.

[0091] Each of the above units (receiving unit 102, determining unit 103, estimating unit 104, calculating unit 105, recommendation value determining unit 106, and output control unit 107) is realized, for example, by one or more processors. For example, each of the above units may be realized by having a processor such as a CPU (Central Processing Unit) execute a program, that is, by software. Each of the above units may be realized by a processor such as a dedicated IC (Integrated Circuit), that is, by hardware. Each of the above units may be realized by a combination of software and hardware. When multiple processors are used, each processor may realize one of the units, or two or more of the units.

[0092] Next, a description will be given of the optimum value determination process performed by the information processing device 100 according to this embodiment. Fig. 5 is a flowchart showing an example of the determination process according to this embodiment.

[0093] The recommended value determination unit 106 recommends an initial value for the setting value (step S101). As described above, the initial value may be a predetermined value, or may be a value selected from values ​​within a setting range based on predetermined rules. The initial value is output from the information processing device 100 to, for example, a user conducting an experiment or a simulator (such as the evaluation device 200).

[0094] An experiment is performed using the recommended initial setting values. The evaluation device 200 or simulator calculates objective function values ​​and constraint function values ​​based on the results of the experiment using the recommended setting values.

[0095] The receiving unit 102 receives the calculated objective function values ​​and constraint function values ​​from the evaluation device 200 or the simulator (step S102). The receiving unit 102 associates the recommended setting values ​​with the calculated objective function values ​​and constraint function values, and stores them in a data set in the storage unit 101 (step S103).

[0096] The determining unit 103 determines whether to determine the optimum value based on the termination condition (step S104). The termination condition is determined in advance as described above.

[0097] If it is determined that the optimal values ​​should not be determined (step S105: No), the estimation unit 104 estimates the estimated values ​​and estimation errors of the objective function values ​​and constraint function values ​​of each parameter based on the stored data set (recommended setting values, corresponding objective function values, and constraint function values) (step S106).

[0098] The calculation unit 105 calculates a robust satisfaction probability, which is the probability that each parameter satisfies the robust constraint, based on the estimated value and estimation error of the constraint function value (step S107).

[0099] The recommended value determination unit 106 determines and outputs the next setting value to be recommended (recommended value) based on the estimated value and estimation error of the constraint function value and the robust fulfillment probability (step S108). For example, the recommended value determination unit 106 determines the setting value that maximizes the robust acquisition function, which is the product of the robust fulfillment probability and the expected improvement, as the next recommended value. The recommended value determination unit 106 may also determine a setting value close to the determined setting value as the next recommended value.

[0100] The next experiment is performed using the set values ​​output in step S108. After that, the process returns to step S102 and the process is repeated. That is, the determination and judgment of the set values ​​are repeated.

[0101] If it is determined in step S105 that an optimal value is to be determined (step S105: Yes), the determination unit 103 determines the optimal value based on the setting values ​​recommended up to that point (step S109). The output control unit 107 outputs the determined optimal value (step S110), and the optimal value determination process ends.

[0102] Next, an example of output by the output control unit 107 will be described. The output control unit 107 may be configured to output a robust satisfying probability. FIG. 6 is a diagram showing an example of a display screen displaying an estimated robust satisfying probability. The vertical and horizontal axes in FIG. 6 represent different parameter setting values. The contour lines represent the robust satisfying probability. The display screen in FIG. 6 is an example of information showing the relationship between parameter setting values ​​and robust satisfying probability. By displaying a display screen such as that in FIG. 6, a user can quickly check, for example, whether or not a parameter satisfies a robust constraint.

[0103] FIG. 7 is a diagram showing an example of a display screen displaying an estimated optimum value and a robust satisfying probability. Point 701 represents the estimated optimum value. As in FIG. 6, the vertical and horizontal axes represent the setting values ​​of different parameters, and the contour lines represent the robust satisfying probability. As shown in FIG. 7, the optimum value (point 701) is located at a position where the robust satisfying probability is high. In step S110 of FIG. 5, the optimum value may be output on a display screen such as that shown in FIG. 7.

[0104] As described above, the information processing device 100 of this embodiment estimates a relational expression between a setting value and a robust fulfillment probability associated with the setting value, and recommends a setting value to be used in the next experiment based on the relational expression. By continuously recommending setting values ​​and repeating experiments, it is possible to determine an optimal setting value that is within a nearby range, always satisfies the constraint function value, i.e., satisfies the robust constraint, and has a small objective function value. Furthermore, by using Bayesian optimization, it is possible to determine a setting value that satisfies the robust constraint and reduces the objective function value with fewer experiments.

[0105] In this embodiment, since it is not necessary to perform multiple experiments (simulations) for each parameter, the time required to determine the optimal parameter setting value can be shortened. In other words, the process of determining the parameter setting value can be executed more efficiently. Furthermore, by visualizing the robust fulfillment probability for each parameter, it is possible to easily check whether the determined setting value is optimal.

[0106] Next, a hardware configuration of the information processing device according to the embodiment will be described with reference to Fig. 8. Fig. 8 is an explanatory diagram showing an example of the hardware configuration of the information processing device according to the embodiment.

[0107] The information processing device of the embodiment includes a control device such as a CPU 51, a storage device such as a ROM (Read Only Memory) 52 or a RAM 53, a communication I / F 54 that connects to a network and communicates, and a bus 61 that connects each part.

[0108] The programs executed by the information processing device according to the embodiment are provided in advance in the ROM 52 or the like.

[0109] The program executed by the information processing device according to the embodiment may be configured to be provided as a computer program product by being recorded in an installable or executable file format on a computer-readable recording medium such as a CD-ROM (Compact Disk Read Only Memory), a flexible disk (FD), a CD-R (Compact Disk Recordable), or a DVD (Digital Versatile Disk).

[0110] Furthermore, the program executed by the information processing device according to the embodiment may be stored on a computer connected to a network such as the Internet and provided by being downloaded via the network. Also, the program executed by the information processing device according to the embodiment may be provided or distributed via a network such as the Internet.

[0111] The program executed by the information processing device according to the embodiment can cause a computer to function as each unit of the information processing device described above. In this computer, the CPU 51 can read the program from a computer-readable storage medium onto a main storage device and execute the program.

[0112] Although several embodiments of the present invention have been described, these embodiments are presented as examples and are not intended to limit the scope of the invention. These novel embodiments can be embodied in various other forms, and various omissions, substitutions, and modifications can be made without departing from the spirit of the invention. These embodiments and their modifications are included within the scope and spirit of the invention, and are also included in the scope of the invention and its equivalents as defined in the claims.

[0113] A configuration example of the embodiment will be described below. (Configuration example 1) estimating a first estimate and a first estimation error of the constraint function value based on a constraint function value that is an output of the constraint function when one or more first setting values ​​for one or more parameters are input; calculate a robust satisfaction probability, which represents the probability that the second setting value satisfies a robust constraint, which is a constraint that the constraint function value should satisfy when a plurality of third setting values ​​obtained by changing the second setting value within a predetermined neighborhood range based on one or more second setting values ​​for the parameter are input, based on the first estimated value and the first estimation error; Processing section An information processing device comprising: (Configuration example 2) The processing unit Find a relational expression for calculating a fulfillment probability that represents the probability that the constraint function value satisfies the condition; calculating the fulfillment probability for each of the plurality of third setting values ​​using the relational expression; calculating the robust fulfillment probability using the fulfillment probabilities calculated for the third setting values; The information processing device according to configuration example 1. (Configuration example 3) the processing unit calculates, as the robust fulfillment probability, a product of the fulfillment probabilities calculated for the third setting values. The information processing device according to configuration example 2. (Configuration Example 4) The processing unit estimating a second estimate value and a second estimation error of the objective function value based on an objective function value that is an output of the objective function when the first setting value is input; determining a recommended value, which is a setting value to be recommended, based on the robust satisfying probability, the second estimated value, and the second estimation error; The information processing device according to any one of configuration examples 1 to 3. (Configuration Example 5) the processing unit determines, as the recommended value, a setting value for which the robust satisfying probability is equal to or greater than a threshold and which is within a setting range representing a range that a setting value can take, and for which the second estimated value is smaller than other setting values. The information processing device according to configuration example 4. (Configuration Example 6) The processing unit calculating a first acquisition function based on the second estimated value and the second estimation error; calculating a second acquisition function that is a product of the robust satisfying probability and the first acquisition function; determining, as the recommended value, a setting value that optimizes the output of the second acquisition function within a setting range that represents a range that the setting value can take; The information processing device according to configuration example 4. (Configuration Example 7) The processing unit determining, as new recommended values, a plurality of setting values ​​selected or searched from within the neighborhood range based on the determined recommended value; The information processing device according to configuration example 4. (Configuration Example 8) The processing unit determining, as a new recommended value, a setting value that minimizes a fulfillment probability, which represents a probability that the condition of the constraint function value is satisfied, within the neighborhood range based on the determined recommended value; The information processing device according to configuration example 4. (Configuration Example 9) the processing unit determines, among the plurality of recommended values ​​determined for the plurality of constraint function values ​​and the plurality of objective function values ​​that are outputs of the objective function when a first setting value is input, the candidate setting value whose robust satisfying probability is equal to or greater than a threshold and whose objective function value is smaller or larger than other candidate setting values, as an optimal value representing an optimal setting value; The information processing device according to configuration example 4. (Configuration Example 10) the processing unit determines, as the optimal value, the candidate setting value for which the robust satisfying probability is equal to or greater than a threshold and the objective function value is minimum or maximum, among the plurality of recommended values ​​determined for the plurality of constraint function values ​​and the plurality of objective function values. The information processing device according to configuration example 9. (Configuration Example 11) further comprising an output control unit that outputs the robust satisfying probability; The information processing device according to any one of configuration examples 1 to 10. (Configuration Example 12) the output control unit outputs information indicating a relationship between the setting value of the parameter and the robust satisfying probability. The information processing device according to configuration example 11. (Configuration Example 13) The processing unit an estimation unit that estimates the first estimated value and the first estimation error; a calculation unit for calculating the robust fulfillment probability; Equipped with 13. The information processing device according to any one of configuration examples 1 to 12. (Configuration Example 14) An information processing method executed by an information processing device, estimating a first estimate and a first estimation error of the constraint function value based on a constraint function value that is an output of the constraint function when one or more first setting values ​​for one or more parameters are input; calculating a robust satisfying probability, based on the first estimated value and the first estimation error, that indicates the probability that the second setting value satisfies a robust constraint, which is a constraint that the constraint function value must satisfy when a plurality of third setting values ​​are input, which are obtained by changing the second setting value within a predetermined neighborhood range based on one or more second setting values ​​for the parameter; An information processing method including: (Configuration Example 15) On the computer, estimating a first estimate and a first estimation error of the constraint function value based on a constraint function value that is an output of the constraint function when one or more first setting values ​​for one or more parameters are input; calculating a robust satisfying probability, based on the first estimated value and the first estimation error, that indicates the probability that the second setting value satisfies a robust constraint, which is a constraint that the constraint function value must satisfy when a plurality of third setting values ​​are input, which are obtained by changing the second setting value within a predetermined neighborhood range based on one or more second setting values ​​for the parameter; A program to execute. [Explanation of symbols]

[0114] 10 Information Processing Systems 100 Information processing device 101 Storage section 102 Reception 103 Judgment section 104 Estimation part 105 Calculation Unit 106 Recommendation value determination unit 107 Output control section 200 Evaluation Device

Claims

1. estimating a first estimate and a first estimation error of the constraint function value based on a constraint function value that is an output of the constraint function when one or more first setting values ​​for one or more parameters are input; calculate, based on the first estimated value and the first estimation error, a robust satisfaction probability that indicates the probability that the second setting value satisfies a robust constraint, which is a constraint that the constraint function value should satisfy when a plurality of third setting values ​​obtained by changing the second setting value within a predetermined neighborhood range based on one or more second setting values ​​for the parameter are input; Processing section An information processing device comprising:

2. The processing unit Find a relational expression for calculating a fulfillment probability that represents the probability that the constraint function value satisfies the condition; calculating the fulfillment probability for each of the plurality of third setting values ​​using the relational expression; calculating the robust fulfillment probability using the fulfillment probabilities calculated for the third setting values; The information processing device according to claim 1 .

3. the processing unit calculates, as the robust fulfillment probability, a product of the fulfillment probabilities calculated for the third setting values; The information processing device according to claim 2 .

4. The processing unit estimating a second estimate value and a second estimation error of the objective function value based on an objective function value that is an output of the objective function when the first setting value is input; determining a recommended value, which is a setting value to be recommended, based on the robust satisfying probability, the second estimated value, and the second estimation error; The information processing device according to claim 1 .

5. the processing unit determines, as the recommended value, a setting value for which the robust satisfying probability is equal to or greater than a threshold and which is within a setting range representing a range that a setting value can take, and for which the second estimated value is smaller than other setting values. The information processing device according to claim 4 .

6. The processing unit calculating a first acquisition function based on the second estimate and the second estimation error; calculating a second acquisition function that is a product of the robust satisfying probability and the first acquisition function; determining, as the recommended value, a setting value that optimizes the output of the second acquisition function within a setting range that represents a range that the setting value can take; The information processing device according to claim 4 .

7. The processing unit determining, as new recommended values, a plurality of setting values ​​selected or searched from within the neighborhood range based on the determined recommended value; The information processing device according to claim 4 .

8. The processing unit determining, as a new recommended value, a setting value that minimizes a fulfillment probability, which represents a probability that the condition of the constraint function value is satisfied, within the neighborhood range based on the determined recommended value; The information processing device according to claim 4 .

9. the processing unit determines, among the plurality of recommended values ​​determined for the plurality of constraint function values ​​and the plurality of objective function values ​​that are outputs of the objective function when a first setting value is input, the candidate setting value whose robust fulfillment probability is equal to or greater than a threshold and whose objective function value is smaller or larger than other candidate setting values, as an optimal value that represents an optimal setting value; The information processing device according to claim 4 .

10. the processing unit determines, as the optimal value, the candidate setting value for which the robust satisfying probability is equal to or greater than a threshold and the objective function value is minimum or maximum, among the plurality of recommended values ​​determined for the plurality of constraint function values ​​and the plurality of objective function values. The information processing device according to claim 9 .

11. further comprising an output control unit that outputs the robust satisfying probability; The information processing device according to claim 1 .

12. the output control unit outputs information indicating a relationship between the setting value of the parameter and the robust satisfying probability. The information processing device according to claim 11.

13. The processing unit an estimation unit that estimates the first estimated value and the first estimation error; a calculation unit for calculating the robust fulfillment probability; Equipped with The information processing device according to claim 1 .

14. An information processing method executed by an information processing device, estimating a first estimate and a first estimation error of the constraint function value based on a constraint function value that is an output of the constraint function when one or more first setting values ​​for one or more parameters are input; calculating a robust satisfaction probability, based on the first estimated value and the first estimation error, which indicates a probability that the second setting value satisfies a robust constraint, which is a constraint that the constraint function value should satisfy when a plurality of third setting values ​​obtained by changing the second setting value within a predetermined neighborhood range based on one or more second setting values ​​for the parameter are input; An information processing method including:

15. On the computer, estimating a first estimate and a first estimation error of the constraint function value based on a constraint function value that is an output of the constraint function when one or more first setting values ​​for one or more parameters are input; calculating a robust satisfaction probability, based on the first estimated value and the first estimation error, which indicates a probability that the second setting value satisfies a robust constraint, which is a constraint that the constraint function value should satisfy when a plurality of third setting values ​​obtained by changing the second setting value within a predetermined neighborhood range based on one or more second setting values ​​for the parameter are input; A program to execute.

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