Parameter optimization device, parameter optimization system, and parameter optimization method

Abstract

To optimize parameters while reducing the risk of degrading the search efficiency of parameter optimization. [Solution] The acquisition unit acquires observation samples, which are combinations of observation points (points in the parameter vector space) and observed values ​​of the object being observed at those observation points, and / or missing points, which are observation points where the observation of the object was unsuccessful. The storage unit stores the observation samples as elements of a first set and the missing points as elements of a second set. The calculation unit calculates an acquisition function based on the observation samples. The first proposal unit proposes the argument that maximizes the value of the acquisition function as an observation candidate point. The second proposal unit determines whether the missing points whose distance from the observation candidate points is less than or equal to a threshold are included in the second set. If it is determined that they are included, it generates a perturbation point for the observation candidate point and proposes it as a proposed point. If it is determined that they are not included, it proposes the observation candidate point as a proposed point. The output unit outputs observation point information from the first set that meets the output conditions.

Description

[Technical Field]

[0001] Embodiments of the present invention relate to a parameter optimization device, a parameter optimization system, and a parameter optimization method. [Background technology]

[0002] Society consists of various devices, equipment, and application software, all of which are made up of various components. These devices, equipment, application software, and components are designed, manufactured, and utilized.

[0003] During the design phase, devices, equipment, application software, and components are sometimes designed to meet specific specifications. In this process, a parameter vector, which has one or more adjustable parameters as elements, is changed to various values. By conducting simulations, experiments, and surveys, observed characteristic values ​​are obtained that numerically represent the characteristics when designed with these parameter vector values. The parameter vector value that satisfies these observed characteristic values ​​is then determined. Here, characteristics include, for example, the performance, manufacturing cost, and customer satisfaction of the device, equipment, application software, or component. Better performance is desirable for devices and components, lower manufacturing costs are desirable, and higher customer satisfaction is desirable. When a larger characteristic value is desirable, it is required to find the parameter vector value that maximizes that characteristic value with minimal time, effort, and expense. When a smaller characteristic value is desirable, it is required to find the parameter vector value that minimizes that characteristic value with minimal time, effort, and expense.

[0004] Finding a parameter vector value that maximizes or minimizes a characteristic value, or finding a parameter vector value close to a given target value, is called parameter optimization. In parameter optimization, the desired parameter vector value is obtained by maximizing or minimizing an objective function relating to the parameter vector value. Here, the objective function is defined by the user. If there is only one characteristic to be optimized, the objective function is defined by, for example, the value of that characteristic. Alternatively, the objective function is defined by the square of the difference between the characteristic value and the target value. If there are two or more characteristics to be optimized, the objective function is defined by, for example, the combined value of all characteristic values. Alternatively, the same number of objective functions as there are characteristics are set, and the value of each objective function is defined by the value of the corresponding characteristic.

[0005] Simulations, experiments, and surveys are means of observing characteristic values ​​and objective function values. Characteristic values ​​for each parameter vector are often unknown until they are observed through simulations, experiments, or surveys. The value of the objective function for a given parameter vector is also unknown until observed. During observation, noise may be introduced into both the characteristic values ​​and the objective function.

[0006] Parameter optimization may also be used during the manufacturing stage. For example, the parameter vector values ​​that allow the device, equipment, application software, components, or materials delivered to the user to perform at their maximum potential in the user's operating environment may be determined during the user's initial setup or periodic adjustments.

[0007] If D represents the number of parameters to be adjusted, then the dimension of the parameter vector is D. A given D-dimensional parameter vector value can be considered as a single point in the D-dimensional space. Therefore, the space in which the optimal D-dimensional parameter vector value is searched is the D-dimensional space. If there are no upper or lower bounds set for the D-dimensional parameter vector, the range in which the optimal D-dimensional parameter vector value is searched is the entire D-dimensional space. If there are upper and lower bounds set for the D-dimensional parameter vector, that is, if the D-dimensional parameter vector has a domain, then the range in which the optimal D-dimensional parameter vector value is searched is that domain within the D-dimensional space. The larger D is, the wider the search range becomes, making optimization more difficult. Hereafter, D-dimensional parameter vector values ​​may be simply abbreviated as parameter vector values ​​or parameter values. Also, the description of the domain will be omitted. Even if the description of the domain is omitted, the search range will be limited to the domain. Hereafter, the D-dimensional space of the D-dimensional parameter vector will be called the parameter space.

[0008] Bayesian optimization is a known method for finding parameter vector values ​​that satisfy the specifications for all characteristic values. In Bayesian optimization, a proposal step is performed to propose a point where the value of the objective function should be observed next, and an observation step is performed to observe the value of the objective function at the proposed point. If a missing value occurs in this observation step, the observation sample is not added to the observation sample set (observation data), and therefore the acquired function is not updated. As a result, in the proposal step, the proposed point where a missing value occurred in the previous observation step is proposed again. If the missing value at the same proposed point is reproducible, the proposal and missing value of the same proposed point will be repeated, and the optimization of the parameters will stagnate.

[0009] In response to this, a method is known to generate observational samples by imputing the observed values ​​of the objective function at proposed points where data is missing with the worst known observed values. However, using the worst known observed values, which differ from the true values, may degrade the search efficiency for parameter optimization. [Prior art documents] [Patent Documents]

[0010] [Patent Document 1] Japanese Patent Publication No. 2020-27370 [Non-patent literature]

[0011] [Non-Patent Document 1] YK Wakabayashi, T. Otsuka, Y. Krockenberger, et al., “Bayesian optimization with experimental failure for High-throughput materials growth,” npj Comput. Mater. 8, 180 (2022). [Overview of the project] [Problems that the invention aims to solve]

[0012] The problem that this invention aims to solve is to provide a parameter optimization device, a parameter optimization system, and a parameter optimization method that can optimize parameters while reducing the risk of deterioration in the search efficiency of parameter optimization. [Means for solving the problem]

[0013] The parameter optimization device according to the embodiment includes an acquisition unit, a storage unit, a calculation unit, a first proposal unit, a second proposal unit, and an output unit. The acquisition unit acquires observation samples, which are combinations of observation points, which are points in a parameter vector space having a parameter vector having the values ​​of one or more types of parameters as elements, and the observed values ​​of the object being observed at the observation points, and / or missing points, which are observation points where the observation of the object being observed was unsuccessful. The storage unit stores the observation samples as elements of a first set and stores the missing points as elements of a second set. The calculation unit calculates an acquisition function based on the observation samples. The first proposal unit proposes the argument that maximizes the value of the acquisition function as an observation candidate point for the next observation. The second proposal unit determines whether the missing point, whose distance from the observation candidate point is less than or equal to a threshold, is included in the second set. If it is determined that it is included, it generates a perturbation point for the observation candidate point and proposes the perturbation point as a proposed point for the next observation. If it is determined that it is not included, it proposes the observation candidate point as the proposed point. The output unit outputs to the outside the observation point information that matches the output conditions from the first set. [Brief explanation of the drawing]

[0014] [Figure 1] This figure shows an example configuration of a parameter optimization device according to the first embodiment. [Figure 2] A diagram illustrating the processing procedure of the parameter optimization process according to the first embodiment. [Figure 3] A block diagram schematically showing the data flow of the parameter optimization system according to the first embodiment. [Figure 4] A diagram illustrating the detailed processing procedure for the proposed point in the first embodiment. [Figure 5] A diagram illustrating the perturbation range according to the first embodiment. [Figure 6] A diagram illustrating the probability density distribution according to the first embodiment. [Figure 7] A diagram illustrating the detailed processing procedure for the proposed points related to Modification Example 1. [Figure 8] A diagram illustrating the probability density distribution related to Modification Example 3. [Figure 9] A diagram illustrating the method for creating the probability density distribution related to Modification 4. [Figure 10] Figure illustrating the probability density distribution related to Modification 4 [Figure 11] Figure 1 illustrates the display screen related to Modification Example 8. [Figure 12] Figure 2 illustrates the display screen related to Modification Example 8. [Figure 13] Figure 3 illustrates the display screen related to Modification Example 8. [Figure 14] Figure 4 illustrates the display screen related to Modification Example 8. [Modes for carrying out the invention]

[0015] The parameter optimization apparatus, parameter optimization system, and parameter optimization method according to this embodiment will be described below with reference to the drawings. Hereafter, the D-dimensional parameter vector value may be simply referred to as the parameter vector value. The description of the domain will be omitted. Even if the description of the domain is omitted, the search range will be limited to within the domain. Also, since the parameter vector value represents a point in the D-dimensional parameter vector space, it may also be called an observation point. "D" is a natural number greater than or equal to 1.

[0016] (First Embodiment) Figure 1 shows an example of the hardware configuration of the parameter optimization system 100 according to the first embodiment. As shown in Figure 1, the parameter optimization system 100 is a computer system having a parameter optimization device 110 and an observation device 120. The parameter optimization device 110 and the observation device 120 are connected to each other via wired or wireless communication. The parameter optimization device 110 is a computer that proposes parameter vector values ​​(proposed points) where the value of the objective function should be observed next. The observation device 120 obtains the observed value of the objective function at the proposed points by observing the value of the objective function at the proposed points. Observation involves observing characteristic values, such as the performance, manufacturing cost, and satisfaction level, from an object of observation, including devices, equipment, applications, software, parts, materials, and / or simulations, and observing the value of the objective function based on these characteristic values. Specifically, observation is performed by simulations, experiments, and questionnaires based on parameter values ​​for purposes such as device and material design, system and robot control, and hyperparameter tuning of machine learning models. Characteristic values ​​related to device and material design include, for example, resistance, thermal conductivity, and density. Characteristic values ​​related to the control of a system or robot are evaluation function values, such as the root mean square error, root mean square logarithmic error, and mean absolute error. Characteristic values ​​related to the tuning of the hyperparameters of a machine learning model are the accuracy, loss, and inference speed of that machine learning model. As an example, the simulation is a TCAD (Technology Computer Aided Design) simulation. The parameter optimization system 100 repeatedly proposes suggested points by the parameter optimization device 110 and acquires observed values ​​of the objective function at the suggested points by the observation device 120, and outputs the parameter vector value corresponding to the smallest observed value as the optimal point to the outside. The parameter optimization system 100 can also be used, for example, from an external edge device via cloud computing. Hereafter, observed values ​​of characteristics and objective functions may be abbreviated as characteristic values ​​and objective function values, respectively. Also, observed values ​​of the objective function may be abbreviated as observed values.

[0017] Parameter optimization can involve either maximizing or minimizing the value of an objective function. Maximizing is equivalent to minimizing by multiplying the objective function value by -1. For simplicity, the following explanation will focus on finding the parameter vector value that minimizes the objective function. However, the parameter optimization described in this embodiment is not limited to minimization. The parameter optimization described in this embodiment can also be applied to problems that maximize the value of an objective function.

[0018] As shown in Figure 1, the parameter optimization device 110 includes a processor 1, a storage device 2, an input device 3, a display device 4, and a communication device 5. Data and various signals from the processor 1, storage device 2, input device 3, display device 4, and communication device 5 are transmitted and received via a bus.

[0019] Processor 1 is an integrated circuit that controls the overall operation of the parameter optimization device 110. For example, processor 1 has a CPU (Central Processing Unit), a GPU (Graphics Processing Unit), a DSP (Digital Signal Processor), and / or an FPU (Floating-Point Unit). Processor 1 may also have internal memory and I / O interfaces. Processor 1 performs various processes by interpreting and calculating programs pre-stored in a storage device 2 or the like. Processor 1 may be partially or entirely implemented by hardware such as an ASIC (Application Specific Integrated Circuit) or FPGA (Field Programmable Gate Array).

[0020] The storage device 2 is a volatile memory and / or non-volatile memory that stores various types of data. For example, the storage device 2 stores data and settings used by the processor 1 when it performs various processes, data generated by various processes performed by the processor 1, and observation samples and missing points described later. The storage device 2 is composed of ROM (Read Only Memory), RAM (Random Access Memory), HDD (Hard Disk Drive), SSD (Solid State Drive), integrated circuit memory, etc. The storage device 2 may also have a non-temporary computer-readable storage medium that stores programs executed by the processor 1.

[0021] Input device 3 receives various inputs from the operator. Input device 3 can include a keyboard, mouse, various switches, touchpad, touch panel display, etc. Electrical signals corresponding to the received inputs (hereinafter referred to as operation signals) are supplied to processor 1.

[0022] Display device 4 displays various data according to the control of processor 1. Display device 4 can be a CRT (Cathode-Ray Tube) display, liquid crystal display, organic EL (Electro-Luminescence) display, LED (Light-Emitting Diode) display, plasma display, or any other display as appropriate. Display device 4 may also be a projector.

[0023] The communication device 5 includes a communication interface such as a network interface card (NIC) for data communication with various devices connected to the parameter optimization device 110 via a network. Operation signals may be supplied from a computer connected via the communication device 5 or from an input device on that computer, and various data may be displayed on a display device on a computer connected via the communication device 5. However, for the sake of simplicity in the following explanation, unless otherwise specified, the source of the operation signals will be the input device 3, and the destination for the display of various data will be the display device 4. The input device 3 can be replaced by a computer connected via the communication device 5 or from an input device on that computer, and the display device 4 can be replaced by a display device on a computer connected via the communication device 5, etc.

[0024] The parameter optimization device 110 does not need to include all of the processor 1, storage device 2, input device 3, display device 4, and communication device 5. Some of the storage device 2, input device 3, display device 4, and communication device 5 may be omitted as needed. The parameter optimization device 110 may be provided with any additional hardware devices useful for executing the processing according to this embodiment. The parameter optimization device 110 does not need to consist of a single physical computer; it may consist of a computer system having multiple computers connected communicably via wired or network lines. The assignment of the series of processes according to this embodiment to the multiple processors 1 implemented in each of the multiple computers can be arbitrarily configured. All processors 1 may execute all processes in parallel, or specific processes may be assigned to one or some of the processors 1, and the series of processes according to this embodiment may be executed by the entire computer system.

[0025] As shown in Figure 1, the processor 1 has a functional configuration including an acquisition unit 11, a calculation unit 12, a first proposal unit 13, a second proposal unit 14, an output unit 15, and a control unit 16.

[0026] The acquisition unit 11 acquires various data related to parameter optimization. For example, the acquisition unit 11 acquires observation samples or missing points from the observation device 120. An observation sample is a pair of observation points where observations were successful and the corresponding observed values ​​of the objective function. Missing points are observation points where the objective function value was not observed. Observation points are parameters related to the device or material to be designed, the system or robot to be controlled, or the machine learning model. In the design of a power device, observation points are, for example, dimensions including width and height that define the structure of the power device. In the design of a material, observation points are, for example, the amount or ratio of material substances to be mixed, concentration, temperature and pressure of the material substances and manufacturing environment, and processing time. In the control system of a system or robot, observation points are, for example, adjustable parameters of the control equipment.

[0027] The calculation unit 12 calculates the acquisition function based on the observed samples. The acquisition function is used to search for the parameter vector values ​​for which the objective function value should be observed next.

[0028] The first proposal unit 13 proposes candidate observation points as points where the observation device 120 should next observe the objective function value, based on the value of the acquisition function. Hereafter, in the first proposal unit 13, "propose" means outputting the candidate observation points to the second proposal unit 14, which will be described later.

[0029] The second proposal unit 14 determines the next point to be observed based on the candidate observation points and proposes it as a proposed point. Hereafter, in the second proposal unit 14, "propose" means outputting the proposed point to an observation device outside the parameter optimization device 110. As an example, the observation device to which the proposed point is output will be described as observation device 120.

[0030] The output unit 15 outputs optimized parameters. The output unit 15 outputs observation point information to the outside, for example, for observation points that meet the output conditions from the first set. The observation point information is information that includes parameter vector values ​​corresponding to the observed values.

[0031] The control unit 16 comprehensively controls the parameter optimization device 110. Specifically, the control unit 16 controls the acquisition of observation samples or missing points by the acquisition unit 11, the storage of observation samples or missing points in the memory device 2, the calculation of the acquisition function by the calculation unit 12, the proposal of candidate observation points by the first proposal unit 13, and the proposal of proposed points by the second proposal unit 14, to be repeated until the termination condition is met, in response to the acquisition of observation values ​​by the observation device 120. In order to control the system in response to the acquisition of observation samples or missing points from the observation device 120, the control unit 16 has a function to monitor the acceptance of the observation samples or missing points by the acquisition unit 11 and a function to monitor the transmission of proposed points by the second proposal unit 14 to the parameter optimization device 110. The optimal point (parameter vector value) at the end of the repetition is called the optimal point. After the termination condition is met, the optimal point is provided to an external device different from the parameter optimization device 110 by the output unit 15 under the control of the control unit 16.

[0032] Figure 2 is a diagram showing the flow of parameter optimization processing by the parameter optimization system 100 according to the first embodiment. Figure 3 is a block diagram illustrating the data flow of the parameter optimization processing shown in Figure 2.

[0033] As shown in Figure 2, the control unit 16 performs initialization of the parameter optimization device 110 (step S201). The control unit 16 sets time t to 0 at the start of step S201 and sets time t to 1 at the end of step S201. Time t is the time used for the parameter optimization process and represents the number of iterations of the processing loop in Figure 2.

[0034] Furthermore, in step S201, the control unit 16 initializes the storage device 2 and the extracted sample set (extracted data) E described later. t The data is supplied to the calculation unit 12, and the set of missing points F tIt is supplied to the second proposal unit 14. As initialization of the storage device 2, for example, at least one or more observation samples, which are combinations of parameter vector values and observed values of the objective function corresponding to the parameter vector values, are stored in the storage device 2 as initial values. Specifically, when there are observed observation samples, the initial value is the observed sample, and when there are no observed observation samples, the initial value is an observation sample that is a combination of a randomly given observation point and the objective function value corresponding to the observation point.

[0035] The storage device 2 stores the observation sample as an element (member) of the first set D t and stores the missing point as an element (member) of the second set F t . The first set D t is called an observation sample set (observation data). The second set F t is called a missing point set. Let the observation point, which is the n-th D-dimensional parameter vector value stored in the storage device 2, be x n (n = 0, 1,..., N t-1 ), the objective function value related to x n be y n , the observation sample be (x n , y n ), and the m-th missing point be x (F),m (m = 0, 1,..., M t-1 ). Then, the observation sample set D t and the missing point set F t at time t are respectively represented by the following equations (1) and (2).

[0036]

Equation

[0037] N t represents the number of elements of the observation sample set D t and is an integer of 1 or more. M t represents the number of elements of the missing point set F t and is an integer of 0 or more. When M t is 0, the missing point set F t is an empty set.

[0038] Extracted sample set E t This is the observed sample set D t This is data from which samples satisfying predetermined conditions are extracted from the elements of the observed sample set D. t It is a subset of E. Since it is a subset, the sample set E is t This is the observed sample set D t It is acceptable for it to be the same as the other sample. A sample that satisfies the specified conditions is, for example, the observed sample set D. t Number of elements N t N of t A few K, which is less than that. t These are samples selected randomly. In this case, the extracted sample set E t The number of elements is K. t This is a set of samples. Extracted sample set E t Number of elements K t For example, there are about 100 of them.

[0039] Note that observation sample set D t Sample set E extracted from t The conditions for extraction are not limited to those mentioned above. Extraction sample set E t Any condition can be set as long as the set is not empty. Also, the set of missing points F t If the missing points F are not stored in memory device 2, t It is not necessary to supply the second proposal section 14, and the set of missing points F t You may also supply a signal that indicates the set is empty.

[0040] Below is the objective function value y. n Although this is treated as a scalar value, this embodiment is also applicable to vector values.

[0041] When step S201 is performed, the calculation unit 12 calculates the observation sample set D stored in step S201. t Based on this, the acquisition function is calculated (step S202). As an example, the calculation unit 12 calculates the extracted sample set E t From the function a tThe calculated acquisition function a t This is supplied to the first proposal unit 13. Here, the acquisition function a t The input to this is the parameter vector value x.

[0042] Acquisition function a t Examples of acquisition functions include the Lower Confidence Bound multiplied by -1, which is calculated based on Gaussian process regression (GP regression), random forests, TPE (Tree-structured Parzen Estimator), etc., as well as Expected Improvement, Probability of Improvement, Information Grain, Entropy Search, and Knowledge Gradient. In problems where the objective function value is to be maximized rather than minimized, the acquisition function can be the Upper Confidence Bound.

[0043] Here, the acquisition function a t When calculating this using GP regression, the high computational cost of the inverse matrix required in the calculation process can be a problem. The computational cost of the inverse matrix is ​​O(N). 3 It is known that ) , where N represents the number of samples input to the GP regression. Extracted sample set E t As such, the observed sample set D t If we adopt this approach, the computational cost of the inverse matrix is ​​O(N). t 3 ) and the number of observed samples N t It increases exponentially as [the value] increases.

[0044] On the other hand, observation sample set D t A set of extracted samples E with fewer elements than E. t By using parameter optimization, the computational cost of this embodiment is O(K t 3 ) and K t <N t Therefore, the observed sample set D t The computational cost when using this approach is O(N t 3This makes it possible to reduce the computational cost of GP regression compared to ). t If we treat as a constant independent of time t, the computational cost will also be a constant value.

[0045] When step S202 is performed, the first proposal unit 13 proposes the argument that maximizes the value of the acquisition function calculated in step S202 as an observation candidate point (step S203). As an example, the first proposal unit 14 selects the acquisition function a from the domain of the parameter vector value x. t The system calculates the point where the value is large, proposes it as a candidate observation point x', and supplies this x' to the second proposal unit 14. Acquisition function a t To calculate the points where the value becomes large, methods such as grid search, random search, L-BFGS (Limited-memory Broyden-Fletcher-Goldfarb-Shanno) and evolutionary strategies can be used.

[0046] When step S203 is performed, the second proposal unit 14 proposes a proposed point based on the candidate observation point (step S204). The second proposal unit 14 proposes a proposed point, for example, in response to a determination of whether or not the set of distances between each missing point and a candidate observation point stored in the memory device 2 contains any points below a threshold. As an example, the threshold is 10 -8 It is to that extent.

[0047] The threshold is not limited to the values ​​mentioned above. For example, if it is experimentally or theoretically known that observation points within a predetermined distance from a missing point are missing points, the threshold may be set to the value of that predetermined distance. The threshold may also be obtained via the input device 3, or it may be obtained from outside the parameter optimization device 110 by being received via the communication device 5. This allows the user to specify the threshold.

[0048] As an example, the detailed processing of step S204 will be explained below using Figure 4. Figure 4 is a diagram showing the detailed processing flow of step S204 in Figure 2 by the parameter optimization system 100 according to the first embodiment.

[0049] When step S203 is performed, the second proposal unit 14 determines whether or not there are any missing points in the set of missing points stored in the memory device 2 whose distance from the candidate observation point proposed in step S203 is less than or equal to a threshold (step S241). The distance used for the determination by the second proposal unit 14 is, for example, the Euclidean distance or the Mahalanobis distance. If the set of missing points is empty, or if it is determined that the distance from the candidate observation point to all missing points in the set of missing points is not less than or equal to a threshold (step S241: NO), the candidate observation point proposed in step S203 is proposed as a proposed point (step S242).

[0050] If it is determined that the distance from any missing point in the set of missing points to a candidate observation point is less than or equal to a threshold (step S241: YES), the second proposal unit 14 generates a perturbation point based on the candidate observation point proposed in step S203 (step S243). The second proposal unit 14 generates the perturbation point by, for example, adding a random vector value that follows a predetermined probability density distribution to the parameter vector value representing the candidate observation point. Hereinafter, the condition that the distance from a missing point is less than or equal to a threshold will be referred to as matching a missing point.

[0051] Figure 5 shows the candidate observation point x'. (t+1) This figure illustrates an example. The horizontal axis represents the value of parameter x, and the vertical axis represents the value of the objective function. The dashed line represents the unknown objective function. The region enclosed by the dashed line around the parameter values ​​represents the perturbation range. The perturbation range is the range of parameter values ​​for which the probability density of the probability density distribution followed by the random numbers used to generate the perturbation points is positive. If there are multiple parameters, the horizontal axis cannot be represented in one dimension, but for the sake of simplifying the figure, the horizontal axis is represented in one dimension. Observation candidate point x' in step S241 (t+1) The missing point x (F),m If it is determined to match, the second proposal unit 14, for example, the observation candidate point x' (t+1) It is preferable to generate perturbation points using random numbers that follow a probability density distribution whose probability density is positive only in the perturbation range in the vicinity of x'. The perturbation range is at least the observed candidate point x' in step S241. (t+1)It is preferable to set the perturbation range wider than the minimum range that includes the missing points that are determined to be matched. For example, the perturbation range is within ±1 centered on the candidate observation point. (t+1) By setting the perturbation range wider than the minimum range that includes missing points that are determined to be matched, it is possible to reduce the probability that the generated perturbation points will match missing points. Furthermore, by setting the perturbation range only to the vicinity of the candidate observation points, it is possible to search for parameters in the vicinity of missing points or candidate observation points without delaying the parameter search.

[0052] Figure 6 shows an example of a probability density distribution. The upper graph (a) is the same as in Figure 5, and the lower graph (b) shows a probability density distribution where the perturbation range is set only in the vicinity of the candidate observation point. In the lower graph (b), the horizontal axis represents the parameter value and the vertical axis represents the probability density. The thick line in graph (b) represents a probability density distribution with a uniform probability density within the perturbation range (a uniform distribution within the perturbation range). Generally, there are multiple parameters and therefore it cannot be represented in one dimension, but for the sake of simplifying the figure, the horizontal axis is represented in one dimension. In this probability density distribution, the candidate observation point x' (t+1) The probability density is positive and uniform only within the perturbation range in the vicinity of the point, and is zero outside the perturbation range. Therefore, perturbation points are generated with equal probability from points within the perturbation range.

[0053] Once step S242 is performed, the second proposal unit 14 proposes the perturbation points generated in step S243 as proposal points (step S244).

[0054] When step S242 or step S244 is performed, the acquisition unit 11 acquires observation samples or missing points as observation results for the proposed points proposed in step S242 or step S244 (step S205). As an example, the acquisition unit 11 acquires the proposed points x outside the parameter optimization device 110 (t+1) The objective function value y is determined based on one or more characteristic values. (t+1)is observed without problems and no missing measurement occurs, the acquisition unit 11 acquires an observation sample (x (t+1) , y (t+1) ) from outside the parameter optimization device 110. Also, when a missing measurement occurs in the observation at the proposed point outside the parameter optimization device 110, the acquisition unit 11 acquires x (t+1) as a missing measurement point from outside the parameter optimization device 110. As an example, the acquisition unit 11 acquires an observation sample or a missing measurement point from the observation device 120.

[0055] When step S205 is performed, the control unit 16 stores the observation sample or missing measurement point acquired in step S205 in the storage device 2 (step S206). As an example, when the acquisition unit 11 acquires an observation sample (x (t+1) , y (t+1) ) in step S205, the control unit 16 stores the observation sample (x (t+1) , y (t+1) ) in the storage device 2 as an element of the observation sample set D t (D t+1 ←D t ∪(x (t+1) , y (t+1) )), advances the time by one (t←t + 1), sends the extraction sample set E t to the calculation unit 12, and supplies the missing measurement point set F t to the second proposal unit 14. Alternatively, when the acquisition unit 11 acquires x (t+1) as a missing measurement point in step S205, the control unit 16 stores x (t+1) in the storage device 2 as an element of the missing measurement point set F t+1 (F t+1 ←F t ∪x (t+1) ), advances the time by one (t←t + 1), sends the extraction sample set E t to the calculation unit 12, and supplies the missing measurement point set F t to the second proposal unit 14. The observation at the proposed point is made, for example, by the observation device 120.

[0056] When step S206 is performed, the control unit 16 determines whether or not to terminate the loop based on the termination condition (step S207). The termination condition is, for example, the number of observations (N t +M t ) and the number of observed samples N t The condition is that the parameter reaches a predetermined value. Other predetermined termination conditions include the elapsed time reaching a predetermined value, and the monetary cost, including the budget for observation with the observation device 120, reaching a predetermined value. The elapsed time is the time required for the parameter optimization process and is distinct from time t.

[0057] Note that the termination conditions are not limited to the above conditions. For example, in an objective function maximization problem, the termination condition may be that the observed value of the objective function exceeds a predetermined threshold, and in an objective function minimization problem, the termination condition may be that the observed value of the objective function falls below a predetermined threshold.

[0058] If it is determined that the loop should not be terminated (step S207: NO), the process returns to step S202. Then, the process from step S202 to step S207 in Figure 2 is repeated until the termination condition is met.

[0059] If it is determined that the loop should be terminated (step S207: YES), the observation point information for the observation points that meet the output conditions among the elements of the observation sample set is output (step S208). The output unit 15 outputs the observation sample set D stored in the storage device 2. t From among these, the parameter optimization device 110 outputs to the outside the observation point x that corresponds to the observation value that best represents the objective function. In the case of an objective function minimization problem, the output condition is that the corresponding observation value is in the observation sample set D. N The condition is that the output value is the minimum of the observed values ​​of the objective function included in the set of observed samples D. Furthermore, if it is a problem of maximizing the objective function, the output condition is that the corresponding observed value is the minimum of the observed sample set D. NThe condition is that it is the maximum value among the observed values ​​of the objective function included. As an example, the output unit 15 outputs the optimal observation point to the edge device that has requested parameter optimization processing from the parameter optimization system 100. The output unit 15 may also output the objective function value or characteristic value corresponding to the optimal observation point. In addition, in order to output the characteristic value, it is advisable to store the observed value of the characteristic value corresponding to each observation point in the memory device 2 during the processing.

[0060] Note that the output conditions are that the corresponding observed value is in the observation sample set D. t The condition is not limited to the best observation value among them. For example, the output condition may be that the corresponding observation value is above or below a predetermined threshold, or the observation sample set D t The condition may also be that it is included in the observation sample set D. The output unit 15 may output observation point information for all observation points that satisfy the output condition. t If the condition is that it is included in the observed sample set D, t The observation point information for all observation points included in the output is displayed. In this case, the user can obtain all the historical data from the parameter optimization process.

[0061] When step S208 is performed, the parameter optimization process by the parameter optimization system 1 according to the first embodiment is terminated.

[0062] Note that the set of missing points F t If the set contains multiple missing points, the second proposal unit 14 determines whether the candidate observation point matches each of the multiple missing points. t If it is determined that the candidate observation point does not match any of the missing points included in the set F, the second proposal unit 14 proposes the candidate observation point as a proposed point. t If it is determined that the observed candidate point matches at least one of the missing points included in the list, the second proposal unit 14 generates a perturbation point different from each of the multiple missing points based on the observed candidate point and proposes the perturbation point as the proposed point.

[0063] Furthermore, in step S243, the perturbation points do not necessarily have to be generated by random numbers. For example, the second proposed unit 14 may generate perturbation points by moving the observation candidate points by a predetermined amount. As an example, the predetermined amount may be set to approximately 0.01 times the distance from one endpoint to the other in the domain.

[0064] Also, the extracted sample set E t This is the observed sample set D t K, randomly selected from among t It does not have to be a set of individual samples.

[0065] In the following steps, the first proposed section 13 obtains the function a in step S203. t We search for points where x becomes large in a space with a lower dimension than the parameter space, and then find the next observation point x (t+1) The following describes the case where a proposal is made. The space being searched is called the low-dimensional search space. As an example, the low-dimensional search space is an R-dimensional affine subspace (where R is an integer between 1 and D, inclusive) that passes through a point represented by a predetermined parameter vector value in a D-dimensional space. As the predetermined parameter vector value, for example, the parameter vector value corresponding to the smallest observation value among multiple observation values ​​stored in memory device 2 is adopted. When the second proposal unit 14 searches for a proposal point from the low-dimensional space, the extracted sample set Et is the observation sample set D t This is the set of observational samples included in the , corresponding to observation points whose distance to the low-dimensional search space is below a predetermined threshold. The distance can be either Euclidean distance or Mahalanobis distance. The diagonal component vector of the covariance matrix of the Mahalanobis distance should be the length scale vector of the kernel function obtained by GP regression considering ARD (Automatic Relevance Determination), and the components other than the diagonal components should be set to 0.

[0066] Extracted sample set E t The number of samples is K t This is represented by the extracted sample set E. t This is the observed sample set D tThe extracted sample set E is a set of observational samples that correspond to observation points whose distance to the low-dimensional search space is less than or equal to a predetermined threshold. t and the observed sample set D t The relationship with the number of samples is K if the threshold is set small. t <N t This is the relationship with the number of samples K. t <N t Therefore, the aforementioned extracted sample set E t Similarly, it has the effect of reducing computational costs.

[0067] Observation sample set D t Sample set E extracted from t By adopting the condition that the distance to the low-dimensional search space is below a predetermined threshold as a predetermined condition for extracting the parameters, the search efficiency is improved when the number of parameters D to be adjusted is large.

[0068] If the first proposed part 13 searches for the next observation point in a D-dimensional parameter space, then if D is large, it becomes impossible to secure enough observational samples to construct a surrogate model for the high-dimensional objective function of D dimensions. Here, the problem that the number of samples required to construct a highly accurate model increases exponentially with the number of dimensions of the space is known as the curse of dimensionality. When D is large, the acquisition function tends to become flat due to the curse of dimensionality. In Bayesian optimization, the next observation point is proposed based on the concavity of the acquisition function, which is a surrogate model for the objective function. Therefore, if the acquisition function becomes flat, it becomes impossible to appropriately propose the next observation point. As a result, the search efficiency decreases.

[0069] As mentioned above, the observation sample set D is the set of observation points that correspond to short observation points whose distance to the low-dimensional search space is below a predetermined threshold. t Extracted sample set E t By using this, the acquisition function a tThe search range for points where the value is large is limited to a lower-dimensional search space, rather than a high-dimensional parameter space of D dimensions. By lowering the dimension of the search space, we are freed from the curse of dimensionality, and the acquisition function no longer becomes flat, allowing us to propose appropriate points, at least within the lower-dimensional search space. This improves the search efficiency when the number of parameters D is large.

[0070] In this case, in step S243, the second proposed unit 14 may generate perturbation points using a probability density distribution defined in the low-dimensional search space.

[0071] According to the first embodiment, the observation candidate point x' (t+1) The missing point x (F),m If it is determined to match, the observation candidate point x' (t+1) The perturbation point generated in the vicinity of is the proposed point x for the next observation. (t+1) Since it is proposed as such, if the perturbation range is wider than the threshold, the proposed point x (t+1) The observation candidate point x' has a high probability of being (t+1) It does not match. Therefore, proposed point x (t+1) It is highly likely that this is not a missing point. This means that even if the missing data at the same point is reproducible, the parameter optimization will not stagnate and will proceed. Also, observation candidate point x' (t+1) The proposed point x is a point perturbed in the neighborhood of the missing point, i.e., in the neighborhood of the missing point. (t+1) Since it is proposed in this way, it is possible to search for the optimal solution without missing any neighboring data points.

[0072] (Variation 1) In the first embodiment, in step S243 of Figure 4, the second proposal unit 14 is located at the observation candidate point x' (t+1) An example of generating perturbed points by perturbing the following was shown. The second proposal part 14 is a set of missing points F t Generates a perturbation point that does not match any of the elements.

[0073] The following describes the changes from the first embodiment in Modification 1 with reference to Figure 7. Figure 7 is a diagram showing the detailed processing flow of step S204 in Figure 2 by the parameter optimization system 100 according to Modification 1. Steps S251, S252, and S255 correspond to steps S241, S242, and S244 in Figure 4, respectively. Therefore, steps S253 and S254 will be described in detail.

[0074] If it is determined that the candidate observation point matches any missing point included in the set of missing points (step S251: YES), the second proposal unit 14 generates a perturbation point based on the candidate observation point proposed in step S203 (step S253). The second proposal unit 14 generates the perturbation point, for example, in the same manner as in step S243 of Figure 4.

[0075] When step S253 is performed, the second proposal unit 14 determines whether the perturbation point generated in step S253 matches any element included in the set of missing points (step S254). The threshold used to determine whether they match may be the same as in step S251. If it is determined that the perturbation point generated in step S253 does not match any of the missing points included in the set of missing points Ft (step S254: NO), the second proposal unit 14 proposes the perturbation point as a proposed point (step S255).

[0076] If it is determined that the perturbation point generated in step S253 matches any missing point included in the set of missing points (step S254: YES), the process returns to step S253.

[0077] Note that the threshold values ​​for step S251 and step S254 may be set to different values.

[0078] According to variation 1, proposed point x (t+1) This is the set of missing points F tIt is guaranteed that all elements will not match. Therefore, even if the missing data at the same point is reproducible in the observation device 120, the optimization of the parameters will proceed without stagnation. Also, the observation candidate point x' (t+1) The proposed point x is a point perturbed in the neighborhood of the missing point, i.e., in the neighborhood of the missing point. (t+1) As proposed, the parameter optimization device 110 according to Modification 1 can search for an optimal solution even if one exists near a missing point, without missing it. In particular, when the observation device 120 is a simulator that numerically solves differential equations, missing data may occur near missing points due to calculation errors, etc. Therefore, by avoiding the proposal of observation points near missing points, it is possible to suppress the probability of missing data occurring at the proposed points, and consequently improve the efficiency of parameter search.

[0079] (Modification 2) In the first embodiment, in step S243 of Figure 4, the second proposal unit 14 is located at the observation candidate point x' (t+1) An example of generating perturbation points by perturbing is shown. In the second proposed unit 14 according to modified example 2, multiple perturbation points are generated in step S243 of Figure 4.

[0080] The following describes the changes from the first embodiment in Modification 2 with reference to Figures 2 and 4. Since steps S201, S203, S205, S206, and S207 in Figure 2, and steps S241 and S242 in Figure 4 are the same as in the first embodiment, steps S202, S243, and S244 will be described in detail. Note that the parameter optimization device 110 in Modification 2 is not shown.

[0081] In step S202, the control unit 16 calculates the acquisition function a in step S202. t This will be supplied to the second proposal section 14.

[0082] In step S243, the second proposal unit 14 generates a plurality of perturbation points based on the candidate observation points proposed in step S203. The second proposal unit 14 performs, for example, the process of step S243 in the first embodiment multiple times.

[0083] In step S244, the second proposal unit 14 proposes as a proposed point the point among the multiple perturbation points generated in step S243 that maximizes the acquisition function calculated in step S202.

[0084] Furthermore, similar to Modification 1, multiple perturbation points are missing from the set of points F. t It may be determined whether each element matches. In this case, in step S254 of Figure 7, the multiple perturbation points generated in step S253 are the missing point set F t The system determines whether each element matches. If it is determined that at least one of the multiple perturbation points does not match any element of the set of missing points (step S254: NO), the second proposal unit 14 proposes the point with the maximum value of the acquisition function among the one or more perturbation points that were determined not to match any missing points as a proposed point. If it is determined that all of the multiple perturbation points match any of the missing points included in the set of missing points (step S254: YES), the system returns to the process in step S253. In this case, one perturbation point may be generated in step S253. Also, if there are multiple points with the maximum value of the acquisition function, the second proposal unit 14 may select one of the multiple points with the maximum value of the acquisition function and propose the selected point as a proposed point. The second proposal unit 14 may select the point closest to the observation candidate point, select one point according to the observation order, or select one point according to the density of neighboring missing points.

[0085] According to Modification 2, compared to the case where only one perturbation point is generated, the proposed point x (t+1) Acquisition function a in t The probability of the value becoming larger increases. Therefore, proposed point x (t+1) This is expected to improve the value of the objective function. Therefore, it is possible to improve the parameter search efficiency per observation.

[0086] (Variation 3) In the first embodiment, in step S243 of Figure 4, the second proposal unit 14 demonstrates an example in which it generates perturbation points using random numbers that follow a probability density distribution in which the probability density is set to positive only in the perturbation range near the candidate observation point. In the third modification, the second proposal unit 14 generates perturbation points using random numbers that follow a normal distribution with the candidate observation point as the mean.

[0087] The following describes the changes from the first embodiment in Modification 3 with reference to Figure 4. Since steps S241, S242, and S244 are the same as in the first embodiment, step S243 will be described in detail.

[0088] In step S243, the second proposed unit 14 determines the observation candidate point x' (t+1) Perturbation points are generated using random numbers (normal random numbers) that follow a multivariate normal distribution with the mean vector as . If there is no prior knowledge about the likelihood of missing data, the covariance matrix of the multivariate normal distribution should be set to a constant multiple of the identity matrix. If there is prior knowledge about the likelihood of missing data, the covariance matrix of the multivariate normal distribution should be set to a covariance matrix that reflects the prior knowledge. The covariance matrix should be set by the second proposal section 14 or the control section 16. Hereinafter, the multivariate normal distribution will simply be referred to as the normal distribution.

[0089] Figure 8 shows an example of a normal distribution used in Modification 3. The upper graph (a) is the same as in Figure 5, and the solid line in the lower graph (b) represents the normal distribution. The horizontal axis of the lower graph (b) represents the parameter values, and the vertical axis of the lower graph (b) represents the probability density. Generally, there are multiple parameters and therefore it cannot be represented in one dimension, but for the sake of simplifying the figure, the horizontal axis is represented in one dimension. In the normal distribution of the lower graph (b), the candidate observation point x' (t+1) The probability density is high in the vicinity of x', and the candidate observation point x' (t+1) The probability density is small at positions far from the point. Therefore, the perturbation point is the candidate observation point x'. (t+1) It is likely to be generated in the vicinity of [this location].

[0090] According to Variation 3, the candidate observation point x' (t+1) The set of missing points F t If it is determined to match any of the elements contained in, the observation candidate point x' (t+1) Since the proposed points are perturbation points generated by random numbers following a normal distribution with mean vector x, the proposed points x (t+1) This is the observation candidate point x' (t+1) It is easy to obtain values ​​in the vicinity of the missing point. Therefore, the parameter optimization device 110 according to Modification 3 can search for an optimal solution even if one exists in the vicinity of the missing point, without missing it. In addition, if the standard deviation of the normal distribution is set to be large, the probability that a perturbation point generated by a normally distributed random number coincides with a missing point is not high, so the parameter optimization can proceed without stagnation.

[0091] (Modification 4) In the third modification, in step S243 of Figure 4, the second proposed unit 14 is the observation candidate point x' (t+1) An example was shown in which perturbation points are generated using random numbers following a normal distribution with mean vector as the mean vector. The second proposed part 14 relating to modification 4 generates perturbation points using random numbers following a probability density distribution obtained by modifying the normal distribution so that the probability density at all missing points in the set of missing points is small. For the sake of simplicity, we will explain using the case where the number of elements in the set of missing points is 1 as an example. When the number of elements in the set of missing points is 1, the observed candidate point x' (t+1) It is determined that this coincides with the only missing data point.

[0092] The following describes the changes from Modification 3 in Modification 4 with reference to Figure 4. Steps S241, S242, and S244 are the same as in the first embodiment, so step S243 will be described in detail. A probability density distribution obtained by modifying the normal distribution is called a modified distribution.

[0093] In step S243, the second proposed unit 14 determines the observation candidate point x' (t+1) Perturbation points are generated using random numbers that follow a modified distribution based on a normal distribution with as its mean vector. As an example, the second proposed part 14 generates perturbation points using the set of missing points F supplied in step S201. tA modified distribution may be created based on this.

[0094] Figure 9 shows an example of a method for creating the modified distribution used in Modification 4. The solid line in the upper graph (a) represents the normal distribution of Modification 3. The solid line in the middle graph (b) represents the function of the coefficients related to each parameter vector value. The solid line in the lower graph (c) represents the modified distribution used in Modification 4. The modified distribution in graph (c) is preferably created by multiplying the normal distribution in graph (a) by the function of the coefficients in graph (b) and normalizing it so that the integral value over the entire range is 1. As an example, the function of the coefficients is a function obtained by inverting the magnitude of the values ​​of a normal distribution whose covariance matrix is ​​0.5 times that of the identity matrix, where the covariance matrix of the normal distribution to be modified is the identity matrix, and normalizing the range from 0 to 1. Here, we are explaining using the example of a case where there is only one missing point, so this missing point is x' in the figure. (t+1) This matches. The modified distribution created by this coefficient has a probability density of 0 at the missing point, increases sharply as you move away from the missing point, reaches a peak, and then decreases as you move further away from the missing point. This modified distribution has a valley shape near the missing point.

[0095] Figure 10 shows an example of a modified distribution used in Modification 4. The upper graph (a) is the same as in Figure 3, and the lower graph (b) is the same as graph (c) in Figure 9. In the lower graph (b), the horizontal axis represents the parameter values, and the vertical axis represents the probability density. Generally, there are multiple parameters and therefore it cannot be represented in one dimension, but for the sake of simplifying the figure, the horizontal axis is represented in one dimension. The perturbation points generated by random numbers following the modified distribution in graph (b) are the candidate observation points x'. (t+1) It tends to be generated at a location slightly away from both the data points and the missing data points.

[0096] Although Figures 9 and 10 illustrate the case with one missing point, Modification 4 is also applicable to cases with multiple missing points. The second proposed part 14 creates a modified distribution by, for example, creating a function of coefficients for each of the multiple missing points and multiplying the function of all the created coefficients by a normal distribution. The modified distribution thus created has a valley shape in the vicinity of each missing point.

[0097] According to Modification 4, the perturbation points generated by random numbers following the modified distribution are the proposed points x (t+1) Therefore, the proposed point x (t+1) This is the observation candidate point x' (t+1) The vector value tends to be located slightly away from the point. Therefore, the parameter optimization device 110 according to modified example 4 can search for an optimal solution in the vicinity of a missing point without missing it. Also, the set of missing points F t By modifying the system so that the probability density at each missing point included in the system becomes 0, the proposed point x (t+1) This is the set of missing points F t It is guaranteed that it will not coincide with any other element. Therefore, even if the missing data at the same point is reproducible in the observation device 120, the optimization of the parameters will proceed without stagnation.

[0098] (Variation 5) In the first embodiment, in step S243 of Figure 4, the second proposal unit 14 demonstrates an example in which it generates perturbation points using random numbers whose probability density follows a positive probability density distribution only within the perturbation range near the candidate observation point. In the modified example 5, the second proposal unit 14 controls the perturbation range, which is a parameter of the probability density distribution, based on the degree of density of missing points.

[0099] Specifically, a function of the density of missing points related to the parameter vector values ​​is estimated using kernel density estimation. As a result, a kernel density estimator is obtained in which the value is large for parameter vector values ​​with a high density of missing points and small for parameter vector values ​​with a low density of missing points. The perturbation range includes the candidate observation points and is defined as the range in which the estimated density of missing points is above a predetermined threshold.

[0100] According to Modification 5, if there is a high concentration of missing data points near the candidate observation point, the perturbation range is wide, and if there is no high concentration, the perturbation range is narrowed. Therefore, the proposed point x is set to be as close as possible to the candidate observation point. (t+1) While proposing it as such, the proposed point x (t+1) This can avoid missing data.

[0101] (Experimental variation 6) In Modification 3 or Modification 4, in step S243 of Figure 4, the second proposal unit 14 shows an example in which perturbation points are generated using random numbers following a normal distribution or a modified distribution with the observed candidate points as the mean. In Modification 6, the second proposal unit 14 generates perturbation points using random numbers following a normal distribution or a modified distribution whose parameters are controlled by the density of missing points. Here, the parameters of the normal distribution controlled by the density of missing points are at least one value included in the mean vector and the covariance matrix. The parameters of the modified distribution controlled by the density of missing points are at least one value included in the parameters of the function of the aforementioned parameters and coefficients of the normal distribution.

[0102] Specifically, a function of the density of missing points related to the parameter vector values ​​is estimated using kernel density estimation. As a result, a kernel density estimator is obtained that is large for parameter vector values ​​with a high density of missing points and small for parameter vector values ​​with a low density of missing points. If the probability density distribution is a normal distribution, for example, the mean vector and covariance matrix can be obtained by Gaussian fitting to fit the distribution obtained by multiplying a given normal distribution by a kernel density estimator. When controlling parameters such as the mean vector and covariance matrix based on the density of missing points, the degrees of freedom of these parameters may be reduced. For example, the mean vector of the normal distribution may be fixed to the parameter vector value representing the candidate observation point. In this case as well, the covariance matrix can be obtained by Gaussian fitting. Since the covariance matrix has a high degree of freedom, it may be assumed that the covariance matrix is ​​expressed as a coefficient multiple of the unit vector, and only that coefficient may be controlled. For example, that coefficient may be the smallest value such that the density of missing points at all points within the range containing candidate observation points and where the density of missing points estimated by kernel density estimation is above a predetermined threshold. The covariance matrix may be assumed to be a diagonal matrix, and its diagonal components may be set to larger values ​​the wider the range where the density of missing points is above a predetermined threshold. The diagonal elements of the covariance matrix represent the variance for each parameter in the normal distribution, and therefore represent the spread of the normal distribution in the parameter space.

[0103] If the probability density distribution is a modified distribution, for example, the higher the density of missing points, the larger the values ​​of the elements in the covariance matrix of the coefficient function should be set. Alternatively, the mean vector and covariance matrix of the normal distribution exemplified in Figure 9(a) can be estimated as described above, and the covariance matrix of the coefficient function exemplified in Figure 9(b) can be controlled by multiplying the covariance matrix of the normal distribution by a coefficient. The coefficient should be a value greater than 0 and less than 1. The covariance matrix of the coefficient function may be set in the same way as in the 4th modification.

[0104] According to Modification 6, when missing points are densely clustered near candidate observation points, the spread of the normal distribution and the width of the valleys in the modified distribution become wider than when they are not. Therefore, the proposed point x is set to be as close as possible to the candidate observation points. (t+1) While proposing it as such, the proposed point x (t+1) This can avoid missing data.

[0105] (Example 7) In the first embodiment, in step S243 of Figure 4, the second proposal unit 14 demonstrates an example in which it generates perturbation points using random numbers that follow a probability density distribution in which the probability density is set to be positive only within the perturbation range near the candidate observation point. In the modified example 7, the second proposal unit 14 generates perturbation points using random numbers that follow a probability density distribution in which the perturbation range controlled by the length scale of the Gaussian process regression is set to be near the candidate observation point.

[0106] The calculation unit 12 includes, for example, a regression unit (not shown) internally. In step S202, the regression unit learns a GP regression model that has been learned from the observed sample set Dt, taking ARD into consideration. This estimates the length scale of the kernel function used in GP regression for each parameter. The larger the estimated length scale of a parameter, the wider the perturbation range is set.

[0107] Furthermore, in the second proposed section 14 relating to Modification 7, perturbation points may be generated using random numbers following a normal distribution defined by a covariance matrix controlled by the length scale of the GP regression. The covariance matrix of the normal distribution is set, for example, to a coefficient multiple of the identity matrix. The coefficient is set to be larger for parameters with larger estimated length scales.

[0108] According to Modification 7, the larger the length scale value and the lower the sensitivity to the characteristic, the wider the perturbation range becomes, making it easier for the generated perturbation points to avoid missing points. For parameters with a small length scale value and high sensitivity to the characteristic, the perturbation range is narrowed, so the generated perturbation points are closer to the observation candidate point x'. (t+1) This allows for observation of significant changes in characteristic values ​​without missing them. Furthermore, for parameters with a large length scale and low sensitivity to characteristics, the variance of the normal distribution increases, making it easier for generated perturbation points to avoid missing points. For parameters with a small length scale and high sensitivity to characteristics, the variance of the normal distribution decreases, making it easier for generated perturbation points to avoid missing points. (t+1) This brings us closer to the target value, allowing us to observe significant changes in characteristic values ​​without missing them.

[0109] (Variation 8) The parameter optimization device 110 according to modified example 8 is a set of missing points F t The system further includes a display unit (not shown) that displays information regarding missing points included in the data.

[0110] The control unit 16, for example, in steps S201 and S205 of Figure 2, retrieves the observation sample set D from the storage device 2. t and the set of missing points F t The data is sent to the display unit. The display unit displays the sent observation sample set D. t and the set of missing points F t It is preferable to display a screen containing information related to the above. The display screen may be in the form of a table or a plot. The display unit relating to Modification 9 below will be described assuming that it is displayed on the display device 4, but it is not limited to this. For example, the display unit may display the above content on a display connected to an external edge device that outputs the optimal observation point.

[0111] Figure 11 shows the observed sample set D. t or the set of missing points F tAn example of display screen I1 for showing the observation points included in the dataset in tabular format is shown. Display screen I1 includes Table I11, which contains the objective function value in the parameter vector and the parameters of the parameter vector. In this example, the number of dimensions D of the parameter vector is 2. That is, there are two types of parameters to be adjusted: the first parameter and the second parameter. In Table I11, the first column contains the objective function value, the second column contains the value of the first parameter, and the third column contains the value of the second parameter. Table I11 should be displayed in descending order of the time series of observations. The objective function value in the fourth row is labeled "ERR.", indicating that a missing value occurred when the parameter vector value was (34.4, 977.4). The numbers indicating the parameter vector value in the fourth row are highlighted in bold. This makes it easier for the user to notice the missing point. This highlighting makes it easier for the user to notice observation points close to the missing point. In Modification 9, it can be seen that the smallest objective function value of 56.3 was obtained at an observation point near the missing point. Furthermore, highlighting may be achieved not only through font weight, but also by distinguishing between text color, cell color, markings, blinking patterns, font types, and font sizes.

[0112] Figure 12 shows the observed sample set D. t or the set of missing points F t This shows another example of display screen I1 when the observation points included are displayed in a table format. Rows 1 through 4 and row 6 are the same as Table I11 in Figure 11. The numbers showing the parameter vector value (34.5, 977.3) in row 5 are also highlighted in bold because they are observation points generated by perturbation. Highlighting observation points generated by perturbation makes it easier for the user to notice observation points and observation samples generated by perturbation.

[0113] Figure 13 shows the observed sample set D. t or the set of missing points F tThis shows an example of display screen I2 when displaying the observation points included in the set D in plot format. Display screen I2 includes a plot of parameter vector values. In this example, the dimension D of the parameter vector is 2. That is, there are two types of parameters to be adjusted: the first parameter and the second parameter. Display screen I2 shows the observation sample set D on a coordinate plane where the horizontal axis represents the first parameter and the vertical axis represents the second parameter. t and the set of missing points F t The observation points included in the sample set D are plotted. t The observation points included are indicated by black circles, and the set of missing points F t Observation points included in this set are indicated with an "X". Observation sample set D t and the set of missing points F t Information indicating which category a mark belongs to may be highlighted not only by distinguishing the shape of the mark, but also by distinguishing the color, flashing pattern, or size of the mark.

[0114] Figure 14 shows the observed sample set D. t or the set of missing points F t This shows another example of display screen I2 when displaying the observation points included in the plot in a plot format. Points other than those displayed with black triangles are displayed in the same shape as in Figure 13. The observation points displayed with black triangles are observation points generated by perturbation. Observation points generated by perturbation may be highlighted not only by the shape of the mark, but also by distinguishing the color, blinking pattern, or size of the mark. Highlighting observation points generated by perturbation makes it easier for the user to notice them.

[0115] According to Modification 8, the user can focus on the missing points and / or observation points generated by perturbations. This is user-friendly because the user can see at a glance whether there are important observation points with small objective function values ​​near the missing points.

[0116] (Extreme variation 9) The control unit 16 in the modified example 9 determines whether or not to terminate the loop based on the termination conditions related to the characteristic value. For the purpose of explaining this modified example, the nth observation point xn A vector v is formed by listing the observed values ​​for each corresponding characteristic. n This is expressed as follows. Also, the nth observed sample is (x n , v n , y n This is represented by ). Regarding this modified example, only the difference from the parameter optimization process flow by the parameter optimization system 1 according to the first embodiment in Figure 2 will be explained below.

[0117] As part of the initialization of the storage device 2 in step S201, at least one observation sample is stored in the storage device 2 as an initial value, which is a combination of a vector formed by arranging the parameter vector value and the observed values ​​for each characteristic corresponding to the parameter vector value, and the observed value of the objective function corresponding to the parameter vector value. The storage device 2 is then controlled by the control unit 16 {x n ,v n ,y n |n=0,1,…,N t Observing sample set D t Remember it as such.

[0118] At observation device 120, proposed point x (t+1) Based on one or more characteristic values, the characteristic value v (t+1) and the objective function value y (t+1) If both are observed without problems and no missing data occurs, in step S205, the acquisition unit 11 takes the observed sample (x) from outside the parameter optimization device 110. (t+1) , v (t+1) , y (t+1) ) obtain.

[0119] In step S205, the acquisition unit 11 acquires the observed sample (x (t+1) , v (t+1) , y (t+1) If an observed sample (x) is obtained, in step S206 the control unit 16 will (t+1) , v (t+1) , y (t+1) ) Observed sample set D t As an element, it is added to memory device 2 (D t+1 ←D t ∪(x (t+1) , v(t+1) , y (t+1) )), advance the time by one (t←t+1), and extract the sample set E t The missing point set F is sent to the calculation unit 12. t This will be supplied to the second proposal section 14.

[0120] The termination condition for step S207 is, for example, the observation sample set D stored in the memory device 2. t This means that the result contains characteristic values ​​that satisfy predetermined specifications. Here, characteristic values ​​that satisfy the specifications are, for example, characteristic values ​​that are above a predetermined threshold, characteristic values ​​that are below a predetermined threshold, or characteristic values ​​that fall within a predetermined range.

[0121] According to Modification 9, since the termination conditions are based on characteristic values, it is possible to obtain the optimal point for devices, equipment, application software, and components that satisfy the specifications.

[0122] (Variation 10) The first embodiment was described using the case where there is one objective function and the objective function value y is a scalar as an example. There may be multiple objective functions, and there may be as many objective function values ​​for a given observation point as there are objective functions. The output condition for Modification 10 is the condition that it corresponds to a Pareto optimal solution for multiple objective functions, and the output unit 15 outputs information of the observation point that corresponds to the Pareto optimal solution to the outside.

[0123] Let ν represent the number of objective functions. Observation sample set D t It can be expressed by the following formula.

[0124]

number

[0125] Here, the objective function y n is the observation point x n This is a ν-dimensional vector whose elements are ν objective function values ​​corresponding to the given values.

[0126] Even with multiple objective functions, the method for generating perturbation points to avoid re-proposing missing points is the same as in the first embodiment. Therefore, according to Modification 10, the same effect as in the first embodiment can be obtained even with multiple objective functions. Note that the output condition when there are multiple objective functions is not limited to the condition that it corresponds to a Pareto optimal solution for the multiple objective functions. For example, the output condition may be that any one of the observed values ​​is the maximum or minimum.

[0127] Thus, according to some of the embodiments described above, it becomes possible to provide a parameter optimization device, a parameter optimization system, and a parameter optimization method that can optimize parameters while reducing the risk of deterioration in the search efficiency of parameter optimization.

[0128] While several embodiments of the present invention have been described, these embodiments are presented as examples only and are not intended to limit the scope of the invention. These novel embodiments can be carried out in a variety of other forms, and various omissions, substitutions, and modifications can be made without departing from the spirit of the invention. These embodiments and their variations are included in the scope and spirit of the invention, as well as in the claims of the invention and its equivalents. [Explanation of Symbols]

[0129] 1...Processor, 2...Storage device, 3...Input device, 4...Display device, 5...Communication device, 11...Acquisition unit, 12...Calculation unit, 13...First proposal unit, 14...Second proposal unit, 15...Output unit, 16...Control unit, 100...Parameter optimization system, 110...Parameter optimization device, 120...Observation device

Claims

1. An acquisition unit that acquires observation samples which are combinations of observation points, which are points in a parameter vector space having a parameter vector having the values ​​of one or more types of parameters as elements, and the observed values ​​of the object to be observed at said observation points, and / or missing points which are said observation points where the observation of the object to be observed was unsuccessful. A storage unit that stores the observed samples as elements of a first set and stores the missing points as elements of a second set, A calculation unit that calculates the acquisition function based on the observed samples, A first proposal unit proposes an observation candidate point, which is a candidate point for the next observation of the target object, that is the argument that maximizes the value of the acquisition function. A second proposal unit determines whether the missing point, whose distance from the aforementioned candidate observation point is less than or equal to a threshold, is included in the second set. If it is determined that it is included, it generates a perturbation point for the candidate observation point and proposes the perturbation point as a proposed point for the next observation. If it is determined that it is not included, it proposes the candidate observation point as the proposed point. An output unit that outputs observation point information that matches the output conditions from the first set to the outside, A parameter optimization device equipped with the following features.

2. The parameter optimization apparatus according to claim 1, wherein the second proposal unit determines that the missing point whose distance from the observation candidate point is less than or equal to the threshold is included in the second set, generates a perturbation point different from the missing point whose distance is less than or equal to the threshold and proposes it as the proposed point.

3. The parameter optimization apparatus according to claim 2, wherein each time a perturbation point is generated, the second suggestion unit determines whether the missing point whose distance from the perturbation point is less than or equal to the threshold is included in the second set, and if it is determined that it is included, it generates a new perturbation point, and if it is determined that it is not included, it suggests the said perturbation point as the suggestion point.

4. The parameter optimization apparatus according to claim 1, wherein the second proposal unit determines that the missing point whose distance from the observation candidate point is less than or equal to the threshold is included in the second set, generates a perturbation point that is different from any of the missing points included in the second set and proposes it as the proposed point.

5. The parameter optimization apparatus according to claim 1, wherein the second proposal unit determines that the missing point whose distance from the perturbation point is less than or equal to the threshold is included in the second set, generates a plurality of perturbation points of the observation candidate point, and proposes the perturbation point among the plurality of perturbation points that has the maximum value of the acquisition function as the proposed point.

6. The parameter optimization device according to claim 1, wherein the second proposed unit generates the perturbation points based on random numbers that follow a probability density distribution whose probability density is positive and uniform only in the perturbation range near the candidate observation points, a normal distribution with the candidate observation points as the mean, or a probability density distribution which is a modified version of the normal distribution in which the probability density at the missing points is small.

7. The parameter optimization device according to claim 6, wherein the second proposed unit controls the parameters of the distribution to which the random numbers follow based on the degree of density of the missing points.

8. The parameter optimization device according to claim 6, wherein the second proposed part controls the parameters of the distribution to which the random numbers follow based on the length scale of the kernel function of a Gaussian process regression.

9. The parameter optimization apparatus according to claim 7 or claim 8, wherein the parameters of the distribution include the perturbation range or the variance of the normal distribution.

10. The calculation unit calculates the acquisition function based on the observation samples corresponding to the observation points whose distance to a lower-dimensional search space with a lower dimension than the parameter vector space is less than or equal to a threshold, The parameter optimization apparatus according to claim 1, wherein the first proposal unit proposes the argument that maximizes the value of the acquisition function in the low-dimensional search space as the candidate observation point.

11. The parameter optimization device according to claim 1, further comprising a display unit for displaying information relating to the missing points included in the second set.

12. The parameter optimization apparatus according to claim 1, wherein the second proposed unit generates the perturbation points by moving the observation candidate points by a predetermined amount.

13. The parameter optimization device according to claim 1, further comprising a control unit that determines whether or not the output unit outputs the observation point information to the outside based on termination conditions.

14. The parameter optimization apparatus according to claim 13, wherein the termination conditions include reaching a predetermined number of observations, observing an observed value that exceeds or falls below a predetermined threshold, reaching a predetermined time for parameter optimization, and / or reaching a predetermined budget for observations.

15. The parameter optimization apparatus according to claim 1, wherein the output condition is that the observed value is the minimum or maximum.

16. The parameter optimization device according to claim 1, wherein, when multiple observed values ​​are stored in the storage unit for one of the observation points, the output condition is that the observation point is a Pareto optimal solution.

17. The parameter optimization apparatus according to claim 1, wherein the distance includes the Euclidean distance and the Mahalanobis distance.

18. The observed objects include devices, equipment, applications, software, components, materials and / or simulations. The observed values ​​are numerical values ​​that include the performance of the observed object, the manufacturing cost of the observed object, and / or the satisfaction level of the observed object. The parameter optimization apparatus according to claim 1, wherein the parameter includes at least one of the following: dimensions that define the structure of the object to be observed, the amount of material, the mixing ratio of the material, the concentration of the material, the temperature of the material and / or the manufacturing environment, the pressure of the material and / or the manufacturing environment, and hyperparameters of machine learning relating to the object to be observed.

19. It is equipped with an observation device and a parameter optimization device, The observation device observes the observed value for an observation point, which is a point in a parameter vector space having a parameter vector as its element, and defines an observation sample, which is a combination of the observation point where the observation was successful and the observed value at that observation point, and / or a missing point, which is the observation point where the observation was unsuccessful. The parameter optimization device is An acquisition unit that acquires the observation sample and / or the missing points from the observation device, A storage unit that stores the observed samples as elements of a first set and stores the missing points as elements of a second set, A calculation unit that calculates the acquisition function based on the observed samples, A first proposal unit proposes an observation candidate point, which is a candidate point for the next observation of the observed value, that is the argument that maximizes the value of the acquisition function. A second proposal unit determines whether the missing point, whose distance from the candidate observation point is less than or equal to a threshold, is included in the second set. If it is determined that it is included, it generates a perturbation point for the candidate observation point and proposes the perturbation point as the next observation point to observe the observed value. If it is determined that it is not included, it proposes the candidate observation point as the next observation point to observe the observed value. An output unit that outputs observation point information that matches the output conditions from the first set to the outside, A parameter optimization system equipped with the following features.

20. Computers Obtain an observation sample which is a combination of an observation point, which is a point in a parameter vector space having a parameter vector with the values ​​of one or more parameters as elements, and the observed value of the object to be observed at the observation point, and / or a missing point which is an observation point where the observation of the object to be observed was unsuccessful. The observed samples are stored as elements of the first set, and the missing points are stored as elements of the second set. Based on the aforementioned observed samples, calculate the acquisition function, The argument that maximizes the value of the acquisition function is proposed as a candidate observation point, which is a candidate point where the next observed object will be observed. It is determined whether the missing point whose distance from the observation candidate point is less than or equal to a threshold is included in the second set. If it is determined that it is included, a perturbation point is generated for the observation candidate point, and the perturbation point is proposed as the proposed point for the next observation. If it is determined that it is not included, the observation candidate point is proposed as the proposed point. The observation point information that matches the output conditions in the first set is output to the outside. A parameter optimization method that possesses the following characteristics.

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