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 (points in the parameter vector space where 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 the acquisition function based on the observation samples. The update unit generates an updated acquisition function based on the missing points and the value of the acquisition function. The proposal unit proposes the argument that maximizes the value of the updated acquisition function or the value of the acquisition function as the proposed point for the next observation. The output unit outputs the observation point information from the first set that meets the output conditions to the outside.

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, an update unit, a proposal unit, and an output unit. The acquisition unit acquires observation samples, which are combinations of observation points (points in a parameter vector space consisting of one or more types of parameters) and observed values ​​of the object being observed at the observation points, and / or missing points (points in the parameter vector space where 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 update unit generates an updated acquisition function based on the missing points and the value of the acquisition function, in which the value of the acquisition function at the missing points is updated to an updated value smaller than the value of the acquisition function. The proposal unit proposes the value of the updated acquisition function or the argument that maximizes the value of the acquisition function as a proposed point for the next observation. The output unit outputs observation point information to the outside regarding the observation points that meet the output conditions in 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 for parameter optimization according to the first embodiment. [Figure 3] A schematic block diagram showing the data flow of the parameter optimization system according to the first embodiment. [Figure 4] A diagram illustrating the updating of the acquisition function according to the first embodiment. [Figure 5] Other figures illustrating the updating of the acquisition function according to the first embodiment [Figure 6] A diagram illustrating the parameter optimization process of a specific example according to the first embodiment. [Figure 7] A diagram illustrating the shape of the acquisition function and the shape of the coefficient multiplied by the acquisition function in Modification Example 1. [Figure 8] A diagram illustrating the shape of the function used for the non-negative transformation in Modification 4. [Figure 9] A diagram illustrating the non-negative transformation related to Modification Example 4. [Figure 10] A diagram illustrating the display screen related to modified example 9. [Figure 11] Other diagrams illustrating the display screen related to Modification 9 [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, D-dimensional parameter vector values ​​may be abbreviated as simply parameter vector values. 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. Furthermore, since parameter vector values ​​represent points in the D-dimensional parameter vector space, they may also be called observation points.

[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) for which 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 include 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 hyperparameters of a machine learning model include 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, an update unit 13, a 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 D-dimensional parameter vector values ​​for which 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 substance 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.

[0028] The update unit 13 generates an updated acquired function in which the values ​​of the acquired function at the missing points are updated, based on the missing points and the values ​​of the acquired function.

[0029] The suggestion unit 14 proposes a point on which the observation device 120 should next observe the objective function value, based on the value of the updated acquisition function or the value of the acquisition function. This point is called the suggested point.

[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 observed samples or missing points by the acquisition unit 11, the storage of observed samples or missing points in the memory device 2, the calculation of the acquisition function by the calculation unit 12, the generation of the updated acquisition function by the update unit 13, and the proposal of proposed points by the proposal unit 14, to be repeated until the termination condition is met, in response to the acquisition of observed values ​​by the observation device 120. In order to control the system in response to the acquisition of observed samples or missing points from the observation device 120, the control unit 16 has a function to monitor the acceptance of the observed samples or missing points by the acquisition unit 11 and a function to monitor the transmission of proposed points by the proposal unit 14 to an external device other than the parameter optimization device 110. The optimal point (parameter vector value) at the end of the iteration 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 which iteration of the process in 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 update unit 13. As initialization of the storage device 2, for example, at least one or more observation samples, which are a combination of a parameter vector value and an observed value of an objective function corresponding to the parameter vector value, 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 an objective function value corresponding to the observation point.

[0035] The storage device 2 stores observation samples as elements of the first set D t and stores missing points as elements 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 in the observation sample set D t and is an integer greater than or equal to 1. M t represents the number of elements in the missing point set F t and is an integer greater than or equal to 0. 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 update unit 13, 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 acquisition function a t The calculated acquisition function at The acquired function a is supplied to the update unit 13. 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 update unit 13 generates an updated acquired function based on the missing points supplied in step S201 and the acquired function values ​​calculated in step S202, in which the acquired function values ​​at the missing points are updated to values ​​smaller than the acquired function values ​​calculated in step S202 (step S203). As an example, the update unit 13 generates an updated acquired function for the set of missing points F t Based on the acquisition function a t The updated acquisition function u t Generates the updated acquisition function u t The updated acquisition function u is supplied to the proposal unit 14. t The input to is the acquisition function a t Similarly, the parameter vector value x is the updated acquisition function u. t This may also be called the update acquisition function.

[0046] Specifically, the update unit 13 retrieves the missing point x (F),m The value of the acquisition function a t (x (F),m The value of the acquisition function is updated to a value smaller than the maximum value within the domain of the observation point x. As an example of a case where the acquisition function cannot take a negative value, the update unit 13 updates the missing point x (F),m The value of the acquisition function a t (x (F),m The value of the updated acquisition function u after updating ) to 0 t (x (F),m Generates the updated acquisition function u. t For example, the acquisition function a at parameter vector values ​​x other than missing points. t It takes the same value as . Note that the update acquisition function u t The acquired function a is obtained at parameter vector values ​​x other than missing points. t The value of the acquisition function a at different parameter vector values ​​is not limited to taking the same value as , but is not limited to taking the same value as . t It may be generated by any transformation that maintains the relative size relationship between (x).

[0047] As an example of the case where the acquisition function cannot take a negative value, the update process in step S203 will be described while referring to FIG. 4. In the example of FIG. 4, the set of missing points F at time t-1 t-1 is an empty set, and the set of missing points F at time t t ={x (F),0} is assumed. (a) of FIG. 4 shows an example of an acquisition function a t that cannot take a negative value, and (b) of FIG. 4 shows an example of the updated acquisition function u t . In the update of the example of FIG. 4, the updated acquisition function u t is generated by reducing the acquisition function value a t (x) at the missing points included in the set of missing points F t .

[0048] As an example of the case where the acquisition function can take a negative value, the update process in step S203 will be described while referring to FIG. 5. Also in the example of FIG. 5, as in the example of FIG. 4, the set of missing points F at time t-1 t-1 is an empty set, and the set of missing points F at time t t ={x (F),0} is assumed. (a) of FIG. 5 shows an example of an acquisition function a t that can take a negative value, (b) of FIG. 5 shows an example of the acquisition function after non-negative conversion, and (c) of FIG. 5 shows an example of the updated acquisition function u t . In the update of the example of FIG. 5, the acquisition function a t is non-negatively converted, and the updated acquisition function u t is generated by reducing the value of the acquisition function after non-negative conversion at the missing points included in the set of missing points F t . This non-negative conversion is executed, for example, by a non-negative conversion unit installed inside the update unit 13. Illustration of the non-negative conversion unit is omitted. The non-negative conversion unit is not limited to being installed inside the update unit 13, and may be installed at any position where it can be executed by a processor 1 such as a computer connected to the parameter optimization device 110 via the inside of the parameter optimization device 110 or the communication device 5.

[0049] Note that step S203 can be executed even if the non-negative conversion is not performed. Also, the memory unit 2 will process the missing point set F in step S201 and step S205 described later. t The memory unit 2 is not limited to supplying the missing point set F to the update unit 13, but rather, it may also supply the missing point set F before step S203 is performed. t The update unit 13 should be supplied with the missing point set F in step S202. t This is supplied to the update unit 13.

[0050] When step S203 is performed, the proposal unit 14 proposes the argument that maximizes the value of the updated acquisition function updated in step S203 or the value of the acquisition function calculated in step S202 as the proposed point for the next observation (step S204). As an example, the proposal unit 14 selects the updated acquisition function u from the domain of the parameter vector value x. t Calculate the point where x is large, and then the next observation point x (t+1) The proposed result is output to the outside of the parameter optimization device 110. (t+1) For example, it is supplied to the observation device 120. In step S203, the update unit 13 checks for missing points x (F),m By updating the value of the acquisition function at the observation point x to a value smaller than the maximum value within the domain of the observation point x, the missing point x (F),m This makes it possible to suppress the proposal of such points, and consequently avoid stagnation in the search for optimal parameters.

[0051] When step S204 is performed, the acquisition unit 11 acquires observation samples or missing points as observation results for the proposed points proposed in step S204 (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) If the data is observed without any problems and no missing data occurs, the acquisition unit 11 will access the observed sample (x) from outside the parameter optimization device 110. (t+1) , y (t+1)) is acquired. Also, if a missing value occurs in the observation at the proposed point outside the parameter optimization device 110, the acquisition unit 11 acquires x from outside the parameter optimization device 110. (t+1) These are acquired as missing points. For example, the acquisition unit 11 acquires observation samples or missing points from the observation device 120.

[0052] When step S205 is performed, the control unit 16 causes the storage device 2 to store the observed samples or missing points acquired in step S205 (step S206). For example, in step S205, the control unit 16 causes the acquisition unit 11 to store the observed samples (x (t+1) , y (t+1) If ) is obtained, the observed sample (x (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) , 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 The update unit 13 is supplied with the update unit 13. Alternatively, the control unit 16 determines in step S205 that the acquisition unit 11 has a missing point x (t+1) If you obtain x (t+1) The set of missing points F t+1 As an element, it is added to memory device 2 (F t+1 ←F t ∪x (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 is supplied to the update unit 13. Observations at the proposed point are performed, for example, by the observation device 120.

[0053] 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 tThe condition is that the parameter reaches a predetermined value. Other predetermined termination conditions include the elapsed time reaching a predetermined value, and the financial costs, including the budget for observations using 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.

[0054] 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.

[0055] 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.

[0056] 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 memory 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 value among 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 value among the observed sample set D. N The 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.

[0057] 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.

[0058] When step S208 is performed, the parameter optimization process by the parameter optimization system 1 according to the first embodiment is terminated.

[0059] Note that the set of missing points F t If the set is empty, step S202 may be performed without executing step S203, and step S204 may be performed instead.

[0060] 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.

[0061] In the following step S204, the proposed section 14 obtains the function u 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 the memory device 2 is adopted. When the proposal unit 14 searches for a proposal point from the low-dimensional space, the extracted sample set E t This is the observed 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 less than or equal to 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, and the components other than the diagonal components should be set to 0.

[0062] 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 t The 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.

[0063] 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 parameters, the search efficiency is improved when the number of parameters D to be adjusted is large.

[0064] If the space in which proposal 14 searches for the next observation point is a D-dimensional parameter space, then if D is large, it becomes impossible to secure a sufficient number of observation 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 convexity 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.

[0065] 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 the acquisition function u t The 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.

[0066] The following describes a specific example of applying the first embodiment to the automated design of power semiconductor devices, using diagrams. More specifically, the specific example uses a simulator that reproduces the behavior of the development / design target as the observation device 120, and applies the first embodiment by using the width and height of the power semiconductor device as parameters and the on-resistance of the power semiconductor device as the objective function. This specific example is a minimization problem in which the smaller the objective function value after non-negative transformation, the more optimal the parameters are. Furthermore, in step S204, the proposal unit 14 updates the acquired function u 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) This section explains how to propose this approach.

[0067] Figure 6 is a graph illustrating an example of parameter optimization. The horizontal axis represents the number of observations. The vertical axis represents the minimum value of the objective function observed up to that point. The number of observations is calculated using the observation sample set D. t Sample size N t and the missing point sample set F t Sample size M t This corresponds to the sum of the two. In this example, the only missing data occurs at timing T1, indicated by the dotted line. The solid line L11 represents the result of parameter optimization using this embodiment. The dashed line L12 represents the result of parameter optimization using the method described in Non-Patent Literature 1. In this embodiment (solid line L11), it can be seen that the observed value became smaller immediately after the missing data occurred at timing T1, indicated by the dotted line, and the optimization did not stagnate. This is because points near the missing data point are likely to be proposed immediately afterward. In the method described in Non-Patent Literature 1 (dashed line L12), it can be seen that the minimum value among the observed values ​​did not become smaller immediately after the missing data occurred at timing T1, indicated by the dotted line, and the optimization stagnated. This is because the observed value of the missing data point is interpolated with the worst value of the objective function up to that point. From Figure 6, it can be seen that parameter optimization using this embodiment allows for the search for the optimal solution without the optimization of the parameters stagning.

[0068] Here, according to the first embodiment, the acquisition function a t Then, the values ​​at the missing points where the values ​​were large are updated using the acquisition function u t As the values ​​are updated to smaller values, no missing points are proposed. This allows parameter optimization to progress without stalling, even if the missing points at the same location are reproducible. Furthermore, since the value of the acquisition function does not decrease outside of the missing points, it is possible to search for optimal solutions even if they exist outside of the missing points without missing them.

[0069] (Variation 1) The update unit 15 in the modified example 1 updates the value of the acquisition function to an updated value obtained by multiplying it by a coefficient that is smaller in number for points in the parameter vector space that are close to the distance from missing points.

[0070] In principle, the acquisition functions illustrated in the first embodiment include those that can take negative values ​​and those that cannot. In Modification 1, the acquisition function a t As such, the acquired function value a t (x) is selected if it cannot take a negative value, or the acquired function a is selected in the update unit 15. t After applying a non-negative conversion to the value, an update process is performed.

[0071] The acquisition function and the coefficients multiplied by it will be explained below using Figure 7. In Figure 7(a), the horizontal axis represents the value of the parameter vector, the vertical axis represents the value of the acquisition function, and the curve represents the acquisition function a calculated in step S202 at time t-1. t-1 This represents the horizontal axis, which is represented as a one-dimensional space (a straight line), but in reality, it is a space corresponding to the number of dimensions of the parameter vector.

[0072] In step S203 at time t-1, the set of missing points F at time t-1 t-1 Since the set is empty, the update acquisition function u t-1 is the acquisition function a t-1 This is identical. Figure 7(a) shows the acquisition function a t-1 not only, but also the update acquisition function u t-1 It also represents.

[0073] In step S204 at time t-1, the update acquisition function u t-1 The point where the acquisition function value is maximized is the next observation point (proposed point) x (t) It is proposed as follows: Proposal point x (t) This is shown in Figure 7(a).

[0074] In step S205 at time t-1, the storage device 2 receives x from outside the parameter optimization device 110. (t) The missing point is obtained as a missing point, and the set of missing points F t It is added to the memory as an element (F t ←F t-1 ∪x (t) ). The set of missing points F at time t-1. t-1 The set is empty, and the set of missing points F at time t is empty. t ={x (F),0Since}, the set of missing points F t The only element x included (F),0 Proposal point x (t) (x (F),0 =x (t) ). Proposal point x (t) Since this is a missing point, D is used for the observed sample set at time t-1 and time t. t =D t-1 The following relationship holds true.

[0075] At time t, in step S202, D t =D t-1 Therefore, the acquisition function a at time t t Let the acquisition function a at time t-1 be defined as t-1 The same result is calculated. Figure 8(a) shows the acquisition function a at time t-1. t-1 , update acquisition function u at time t-1 t-1 not only that, but also the acquisition function a at time t t It also represents.

[0076] At step S203 at time t, the set of missing points F t The element x (F),0 The closer the distance from the source, the smaller the coefficient function value c. t (x) is obtained as the function value a t The updated acquisition number u is obtained by multiplying (x) by a smaller value for the acquisition function value in the neighborhood. t The value u t Generate (x). Generated update acquisition function value u t (x) is expressed by the following equation (3).

[0077]

number

[0078] Figure 8(b) shows the coefficient function c t An example is shown in Figure 8(c), where the update acquisition function u t This illustrates an example.

[0079] For simplicity, the above assumes a set of missing points F. tThe example given was the case where there is only one element. The missing point set F t If there are multiple elements, in step S203, the coefficient function value c is smaller the shorter the distance from each missing point. t (x) is obtained as the function value a t The updated acquisition function u is obtained by multiplying (x) by a smaller value in the neighborhood. t The value u t It is good to generate (x). Missing point x (F),m The coefficient function c has a smaller value the shorter the distance from it. m This is expressed as follows: coefficient function c t The value c at any point x t (x) can be expressed, for example, by the following equation (4).

[0080]

number

[0081] Even in this case, the above-mentioned effects can be obtained.

[0082] Here, according to variation 1, the acquisition function a t Then, the value at the missing point x(t) where the value was large is updated using the acquisition function u t As the values ​​are updated to smaller values, no missing points are proposed. Similar to the first embodiment, even if the missing data at the same point is reproducible, the parameter optimization can proceed without stagnation. Furthermore, since the value of the acquisition function only decreases in the vicinity of the missing point, it is possible to search for solutions even if they are located at points slightly away from that vicinity, without missing them. In particular, if the observation device 120 is a simulator that numerically solves differential equations, missing data may occur in the vicinity of the missing point due to calculation errors, etc. Therefore, by reducing the proposal of observation points in the vicinity of the missing point, it is possible to improve the efficiency of proposing observable observation points, and consequently improve the efficiency of parameter search.

[0083] (Modification 2) The update unit 15 in the modified example 1 has missing point x (F),mThe coefficient function c has a smaller value as the distance from the source decreases. m An example using this is shown. The update unit 15 in Modification 2 uses a coefficient function c defined based on a normal distribution to obtain the value of the acquisition function. m Update the value by multiplying it by (x).

[0084] The coefficient function c is defined based on the normal distribution. m (x) can be expressed by the following equation (5), where σ is the standard deviation of the normal distribution and α is an arbitrary positive constant.

[0085]

number

[0086] The standard deviation σ is set to any positive value. The constant α is (2πσ). 2 ) -1 / 2 You can set it to either [value] or [value]. (F),m || represents point x and missing point x (F),m This represents the Euclidean distance between the points. The coefficient function c is independent of the value of the constant α. m (x (F),m ) becomes 0, x (F),m At point x other than c m (x) takes positive values. This coefficient function c m (x) takes the shape shown in Figure 8(b). The standard deviation σ is the x of the curve in Figure 8(b). (t) , that is, x (F),0 This parameter controls the steepness of the valley shape in its vicinity.

[0087] Let Σ be the variance-covariance matrix of a multivariate normal distribution, then c m (x) may also be defined by the following equation (6) based on a multivariate normal distribution.

[0088]

number

[0089] Here, T This represents the transpose of a vector, and... -1This represents the inverse of the matrix. The constant α is {(2π) D |Σ|)} -1 / 2 You can set it to either or 1. |·| represents the determinant of a matrix. (xx (F),m ) T Σ -1 (WW (F),m ) is point x and missing point x (F),m It is the square of the Mahalanobis distance between them. The coefficient function c is independent of the value of the constant α. m (x (F),m ) becomes 0, x (F),m At point x other than c m (x) takes a positive value.

[0090] According to Modification 2, since the value of the acquisition function becomes small only in the vicinity of the missing points, it is possible to search for solutions even if they are located at points slightly away from that vicinity, without missing them.

[0091] (Variation 3) In the modified example 2, the update unit 15 modifies the value of the acquisition function with a coefficient function c that is determined based on a normal distribution. m An example is shown in which the updated value is multiplied by (x). The update unit 15 in Modification 3 uses a coefficient function c based on a normal distribution. m The standard deviation σ of (x) is determined by the size of the length scale of the kernel function of the Gaussian process regression, which is learned based on the observed samples stored in memory device 2. Furthermore, the diagonal component vectors of the multivariate normal distribution variance-covariance matrix Σ in equation (6) should be set proportionally to the length scale vector of the GP regression kernel function, which is learned considering ARD (Automatic Relevance Determination) based on the observed samples stored in memory device 2, and the components other than the diagonal components of the multivariate normal distribution variance-covariance matrix Σ should be set to 0. Here, the proportionality constant is a positive value, and the length scale vector is a vector whose samples are the length scale vectors of each coordinate axis in the parameter space.

[0092] The samples input to the GP regression are the extracted sample set E. tThen, depending on the length scale obtained, it is good practice to set the standard deviation σ and the diagonal component vectors of the variance-covariance matrix Σ of the multivariate normal distribution. Acquisition function a t When calculating based on GP regression, GP regression is not necessary just to set the standard deviation σ or the variance-covariance matrix Σ of the multivariate normal distribution, and the acquisition function a t This can be reused in GP regression to calculate [the value].

[0093] When the length scale value or the values ​​of the elements of the length scale vector are large, there is a high probability that the objective function does not have high-frequency components. When the objective function does not have high-frequency components, the objective function value will be close to the missing point, so by setting the standard deviation σ and the diagonal component vector of the multivariate normal distribution's variance-covariance matrix Σ to large values, the missing point x can be measured more efficiently than when the standard deviation σ and the diagonal component vector of the multivariate normal distribution's variance-covariance matrix Σ are small. (F),m Points close to the missing point will have smaller acquisition function values, making them less likely to be selected as the next proposed point. If missing data is likely to occur near a missing point, the vicinity of the missing point will be less likely to be proposed as the next observation point, thus preventing optimization from stalling.

[0094] (Modification 4) The update unit 15 in Modification 4 performs a non-negative transformation based on the sigmoid function. Figure 8 shows an example of the sigmoid function s. Using the sigmoid function, an input x in the range of -∞ to ∞ can be converted to a value in the range of 0 to 1.

[0095] Refer to Figure 9 to explain how the acquisition function is updated in Modification 4. Figure 9(a) shows the acquisition function value a t (x) is a negative value for the acquisition function a t This illustrates an example. Figure 9(b) shows the acquisition function s〇a obtained by non-negative transformation based on the sigmoid function s. t This shows an example. ·〇· represents a composite function, and (s〇a t )(x)=s(a t (x)) Here, the value of the sigmoid function s(x) is given by the following equation (7), where β is the gain.

[0096]

number

[0097] Gain β is a parameter. Depending on the gain β, the slope of the S-shaped curve of the sigmoid function s in Figure 8 changes. When the gain β is large, the slope near 0 on the horizontal axis in Figure 8 becomes steeper, and when the gain β is small, the slope becomes gentler. Figure 9(c) shows the updated acquisition function u updated with coefficients based on a normal distribution. t This illustrates an example of the update acquisition function u. t The value u t (x) is u t (x=c t (x)s(a t It can be expressed in the form (x).

[0098] For a sigmoid function s, the acquired function after non-negative transformation is s〇a. t The range of the value is known in advance to be between 0 and 1. Therefore, it is easier for users to imagine the range of the acquisition function.

[0099] (Variation 5) The gain β of the sigmoid function s in Modification 5 is the acquisition function a t The wider the range of values, the smaller the gain β should be set. The gain β should be varied according to time t. The gain β that has been varied according to time t is β t It is represented as follows.

[0100] β t Specifically, for example, the acquisition function a t Set the value to be proportional to the difference between the maximum and minimum values. Here, the constant of proportionality is a positive value.

[0101] Acquisition function a t The maximum and minimum values ​​of x need to be estimated. For example, multiple acquisition function values ​​a calculated by setting multiple values ​​for x. t The maximum and minimum values ​​in (x) are a tIt is advisable to use these as estimates of the maximum and minimum values ​​of x. Alternatively, one can set multiple initial values ​​for x, find the local maximum and minimum values ​​from each initial value using the gradient method, and use the maximum value of the multiple local maximums and the minimum value of the multiple local minimums as estimates of the maximum and minimum values, respectively.

[0102] In Figure 8, the horizontal axis represents the acquisition function value a before the non-negative transformation. t (x) is the value of the acquisition function s(a) after the non-negative transformation on the vertical axis. t (x)) The gain β of the sigmoid function t The acquisition function a t The wider the range of values, the smaller the value set, so that the slope of the horizontal axis near 0 in Figure 8 becomes gentler, and the acquired function s〇a after non-negative transformation t The range of values ​​widens. Conversely, the gain β t The acquisition function a t The wider the range of values, the larger the value set, and the steeper the slope of the horizontal axis near 0 in Figure 8 becomes, so the acquired function s〇a after non-negative transformation t The range of values ​​becomes narrower.

[0103] According to modification 5, the acquisition function a t The wider the range of values, the greater the gain β. t In order to set it small, the value of the acquisition function after non-negative transformation s(a t (x) is widely distributed in the range of 0 to 1. This makes it possible to prevent loss of precision in the acquisition function values. If loss of precision occurs, the relative magnitudes of the acquisition function values ​​will not be maintained before and after the non-negative transformation, and it will become impossible to find the parameter values ​​that maximize the acquisition function in step S204.

[0104] (Experimental variation 6) Gain β of the sigmoid function in Modification 6 t The wider the range of observed values ​​stored in memory device 2, the smaller the value set.

[0105] Gain β t Specifically, for example, the set of observed samples D stored in memory device 2. t The set of observed values ​​included {y n |n=0,1,…,N tSet the value to be proportional to the difference between the maximum and minimum values ​​of the elements of {-1}. Here, the proportionality constant should be a positive value.

[0106] This results in the acquisition function a t The same effect as in Modification Example 5 can be obtained without estimating the maximum and minimum values.

[0107] (Example 7) Gain β of the sigmoid function in Modification Example 7 t The larger the absolute value between the minimum value and the maximum value of the acquisition function, the smaller the value set.

[0108] Acquisition function a t The estimation of the minimum and maximum values ​​can be the same as in Modification 5. The same effect as in Modification 5 can be obtained in this modification as well.

[0109] (Variation 8) The gain β of the sigmoid function in Modification 8 is set to a smaller value as the larger of the absolute values ​​of the minimum and maximum values ​​stored in memory device 2 increases.

[0110] The minimum and maximum values ​​of the observed values ​​stored in memory device 2 are determined in the same manner as in Modification 6. The same effect as in Modification 6 is obtained in this modification as well.

[0111] (Extreme variation 9) The parameter optimization device 110 according to modified example 9 further includes a display unit that highlights observation point information for observation points whose distance from any missing point included in the set of missing points (second set) is less than or equal to a threshold, using one or more display elements including color, thickness, and markings. For example, the set of missing points F t If the set is not empty, then the set of missing points F stored in memory device 2. t Any missing point x included (F),mObservation points that are close in distance from the target should be highlighted using at least one of the following: a different color, a thicker line, or a unique mark. If the threshold is set to 0, only missing points will be highlighted. The diagram of the display unit is omitted. The display unit relating to Modification 9 below will be described as being displayed on the display device 4, but 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 points. Also, the display elements are not limited to color, thickness, and marks. For example, the display elements may include blinking patterns, font types, character sizes, etc.

[0112] Figure 10 shows the observed sample set D. t or the set of missing points F t This shows an example of display screen I1 when the observation points included are displayed in a table format. Display screen I1 includes Table I11, which contains the objective function value in the parameter vector value and the parameters of the parameter vector value. 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 objective function value is listed in the first column, the value of the first parameter in the second column, and the value of the second parameter in the third column. The objective function value in the fourth row is written as "ERR.", indicating that a missing value occurred when the parameter vector value is (34.4, 977.4). The numbers showing the parameter vector value in the fourth row are highlighted in bold. This makes it easier for the user to notice the missing point. The numbers showing the parameter vector value (34.5, 977.3) in the fifth row are also highlighted in bold because the distance from the missing point (34.4, 977.4), which is the parameter vector value in the fourth row, is short. This highlighting makes it easier for users to notice observation points and samples that are close to missing points. 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.

[0113] According to Modification 9, the user can focus on observation points near missing points. This is user-friendly because the user can see at a glance whether there are important observation points with small objective function values ​​near missing points.

[0114] Here, we have explained an example of highlighting using line thickness, but highlighting with color or other symbols is also acceptable. Figure 11 shows an example where an observation point (34.5, 977.3) close to a missing point (34.4, 977.4) is highlighted with arrow I12. In this case as well, the effect described above can be obtained.

[0115] (Variation 10) The control unit 16 in the modified example 10 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 x n A vector v is formed by listing the characteristic 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.

[0116] 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, and {x n ,v n ,y n |n=0,1,…,N t Observing sample set D t Remember it as such.

[0117] 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.

[0118] 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 is supplied to the update unit 13.

[0119] 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.

[0120] In this modified example, 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.

[0121] (Example 11) 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.

[0122] Let ν represent the number of objective functions. Observation sample set D t It can be expressed by the following formula.

[0123]

number

[0124] 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.

[0125] Even if there are multiple objective functions, the method for updating the acquisition function is the same as in the first embodiment. Therefore, the same effect as in the first embodiment can be obtained. 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.

[0126] 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.

[0127] 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]

[0128] 1…Processor, 2…Storage device, 3…Input device, 4…Display device, 5…Communication device, 11…Acquisition unit, 12…Calculation unit, 13…Update unit, 14…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 an observation sample which is a combination of an observation point, which is a point in a parameter vector space having a parameter vector having the values ​​of one or more parameters as elements, and an observation value of the object to be observed at the observation point, and / or a missing point, which is a point in the parameter vector space 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, An update unit generates an updated acquired function based on the missing points and the acquired function, wherein the value of the acquired function at the missing points is updated to an updated value smaller than the value of the acquired function. A proposal unit that proposes the value of the update acquisition function or the argument that maximizes the value of the acquisition function as the next proposed point for observation, An output unit that outputs observation point information to the outside for the observation points that meet the output conditions in the first set, A parameter optimization device equipped with the following features.

2. The parameter optimization apparatus according to claim 1, wherein the output condition is that the corresponding observed value is the minimum or maximum among those included in the first set.

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

4. The parameter optimization apparatus according to claim 1, wherein the update unit updates the value of the acquisition function to the updated value obtained by multiplying it by a coefficient that is smaller in number than the value of the acquisition function for points in the parameter vector space that are short in distance from the missing points.

5. The parameter optimization apparatus according to claim 4, wherein the coefficient is determined based on a normal distribution.

6. The parameter optimization device according to claim 5, wherein the standard deviation of the normal distribution is defined as the length scale of the kernel function of the Gaussian process regression learned based on the observed samples stored in the memory unit is larger.

7. The system further comprises a transformation unit that applies a non-negative transformation to the aforementioned acquisition function, The parameter optimization apparatus according to claim 1, wherein the update unit generates the updated acquisition function based on the value of the acquisition function that has been subjected to the non-negative transformation.

8. The parameter optimization device according to claim 7, wherein the conversion unit performs the non-negative conversion based on a sigmoid function.

9. The parameter optimization device according to claim 8, wherein the gain of the sigmoid function is set to a number that is smaller the wider the range of the acquisition function, a number that is smaller the wider the range of the observed values ​​stored in the memory unit, a number that is smaller the larger the value between the absolute value of the minimum value of the acquisition function and the absolute value of the maximum value of the acquisition function, or a number that is smaller the larger the value between the absolute value of the minimum value and the absolute value of the maximum value stored in the memory unit.

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 suggestion unit suggests the argument that maximizes the value of the update acquisition function in the low-dimensional search space as the suggestion point.

11. The parameter optimization device according to claim 1, further comprising a display unit that highlights observation point information relating to an observation point whose distance from any of the missing points included in the second set is less than or equal to a threshold, using one or more display elements including color, thickness, and markings.

12. The parameter optimization apparatus according to any one of claims 4, 10, and 11, wherein the distance includes the Euclidean distance and the Mahalanobis distance.

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 objects of observation include devices, equipment, applications, software, components, materials and / or simulators. 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 parameters include 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.

16. It is equipped with an observation device and a parameter optimization device, The observation device observes observed values ​​for points in a parameter vector space having a parameter vector as its element, which is the value of one or more parameters in the object being observed, and defines observation samples which are combinations of observation points which are points in the parameter vector space where observation was successful and the observed values ​​at those observation points, and / or missing points which are points in the parameter vector space where 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, An update unit generates an updated acquired function based on the missing points and the values ​​of the acquired function, wherein the value of the acquired function at the missing points is updated to an updated value smaller than the value of the acquired function. A proposal unit that proposes the value of the update acquisition function or the argument that maximizes the value of the acquisition function as the next proposed point for observation, An output unit that outputs observation point information to the outside for the observation points that meet the output conditions in the first set, A parameter optimization system equipped with the following features.

17. Computers Obtain an observation sample which is a combination of an observation point, which is a point in a parameter vector space whose elements are the values ​​of one or more parameters, where the observation of the object was successful, and the observed value of the object at the observation point, and / or a missing point, which is a point in the parameter vector space where the observation of the object was unsuccessful. The observed samples are stored in memory as elements of the first set, and the missing points are stored in memory as elements of the second set. Based on the aforementioned observed samples, calculate the acquisition function, Based on the missing points and the values ​​of the acquisition function, an updated acquisition function is generated in which the value of the acquisition function at the missing points is updated to an updated value smaller than the value of the acquisition function. The value of the update acquisition function or the argument that maximizes the value of the acquisition function is proposed as the next observation point. The system outputs observation point information to an external source for the observation points that meet the output conditions among the first set. A parameter optimization method that possesses the following characteristics.

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