Model optimization methods, devices, terminals, and media for black-box stochastic optimization

Abstract

This application discloses a model optimization method, apparatus, terminal, and medium for black-box stochastic optimization. In each iteration cycle, the method determines the population gradient and momentum vector for the current iteration cycle based on the model parameters and the current iteration cycle. Based on the momentum vector, model solution parameters, and step size parameters of the current iteration cycle, the model solution parameters for the next iteration cycle are calculated using Gaussian smoothing logic and a normalized descent calculation formula. When the iteration termination condition is not met, the population gradient and momentum vector for the new iteration cycle are calculated based on the model solution parameters of the new iteration cycle using the population gradient calculation formula and momentum update calculation formula. This approach retains the advantages of Gaussian smoothing for handling high-dimensional optimization problems while effectively reducing sampling noise in the solution space through population search, improving optimization efficiency and convergence speed, and enhancing the overall performance and stability of the algorithm.

Description

Technical Field

[0001] This application relates to the field of computer technology, and in particular to a model optimization method, apparatus, terminal and medium for black-box stochastic optimization. Background Technology

[0002] Black-box stochastic optimization is an optimization method, commonly including genetic algorithms, particle swarm optimization, and simulated degeneracy algorithms. In this method, the objective function (also known as the black-box function) is treated as a "black box." This means that the user does not know the internal structure, specific mathematical expression, or derivative information of this function; they can only obtain the corresponding output (objective function value) by inputting some parameters (decision variables) into this black-box function. Furthermore, random factors are introduced during the optimization process. For example, in the search for the optimal solution, the search direction and step size may be determined based on a random strategy.

[0003] In black-box stochastic optimization problems, the gradient information of the objective function is unavailable or inaccessible. For example, in scenarios such as physics simulations, reinforcement learning, and adversarial attacks, the objective function may not be explicitly defined, and its value can only be obtained through random sampling. Traditional gradient-based optimization methods, such as Stochastic Gradient Descent (SGD) and its variants, cannot be directly applied to black-box environments because they rely on gradient information. To address this challenge, zero-order optimization (ZO) methods, represented by Gaussian smoothing, have gradually emerged. ZO methods do not require gradient information; they optimize solely through changes in the objective function value. They obtain unbiased gradient estimates by introducing Gaussian perturbations into the solution space and calculating finite differences. However, due to noise interference in the solution and data spaces, the convergence performance of Gaussian smoothing degrades, making it difficult to provide stable performance in practical applications. Summary of the Invention

[0004] This application provides a model optimization method, apparatus, terminal, and medium for black-box stochastic optimization, which addresses the technical problem of performance instability in existing black-box stochastic optimization algorithm models.

[0005] To address the aforementioned technical problems, the first aspect of this application provides a model optimization method for black-box stochastic optimization, comprising:

[0006] Obtain the model parameters of the target black-box stochastic optimization model, including: model solution parameters, step size parameters, momentum learning rate parameters, smoothing radius parameters, population size, and maximum number of iterations;

[0007] Based on the model parameters and the current iteration cycle, the population gradient and momentum vector for the current iteration cycle are determined sequentially.

[0008] Based on the momentum vector, model solution parameters, and step size parameters of the current iteration cycle, the model solution parameters for the next iteration cycle are calculated using Gaussian smoothing logic and normalized descent calculation formula. When the convergence or number of iterations of the target black-box stochastic optimization model meets the preset iteration termination condition, the current model solution parameters are output. Otherwise, based on the model solution parameters of the next iteration cycle, the population gradient and momentum vector for the corresponding iteration cycle are calculated using the population gradient calculation formula and momentum update calculation formula.

[0009] Preferably, based on the model solution parameters of the next iteration cycle, calculating the population gradient and momentum vector for the corresponding iteration cycle using the population gradient calculation formula and momentum update calculation formula specifically includes:

[0010] Based on the model solution parameters of the next iteration period, data samples corresponding to the population size are extracted from the sampled data distribution, and a Gaussian perturbation vector corresponding to the population size is generated in the solution space.

[0011] After Gaussian smoothing, the gradient components of each pair of Gaussian perturbation vectors and data samples are calculated, and the mean of each gradient component is used as the population gradient for the corresponding iteration period.

[0012] Based on the population gradient of the latest iteration and the population gradient of the current iteration, the momentum vector for the corresponding iteration is calculated according to the momentum update formula.

[0013] Preferably, the population gradient calculation formula is as follows:

[0014]

[0015] In the formula, Let be the population gradient over iteration period t. Let be the gradient components of population k during iteration period t. The parameters of the model solution for the iteration period t. The population size, It is the step size parameter. For the data samples of population k in iteration period t, Let be the Gaussian perturbation vector of population k during iteration period t. Let be the smoothing radius of the iteration period t.

[0016] Preferably, the momentum update calculation formula is as follows:

[0017]

[0018] In the formula, It is the momentum vector of the iteration period t. It is the momentum vector with an iteration period of t+1. The momentum learning rate over the iteration period t. The population gradient at iteration period t+1, Let be the population gradient over the iteration period t.

[0019] Preferably, the normalized descent calculation formula is as follows:

[0020]

[0021] In the formula, For the model solution parameters with iteration period t+1, The parameters of the model solution for the iteration period t. It is the momentum vector of the iteration period t. It is the norm of the momentum vector with iteration period t.

[0022] Preferably, before calculating the momentum vector for the corresponding iteration period according to the momentum update formula based on the population gradient of the latest iteration period and the population gradient of the current iteration period, the method further includes:

[0023] By using a perturbation reuse method, based on the Gaussian perturbation vector and data samples of the next iteration period, combined with the model solution parameters of the current iteration period, the gradient component estimates of each pair of Gaussian perturbation vectors and data samples are calculated through Gaussian smoothing. The average of the estimated gradient components is then used as the population gradient for the current iteration period.

[0024] Meanwhile, a second aspect of this application provides a model optimization apparatus for black-box stochastic optimization, comprising:

[0025] The model parameter acquisition unit is used to acquire the model parameters of the target black-box stochastic optimization model. The model parameters include: model solution parameters, step size parameters, momentum learning rate parameters, smoothing radius parameters, population size, and maximum number of iterations.

[0026] The gradient momentum calculation unit is used to determine the population gradient and momentum vector of the current iteration period in sequence according to the model parameters and the current iteration period.

[0027] The iterative control unit is used to calculate the model solution parameters for the next iteration period based on the momentum vector, model solution parameters, and step size parameters of the current iteration period, using Gaussian smoothing logic and normalized descent calculation formula. When the convergence or number of iterations of the target black-box stochastic optimization model meets the preset iteration termination condition, the current model solution parameters are output. Otherwise, based on the model solution parameters of the next iteration period, the population gradient and momentum vector for the corresponding iteration period are calculated using the population gradient calculation formula and momentum update calculation formula.

[0028] Preferably, the model solution parameters in the iterative control unit based on the next iteration cycle, calculated using the population gradient calculation formula and momentum update formula, specifically for:

[0029] Based on the model solution parameters for the next iteration cycle, the population gradient and momentum vector for the corresponding iteration cycle are calculated using the population gradient calculation formula and the momentum update calculation formula, specifically including:

[0030] Based on the model solution parameters of the next iteration period, data samples corresponding to the population size are extracted from the sampled data distribution, and a Gaussian perturbation vector corresponding to the population size is generated in the solution space.

[0031] After Gaussian smoothing, the gradient components of each pair of Gaussian perturbation vectors and data samples are calculated, and the mean of each gradient component is used as the population gradient for the corresponding iteration period.

[0032] Based on the population gradient of the latest iteration and the population gradient of the current iteration, the momentum vector for the corresponding iteration is calculated according to the momentum update formula.

[0033] A third aspect of this application provides a computer terminal, including: a memory and a processor;

[0034] The memory is used to store program code, which is used to implement a model optimization method for black-box stochastic optimization as provided in the first aspect of this application;

[0035] The processor is used to read and execute the program code.

[0036] The fourth aspect of this application provides a computer-readable storage medium containing program code that is read and executed by a processor to implement a model optimization method for black-box stochastic optimization as provided in the first aspect of this application.

[0037] As can be seen from the above technical solutions, this application has the following advantages:

[0038] In each iteration cycle, the method of this application determines the population gradient and momentum vector of the current iteration cycle based on the model parameters and the current iteration cycle. Based on the momentum vector, model solution parameters, and step size parameters of the current iteration cycle, the model solution parameters for the next iteration cycle are calculated using Gaussian smoothing logic and normalized descent calculation formulas. When the iteration termination condition is not met, the population gradient and momentum vector for the new iteration cycle are calculated based on the model solution parameters of the new iteration cycle using population gradient calculation formulas and momentum update calculation formulas. This method combines Gaussian smoothing technology with a population-based gradient optimization strategy, retaining the advantages of Gaussian smoothing in handling high-dimensional optimization problems while effectively reducing sampling noise in the solution space using population search, thus improving optimization efficiency and convergence speed. This not only reduces the impact of noise in the data space and solution space on the optimization process but also improves the overall performance and stability of the algorithm. Attached Figure Description

[0039] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0040] Figure 1 This is a flowchart illustrating an embodiment of a model optimization method for black-box stochastic optimization provided in this application.

[0041] Figure 2 The gradient and momentum update logic flowchart is provided in the model optimization method for black-box stochastic optimization provided in this application.

[0042] Figure 3 This is a pseudocode logic diagram of a model optimization method for black-box stochastic optimization provided in this application.

[0043] Figure 4 This is a schematic diagram of an embodiment of a model optimization device for black-box random optimization provided in this application.

[0044] Figure 5 This is a schematic diagram of the structure of a computer terminal embodiment provided in this application. Detailed Implementation

[0045] This application provides a model optimization method, apparatus, terminal, and medium for black-box stochastic optimization, which addresses the technical problem of performance instability in existing black-box stochastic optimization algorithm models.

[0046] To make the inventive objectives, features, and advantages of this application more apparent and understandable, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described below are only some embodiments of this application, and not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0047] First, this application provides a detailed description of an embodiment of a model optimization method for black-box stochastic optimization, as follows:

[0048] Please see Figures 1 to 3 This application provides an embodiment of a model optimization method for black-box stochastic optimization, comprising:

[0049] Step 101: Obtain the model parameters of the target black-box random optimization model;

[0050] The model parameters include: model solution parameters, step size parameters, momentum learning rate parameters, smoothing radius parameters, population size, and maximum number of iterations.

[0051] It should be noted that, according to the method provided in this embodiment, firstly, a black-box stochastic optimization algorithm model to be optimized, i.e., the target black-box stochastic optimization model, is obtained; then, the model parameters of the target black-box stochastic optimization model are obtained, wherein the model parameters include: model solution parameters. Step size parameters Momentum learning rate parameter Smooth radius parameter Population size and the maximum number of iterations T, where the model solution parameters Step size parameters Momentum learning rate parameter Smooth radius parameter These are the parameters to be optimized, and their specific values ​​may change with each optimization iteration.

[0052] It is understandable that if we are currently in the first iteration cycle, the model parameters obtained are all initial parameters, such as the initial model solution parameters. Initial step size parameters Initial momentum learning rate parameter Initial smoothing radius parameter If it is not the first iteration cycle, the obtained model parameters are the parameters optimized in the previous iteration cycle.

[0053] Step 102: Based on the model parameters and the current iteration cycle, determine the population gradient and momentum vector for the current iteration cycle in sequence;

[0054] It should be noted that, based on the model parameters obtained in the previous step, for each iteration t=0,1,…,T-1, the population gradient and momentum vector of the current iteration period are calculated sequentially using the preset population gradient calculation formula and momentum update calculation formula.

[0055] Step 103: Based on the momentum vector, model solution parameters, and step size parameters of the current iteration cycle, calculate the model solution parameters for the next iteration cycle using Gaussian smoothing logic and normalized descent calculation formula. If the convergence or number of iterations of the target black-box stochastic optimization model meets the preset iteration termination condition, output the current model solution parameters. Otherwise, calculate the population gradient and momentum vector for the corresponding iteration cycle based on the model solution parameters of the next iteration cycle.

[0056] It should be noted that, using the gradient direction updated with momentum, the model solution parameters are updated according to the following rules to calculate the model solution parameters for the next iteration. :

[0057] ,

[0058] in, It's the step length. It is the norm of the momentum vector. The normalized descent rule ensures adaptability to the step size.

[0059] Then, the convergence and iteration count of the target black-box stochastic optimization model are determined. If the convergence or iteration count of the target black-box stochastic optimization model meets the preset iteration termination condition, the iteration loop can be stopped, and the final model solution parameters are output. If the iteration termination condition is not met, the model solution parameters are then used as the basis for the iteration. The population gradient calculation logic and momentum update logic provided in this embodiment are used to calculate the population gradient for the corresponding iteration period in sequence. and momentum vector Then it proceeds to the next iteration. Understandably, upon entering the next iteration cycle, the model solution parameters calculated in the previous cycle can be utilized. Population gradient and momentum vector As the current iteration cycle Population gradient and momentum vector Continue to participate in subsequent steps.

[0060] More specifically, such as Figure 2 and Figure 3 As shown, the parameter update logic in step 103 of this embodiment specifically includes:

[0061] Step 1031: Based on the model solution parameters of the next iteration period, extract data samples corresponding to the population size from the sampling data distribution, and generate a Gaussian perturbation vector corresponding to the population size in the solution space.

[0062] Step 1032: Calculate the gradient components of each pair of Gaussian perturbation vectors and data samples through Gaussian smoothing, and use the mean of each gradient component as the population gradient for the corresponding iteration period.

[0063] Step 1033: Based on the population gradient of the latest iteration period and the population gradient of the current iteration period, calculate the momentum vector for the corresponding iteration period according to the momentum update formula.

[0064] It should be noted that during iteration t, Gaussian smoothing is used to smooth the current solution. The gradient is estimated. The specific implementation steps are as follows:

[0065] The population size generated in the solution space is... Gaussian perturbation vector :

[0066]

[0067] Where I represents the identity matrix. This represents a multidimensional normal distribution with a mean of 0 and a covariance matrix that is the identity matrix.

[0068] From data distribution Data samples of the same size as the population were extracted. :

[0069] .

[0070] Based on Gaussian smoothing techniques, calculate each pair of perturbation vectors. and data samples The gradient components are calculated using the following expression:

[0071]

[0072] In the formula, Let be the population gradient over iteration period t. Let be the gradient components of population k during iteration period t. The parameters of the model solution for the iteration period t. For population size, It is the step size parameter. For the data samples of population k in iteration period t, Let be the Gaussian perturbation vector of population k during iteration period t. Let be the smoothing radius of the iteration period t;

[0073] Next, the gradient of all gradient components is averaged to obtain the gradient of the current iteration period t. :

[0074] .

[0075] This method is applicable to population size. Increasing this value significantly reduces the gradient estimation error introduced by data sampling and solution space sampling. The upper bound of this estimation error is:

[0076]

[0077] in Represents the stochastic gradient and true smooth gradient The expected value of the mean square error between them. Is with smooth radius noise variance The constants related to the dimension n of the solution space.

[0078] The momentum update calculation formula provided in this embodiment is as follows:

[0079]

[0080] In the formula, It is the momentum vector of the iteration period t. It is the momentum vector with an iteration period of t+1. The momentum learning rate over the iteration period t. The population gradient at iteration period t+1, Let be the population gradient over the iteration period t.

[0081] More specifically, the method provided in this embodiment may further include the following steps:

[0082] Step 10330: By perturbation reuse, based on the Gaussian perturbation vector and data samples of the next iteration period, and combined with the model solution parameters of the current iteration period, calculate the estimated gradient component values ​​of each pair of Gaussian perturbation vectors and data samples through Gaussian smoothing, and use the mean of the estimated gradient component values ​​as the population gradient of the current iteration period.

[0083] It should be noted that, according to the momentum update calculation formula provided in this embodiment, the momentum vector mentioned in step 103 with an update iteration period of t+1... At that time, the latest population gradient needs to be adopted. Population gradient of the previous iteration Among them, the population gradient of the previous iteration period The value of can be obtained by directly reading the population gradient values ​​saved during the calculation of previous iterations, or by using perturbation reuse processing logic to generate another set of Gaussian random perturbations and performing Gaussian smoothing in a manner similar to the current point gradient estimation. That is, the perturbation sample set generated by the previous gradient estimation is reused. A specific implementation example is as follows:

[0084] First, such as Figure 3 As shown, used in The Gaussian perturbation generated at the location { } and data samples { }; then at the previous iteration point Using the same perturbation vector and data samples, the gradient components of the iteration period t are calculated:

[0085]

[0086] Next, the average of all gradient components calculated by the above formula is taken to obtain the estimated value of the population gradient at the previous iteration point. The expression is as follows:

[0087]

[0088] Let be the estimated value of the population gradient over the iteration period t. This is the estimated gradient component of population k during iteration period t.

[0089] It should be noted that the key point of the perturbation reuse strategy is... and The same Gaussian perturbation set was used. and data samples This sharing mechanism enables and The sources of random noise partially overlap, reducing the gradient correction term ( - Random fluctuations.

[0090] Under the assumption of smoothness of the component functions, the gradient estimate given in the algorithm satisfies:

[0091]

[0092] Where L is the smoothness constant of the objective function; when the smoothing radius... , and step length Small enough, correction term ( - The difference can be ignored, and the iteration gradually converges. If the perturbation is regenerated. and data samples Then the variance of the gradient estimate can be decomposed into the superposition of noise in the solution space and the data space, and by reusing... and This causes the gradient estimates of iteration periods t+1 and t to share the same noise source, at which point the momentum term... It exhibits true smooth gradients A Monte Carlo estimation method, which incorporates the boundedness principle of gradient estimation error, allows the variance to gradually decrease during iteration. This method limits the noise fluctuations of the correction term, ensuring the convergence of the algorithm and thus improving the stability and accuracy of the estimation results.

[0093] The boundedness of the gradient estimation error is as follows: Consider using hyperparameters:

[0094] ;

[0095] Under the assumptions described above, the gradient estimation error... The following inequality constraints must be satisfied:

[0096] ;

[0097] in, It is the initial step size. It is the step size of the t-th generation. It is the variance of the noise. It is the smoothness constant of the objective function. It is the bounded constant of the gradient. It is the dimension of the solution space. It refers to population size.

[0098] This embodiment, based on the above method, also provides an example of performance optimization based on the above method:

[0099] When the parameter settings satisfy the conditions for the perturbation reuse logic mentioned above, and the following assumptions are also true, in solving... When the iteration satisfies the following relationship:

[0100]

[0101] in, , representing the initial value of the function with the optimal value The gap between them.

[0102] The aforementioned assumptions include:

[0103] Assumption 1 (Boundedness of the objective function value): The lower bound of the objective function value is some constant. ,Right now: ;

[0104] Assumption 2 (Unbiasedness and Boundedness of Data Sampling): Data sampling is unbiased, that is: ;

[0105] Furthermore, there exists a certain constant. , making ;

[0106] Assumption 3 (Smoothness of the component function): Component function For all exist Above is ;

[0107] Assumption 4 (Boundedness of Gradient Norm): The upper bound of the gradient norm is some constant. ,Right now: .

[0108] When selecting the initial step size Then, the above boundary can be further optimized as follows:

[0109]

[0110] in, Indicates ignoring minor details Item, set population size Furthermore, the smoothness constant L of the objective function and the initial value of the function are set. with the optimal value The gap between The bounded constant G of the gradient and the noise variance If treated as a constant, then PVRE guarantees... The number of iterations required is .

[0111] Because each iteration needs to be performed Function evaluation, PVRE outputs a The function evaluation complexity of the first-order optimal solution with high precision is O(n). This is consistent with the currently known best result, with the only difference being one... The factor, derived from the use of a gradually decreasing step size strategy, combines Gaussian smoothing techniques and a population-based gradient estimation method in this embodiment. This effectively reduces sampling noise in the data space and solution space, enhancing the accuracy of gradient estimation. Compared with existing methods, the main advantage of PVRE lies in its adaptive convergence, as it does not require any prior knowledge about the characteristics of the problem landscape. PVRE employs a gradually decreasing step size rule, thereby achieving stable convergence during the optimization process and improving the performance of black-box stochastic optimization algorithms on computers.

[0112] The above is a detailed description of an embodiment of a model optimization method for black-box stochastic optimization provided by this application. The following is a detailed description of an embodiment of a model optimization apparatus for black-box stochastic optimization provided by this application.

[0113] Please see Figure 4 This application provides a model optimization apparatus for black-box stochastic optimization, comprising:

[0114] The model parameter acquisition unit 201 is used to acquire the model parameters of the target black-box stochastic optimization model. The model parameters include: model solution parameters, step size parameters, momentum learning rate parameters, smoothing radius parameters, population size, and maximum number of iterations.

[0115] The gradient momentum calculation unit 202 is used to determine the population gradient and momentum vector of the current iteration period in sequence according to the model parameters and the current iteration period.

[0116] The iterative control unit 203 is used to calculate the model solution parameters for the next iteration period based on the momentum vector, model solution parameters, and step size parameters of the current iteration period, through Gaussian smoothing processing logic and normalized descent calculation formula. When the convergence or iteration number of the target black-box stochastic optimization model meets the preset iteration termination condition, the current model solution parameters are output. Otherwise, based on the model solution parameters of the next iteration period, the population gradient and momentum vector for the corresponding iteration period are calculated through the population gradient calculation formula and momentum update calculation formula.

[0117] Furthermore, the model solution parameters in the iterative control unit 203 based on the next iteration cycle, through the population gradient calculation formula and momentum update calculation formula, calculate the population gradient and momentum vector for the corresponding iteration cycle, specifically for:

[0118] Based on the model solution parameters of the next iteration, extract data samples corresponding to the population size from the sampled data distribution, and generate Gaussian perturbation vectors corresponding to the population size in the solution space.

[0119] After Gaussian smoothing, the gradient components of each pair of Gaussian perturbation vectors and data samples are calculated, and the mean of each gradient component is used as the population gradient for the corresponding iteration period.

[0120] Based on the population gradient of the latest iteration and the population gradient of the current iteration, the momentum vector for the corresponding iteration is calculated according to the momentum update formula.

[0121] Furthermore, the specific formula for calculating the population gradient is as follows:

[0122]

[0123] In the formula, Let be the population gradient over iteration period t. Let be the gradient components of population k during iteration period t. The parameters of the model solution for the iteration period t. For population size, It is the step size parameter. For the data samples of population k in iteration period t, Let be the Gaussian perturbation vector of population k during iteration period t. Let be the smoothing radius of the iteration period t.

[0124] Furthermore, the momentum update calculation formula is as follows:

[0125]

[0126] In the formula, It is the momentum vector of the iteration period t. It is the momentum vector with an iteration period of t+1. The momentum learning rate over the iteration period t. The population gradient at iteration period t+1, Let be the population gradient over the iteration period t.

[0127] Furthermore, the normalized descent calculation formula is as follows:

[0128]

[0129] In the formula, For the model solution parameters with iteration period t+1, The parameters of the model solution for the iteration period t. It is the momentum vector of the iteration period t. It is the norm of the momentum vector with iteration period t.

[0130] Furthermore, before calculating the momentum vector for the corresponding iteration period based on the population gradient of the latest iteration period and the population gradient of the current iteration period, according to the momentum update formula, the following steps are also included:

[0131] By using perturbation reuse, based on the Gaussian perturbation vector and data samples of the next iteration cycle, combined with the model solution parameters of the current iteration cycle, the gradient component estimates of each pair of Gaussian perturbation vectors and data samples are calculated through Gaussian smoothing. The average of the estimated gradient components is then used as the population gradient for the current iteration cycle.

[0132] In addition, this application also provides a detailed description of embodiments of a computer terminal and a computer-readable storage medium.

[0133] like Figure 5 As shown in the figure, the computer terminal provided in this embodiment mainly includes: a memory 33 and a processor 31;

[0134] The memory 33 is used to store program code, which is used to implement a model optimization method for black-box stochastic optimization as provided in the above embodiments;

[0135] Processor 31 is used to read and execute program code.

[0136] This application provides an embodiment of a computer-readable storage medium containing program code for being read and executed by a processor 31 to implement a model optimization method for black-box random optimization as provided in the above embodiment.

[0137] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the terminals, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0138] In the several embodiments provided in this application, it should be understood that the disclosed terminals, devices, and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection between devices or units through some interfaces, and may be electrical, mechanical, or other forms.

[0139] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a particular order or sequence. It should be understood that such data can be interchanged where appropriate so that embodiments of the application described herein can be implemented, for example, in orders other than those illustrated or described herein. Furthermore, the terms “comprising” and “having,” and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0140] It should be understood that in this application, "at least one (item)" means one or more, and "more than" means two or more. "And / or" is used to describe the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0141] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0142] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0143] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0144] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A model optimization method for black-box stochastic optimization, characterized in that, include: Obtain the model parameters of the target black-box stochastic optimization model, including: model solution parameters, step size parameters, momentum learning rate parameters, smoothing radius parameters, population size, and maximum number of iterations; Based on the model parameters and the current iteration cycle, the population gradient and momentum vector for the current iteration cycle are determined sequentially. Based on the momentum vector, model solution parameters, and step size parameters of the current iteration cycle, the model solution parameters for the next iteration cycle are calculated using Gaussian smoothing logic and normalized descent calculation formula. When the convergence or number of iterations of the target black-box stochastic optimization model meets the preset iteration termination condition, the current model solution parameters are output. Otherwise, based on the model solution parameters of the next iteration cycle, the population gradient and momentum vector for the corresponding iteration cycle are calculated using the population gradient calculation formula and momentum update calculation formula. The calculation of the population gradient and momentum vector for the corresponding iteration period based on the model solution parameters of the next iteration period, using the population gradient calculation formula and momentum update calculation formula, specifically includes: Based on the model solution parameters of the next iteration period, data samples corresponding to the population size are extracted from the sampled data distribution, and a Gaussian perturbation vector corresponding to the population size is generated in the solution space. After Gaussian smoothing, the gradient components of each pair of Gaussian perturbation vectors and data samples are calculated, and the mean of each gradient component is used as the population gradient for the corresponding iteration period. Based on the population gradient of the latest iteration and the population gradient of the current iteration, the momentum vector for the corresponding iteration is calculated according to the momentum update formula.

2. The model optimization method for black-box stochastic optimization according to claim 1, characterized in that, The specific formula for calculating the population gradient is as follows: ； In the formula, Let be the population gradient over iteration period t. Let be the gradient components of population k during iteration period t. The parameters of the model solution for the iteration period t. The population size, For the data samples of population k in iteration period t, Let be the Gaussian perturbation vector of population k during iteration period t. Let be the smoothing radius of the iteration period t.

3. The model optimization method for black-box stochastic optimization according to claim 2, characterized in that, The momentum update calculation formula is as follows: ； In the formula, It is the momentum vector of the iteration period t. It is the momentum vector with an iteration period of t+1. The momentum learning rate over the iteration period t. The population gradient at iteration period t+1, Let be the population gradient over the iteration period t.

4. The model optimization method for black-box stochastic optimization according to claim 1, characterized in that, The normalized descent calculation formula is as follows: ； In the formula, For the model solution parameters with iteration period t+1, The parameters of the model solution for the iteration period t. It is the momentum vector of the iteration period t. It is the norm of the momentum vector with iteration period t. It is the step size parameter.

5. The model optimization method for black-box stochastic optimization according to claim 1, characterized in that, Before calculating the momentum vector for the corresponding iteration period according to the momentum update formula based on the population gradient of the latest iteration period and the population gradient of the current iteration period, the process further includes: By using a perturbation reuse method, based on the Gaussian perturbation vector and data samples of the next iteration period, combined with the model solution parameters of the current iteration period, the gradient component estimates of each pair of Gaussian perturbation vectors and data samples are calculated through Gaussian smoothing. The average of the estimated gradient components is then used as the population gradient for the current iteration period.

6. A model optimization device for black-box stochastic optimization, characterized in that, include: The model parameter acquisition unit is used to acquire the model parameters of the target black-box stochastic optimization model. The model parameters include: model solution parameters, step size parameters, momentum learning rate parameters, smoothing radius parameters, population size, and maximum number of iterations. The gradient momentum calculation unit is used to determine the population gradient and momentum vector of the current iteration period in sequence according to the model parameters and the current iteration period. The iterative control unit is used to calculate the model solution parameters for the next iteration period based on the momentum vector, model solution parameters, and step size parameters of the current iteration period, through Gaussian smoothing processing logic and normalized descent calculation formula. When the convergence or iteration number of the target black-box stochastic optimization model meets the preset iteration termination condition, the current model solution parameters are output. Otherwise, based on the model solution parameters of the next iteration period, the population gradient and momentum vector for the corresponding iteration period are calculated through population gradient calculation formula and momentum update calculation formula. The model solution parameters in the iterative control unit based on the next iteration cycle are used to calculate the population gradient and momentum vector for the corresponding iteration cycle through the population gradient calculation formula and momentum update calculation formula. Specifically, this is used for: Based on the model solution parameters of the next iteration period, data samples corresponding to the population size are extracted from the sampled data distribution, and a Gaussian perturbation vector corresponding to the population size is generated in the solution space. After Gaussian smoothing, the gradient components of each pair of Gaussian perturbation vectors and data samples are calculated, and the mean of each gradient component is used as the population gradient for the corresponding iteration period. Based on the population gradient of the latest iteration and the population gradient of the current iteration, the momentum vector for the corresponding iteration is calculated according to the momentum update formula.

7. A computer terminal, characterized in that, include: Memory and processor; The memory is used to store program code, which is used to implement a model optimization method for black-box stochastic optimization as described in any one of claims 1 to 5; The processor is used to read and execute the program code.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium contains program code, which is read and executed by a processor to implement a model optimization method for black-box stochastic optimization as described in any one of claims 1 to 5.

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