A multi-objective Bayesian optimization method, apparatus, electronic device, and storage medium

Abstract

This invention discloses a multi-objective Bayesian optimization method, apparatus, electronic device, and storage medium. During the multi-objective Bayesian optimization process, a dynamic threshold is used to classify the set of observation points, treating points located on the Pareto front as positive samples and the remaining points as negative samples, ensuring that the positive class completely covers the Pareto set. Density ratio estimation is extended to multi-objective Bayesian optimization by training a classifier using weighted cross-entropy loss, making the density ratio estimation method applicable to any utility acquisition function. The multi-objective Bayesian optimization process is completed, outputting the Pareto set. This process is then applied to multi-object recognition in image processing tasks to obtain multi-object recognition results. The embodiments of this invention ensure that the classification results fully cover the Pareto front while reducing computational costs to a certain extent, making it widely applicable in the field of computer technology.

Description

Technical Field

[0001] This invention relates to the field of computer technology, and in particular to a multi-objective Bayesian optimization method, apparatus, electronic device, and storage medium. Background Technology

[0002] Bayesian optimization (BO) is an efficient optimization technique for expensive black-box functions. It can find an optimal black-box function. The input strategy. During the optimization process, BO will utilize a set of initial observations. To obtain prior information about function f, and through a proxy model. To capture the prior distribution p(y|x,D) of the observations n ), and provide it to the get function. Used to calculate the benefits of different inputs x to the model, thereby obtaining the next observation point x. i+1 The new observation points were used to update... With p(y|x,D) n+1 After a certain number of updates, the surrogate model can be used to estimate the black-box function f and estimate the input policy x that maximizes f. Because Bo uses prior information from observation points during the optimization process and continuously uses the acquisition function to evaluate the utility of the input policy, Bo has a faster optimization speed and better optimization capability compared to black-box optimization methods such as grid search and random search.

[0003] Boolean optimization (BO) models the set of observation points using a surrogate model to obtain the prior distribution of the objective function, and applies it to the evaluation of the acquisition function for any input policy. The acquisition function, based on the prior distribution, selects the optimal input policy from the current perspective. Two commonly used acquisition functions are PI (Probability of Improvement) and EI (Expectation of Improvement). As shown below, PI and EI evaluate the probability and expected improvement of the function value relative to a threshold, respectively. Here, p(y|x) is the conditional probability distribution of y with respect to x, and τ is the threshold. U(y) is the utility function, used to evaluate the merits of y in the optimization problem. The utility function of PI represents the relative merits of y with respect to y. * The probability of improvement is given by the utility function of EI, which represents the expected improvement of y relative to τ.

[0004]

[0005] In multi-objective optimization problems, the optimization objective is Pareto optimality, i.e., calculating an optimal hyperplane. In a min F problem, the objective is to find the optimal hyperplane P. + any point on There must not be a better point y such that... Where o is the dimension of y. The hypervolume (HV) between the optimal hyperplane and the reference point is often used to evaluate the optimization results. To make the optimal hyperplane cover more solutions, the optimization problem is transformed into maximizing the hypervolume of the objective space. Therefore, a common Bayesian optimization idea is to use a scalar to evaluate the output of multiple objectives. For example, the size of the hypervolume can be optimized using a single-objective optimization method. Correspondingly, some acquisition functions suitable for multi-objective optimization problems have also been proposed, such as the combination of hypervolume with EI and PI, EHVI and PHVI, which have the following definitions, where... Let HV(·) be a Pareto set, and let HV(·) denote a hypervolume constructed by a set of points and a reference point.

[0006]

[0007]

[0008] like Figure 1 As shown, the related technology employs a Bayesian optimization framework based on density ratio estimation, proposed in 2022. This framework performs scalarization operations for multi-dimensional optimization objectives, extending the density ratio estimation method from a single-objective problem to a multi-objective problem. This framework directly estimates the acquisition function using a classifier π(x), successfully solving the problems of high computational cost caused by Gaussian Process Regression (GPR) in traditional methods, as well as the error accumulation and high-dimensional incompatibility issues that may arise from Tree Parzen Estimators (TPE). It theoretically demonstrates the rationality of directly estimating the density ratio using a classifier, allowing a single classifier to simultaneously function as a surrogate model and the acquisition function. Compared to other multi-objective Bayesian optimization methods (such as maximum entropy search), this framework uses a simple estimator training process to replace the complex acquisition function calculation process, significantly improving optimization efficiency.

[0009] Before optimization, the framework first samples a set of observation points from the target space. Given the multidimensional nature of the output, a scalarizer is used to simplify the original problem into a single-objective optimization problem. Subsequently, a preset threshold is used to classify the set of observation points, and the two classes of observation points are input into the classifier to fit the sample data. The classifier integrates the surrogate model and the acquisition function, and can directly estimate the density ratio to determine the optimal x value. The set of observation points is then continuously expanded, and the optimization of the multi-objective problem is achieved by modeling a more accurate probability distribution. In this process, the core step is to ensure the accuracy of the classifier probability estimation of the acquisition function, that is, the acquisition function can be represented by the density ratio, and the density ratio can be estimated by the posterior probability output by the classifier. The whole process is shown in Equation (1).

[0010]

[0011] in, and Let represent the conditional probability density of x with respect to y, τ be the threshold, and γ be the proportion of positive and negative samples based on y.

[0012] However, this framework itself faces several limitations, restricting its performance in ATS scenarios and architecture parameter optimization tasks. First, this framework is a direct extension of single-objective optimization methods, and therefore still relies on the selection of a threshold. Second, the framework depends on the classifier's estimation of the acquisition function; although it provides a theoretical proof of this process, its conclusion treats other types of acquisition functions (such as EI) as PI, meaning the framework cannot utilize more efficient acquisition functions. The following is a detailed description of these two problems.

[0013] (1) Fixed threshold problem

[0014] In equation (1), the conditional probability density ratio proportional to x is obtained, while the threshold τ is used to divide the observation points to calculate the conditional probability density. and In single-objective optimization scenarios, the uniqueness of the optimal solution ensures that the classification result covers that optimal solution, while also balancing exploration and exploitation. However, when dealing with multi-objective problems, the Pareto front contains multiple solutions, and using a single threshold for simple classification may not be sufficient to fully cover the Pareto front.

[0015] Figure 2 This example demonstrates a two-dimensional optimization problem involving observation point classification. Both dimensions use the minf approach as the optimization direction, with orange representing the Pareto front of the current observation point set. The hypervolume of each point is calculated and sorted, and the observation points are classified using the 1 / 3 quantile as the dividing threshold. Figure 2As shown in the left half, when the number of observation points is small, one Pareto point cannot be classified into the positive sample; Figure 2 In the right half, as the number of observation points increases, some non-Pareto points are classified as positive samples. This shows that using a fixed threshold for observation point partitioning cannot cover the Pareto set, and noise in the classification results will lead to poorer convergence performance (or slower convergence speed) of the optimization method.

[0016] Classification using a fixed threshold also has efficiency limitations. When new observations are added to the set, the hypervolume improvement of existing observations may change, requiring all points to be rescaled. For high-dimensional tasks with a large number of subproblems, this repetitive scalarization operation is a key bottleneck in optimization efficiency.

[0017] (2) Adaptation problem of non-PI acquisition function

[0018] As mentioned above, the Bayesian optimization framework based on density ratio estimation relies on the premise of the density ratio formula expressed in equation (1). However, in single-objective optimization methods, the proof of this formula contains an error, and its conclusion only applies to a specific type of acquisition function, namely, the case where the acquisition function is PI. The multi-objective optimization framework perpetuates this error, meaning that the framework cannot use other, better acquisition functions. Some studies have pointed out that EHVI can evaluate the expected improvement of candidate points relative to the threshold, and can better balance the accuracy of the surrogate model and the exploration capability of the optimization method, making it a more effective acquisition function than PHVI.

[0019] Figure 3 This paper presents the PHVI and EHVI distributions of a multi-objective optimization problem DTLZ4 (o=2, d=2), where x1 and x2 are the two dimensions of the solution space. The PHVI and EHVI values ​​of the solution space are calculated by randomly selecting 500 observation points and are represented as follows: Figure 3 (a) and Figure 3 (b) On the ordinate. It can be seen that near the solution space where x1 = 0, there exists a region where the PHVI value is 1 but the EHVI value tends towards 0. This means that selecting candidate points at this location can only improve the optimization results to a very limited extent. The existing framework's practice of converting different categories of acquisition functions into PHVI limits the optimization performance of the method. Based on the above analysis, the following will explain the errors existing in the current density ratio estimation methods.

[0020] Existing methods are used to analyze the observation set D. N Based on the threshold τ, the data are divided into two categories, where τ is the γ-th quantile of the observed y sequence, i.e., γ = Φ(τ) = p(y ≤ τ). This results in two probability density functions. and The calculation process for the acquisition function using EI is as follows:

[0021]

[0022] Where α(x; D) N Let ,τ) be the function to be obtained. The numerator and denominator of equation (2) are respectively:

[0023]

[0024] Therefore, we have:

[0025]

[0026] However, in the above calculation of the molecule, p(x|y,D) N The value of τ is considered independent of the distribution of y and is directly extracted from the equation. In fact, as shown in equation (6), due to the existence of the utility function (τ-y), y in D... N The distribution has been disrupted, so we can directly use p(x|y,D) N Extract as This approach is unacceptable, and this error has been mentioned in some papers. It's important to note that the above reasoning holds true when PI is the utility function, because the proof of PI does not include the term (τ-y), therefore it does not change the relationship between y and d. N Distribution within.

[0027] Summary of the Invention

[0028] The main objective of this invention is to propose a multi-objective Bayesian optimization method, apparatus, electronic device, and storage medium that can ensure that the classification results can fully cover the Pareto front while reducing computational costs to a certain extent.

[0029] To achieve the above objectives, one aspect of this invention proposes a multi-objective Bayesian optimization method, comprising the following steps:

[0030] In the multi-objective Bayesian optimization process, a dynamic threshold is used to classify the set of observation points. Points located at the Pareto front are considered positive samples, and the remaining points are considered negative samples, so that the positive class completely covers the Pareto set.

[0031] The density ratio estimation method is extended to multi-objective Bayesian optimization by training a classifier using weighted cross-entropy loss, making the density ratio estimation method applicable to any utility acquisition function.

[0032] Complete the multi-objective Bayesian optimization process and output the Pareto set; then apply the multi-objective Bayesian optimization process to the multi-object recognition task in image processing to obtain the multi-object recognition results;

[0033] The process of classifying the set of observation points using a dynamic threshold in the multi-objective Bayesian optimization includes the following steps:

[0034] Sample n initial observation points in the solution space to generate an initial observation point set;

[0035] Obtain the Pareto set of each observation point in the initial set of observation points;

[0036] Calculate the utility at each observation point;

[0037] Each observation point is assigned a category label based on whether it is within the Pareto set.

[0038] Extending density ratio estimation to multi-objective Bayesian optimization, and training a classifier using weighted cross-entropy loss, includes the following steps:

[0039] The classifier is trained using utility as the weight of the observation points.

[0040] The posterior probability provided by the classifier is used to optimize and determine the next observation point;

[0041] Evaluate new observation points and add them to the observation point set.

[0042] In some embodiments, the step of sampling n initial observation points in the solution space to generate an initial observation point set includes the following steps:

[0043] A set of data is sampled from the solution space using random sampling or grid sampling. The definition of the initial observation set size is:

[0044] Each point in the initial observation set is input into the black-box function F to obtain its observation value D. n :D n ←{(x i ,F(x i ))}.

[0045] In some embodiments, obtaining the Pareto set of each observation point in the initial observation point set specifically involves: determining the Pareto set and the Pareto front in the initial observation point set by judging the dominance relationship; wherein, for the min F problem, the criterion for judging the Pareto set is: for the Pareto front P + any point on There must not be a better point y such that... Where o is the dimension of y.

[0046] In some embodiments, calculating the utility of each observation point includes the following steps:

[0047] If the acquisition function is PHVI, then there is no need to perform scalarization; simply assign a 0-1 utility value to each point based on the Pareto set.

[0048] If other acquisition functions are used, including EHVI, then scalarization is performed on the observations within the Pareto set;

[0049] Among them, the observation point utility u of PHVI i And the observation point effect of EHVI i The calculation is shown in the following equation:

[0050]

[0051] Among them, P + For the obtained Pareto set, P - It is a non-Pareto set; HV() represents a hypervolume constructed by a set of points and a reference point.

[0052] In some embodiments, in the step of assigning a category label to each observation point, it is not necessary to sort the utility values, classify the set of observation points, classify observation points with non-zero utility values ​​into the positive class, and classify observation points with zero utility values ​​into the negative class.

[0053] The process of training a classifier using utility as the weight of observation points includes the following steps:

[0054] A classifier is used to fit the set of observation points, where the specific acquisition function used varies.

[0055] Based on the following loss function, the posterior probability output by the classifier is used as an estimate of the density ratio, thereby estimating the acquisition function; loss function The expression is:

[0056]

[0057] Where θ represents the classifier parameters; and Let represent the conditional probability density of x with respect to y for the two values ​​of y respectively; U(s) represents the utility function independent of x; β represents the proportion of positive samples; and K represents a constant.

[0058] XGBoost, Random Forest, and Multilayer Perceptron are used as classifiers. After training, the posterior probability obtained during training is used as the estimate of the acquisition function to evaluate candidate points.

[0059] In some embodiments, the optimization using the posterior probability provided by the classifier to determine the next observation point includes the following steps:

[0060] Given a set of candidate solutions, the classifier outputs the value of the acquired function, and the point x that maximizes the acquired function is determined by optimization in the solution space. t This is used as the next observation point for the black-box function;

[0061] The evaluation of new observation points and their addition to the observation point set includes the following steps:

[0062] The optimal observation point x was evaluated using the black-box function F. t Add it to the observation point set, and expand the observation point set by acquiring the function for each new observation point.

[0063] In some embodiments, when classifying the set of observation points using a dynamic threshold, it is not necessary to perform scalarization on each observation point; it is only necessary to determine the dominance of each observation point. The dominance relationship of the observation points is determined by comparing the components y. i Size implementation of i∈(1,2,…,q);

[0064] During the training of the classifier using weighted cross-entropy loss, a scalar is first used before performing density ratio estimation. The output of the quantized black-box function F, i.e. Obtain the set of observations U(s) represents a utility function independent of x, p(s|x,D) N P represents the prior distribution provided by the surrogate model. + and P - Let these represent the Pareto set and the non-Pareto set of the function output, respectively, to obtain the function α(x; D). N ) represents the expectation of each input point x with respect to the utility function, where the utility function represents the degree to which the addition of a candidate point improves the hypervolume; the density ratio equation containing the coefficient w is modeled by maximizing the log-likelihood of dr(x) using weighted cross-entropy loss.

[0065] Another aspect of this invention provides a multi-objective Bayesian optimization device, comprising:

[0066] The first module is used to classify the set of observation points using a dynamic threshold during the multi-objective Bayesian optimization process. Points located at the Pareto front are considered positive samples, and the remaining points are considered negative samples, so that the positive class completely covers the Pareto set.

[0067] The second module extends the density ratio estimation to multi-objective Bayesian optimization by training a classifier using weighted cross-entropy loss, making the density ratio estimation method applicable to any utility acquisition function.

[0068] The third module is used to complete the multi-objective Bayesian optimization process and output the Pareto set; and to apply the multi-objective Bayesian optimization process to the multi-object recognition task in image processing to obtain the multi-object recognition result;

[0069] The process of classifying the set of observation points using a dynamic threshold in the multi-objective Bayesian optimization includes the following steps:

[0070] Sample n initial observation points in the solution space to generate an initial observation point set;

[0071] Obtain the Pareto set of each observation point in the initial set of observation points;

[0072] Calculate the utility at each observation point;

[0073] Each observation point is assigned a category label based on whether it is within the Pareto set.

[0074] Extending density ratio estimation to multi-objective Bayesian optimization, and training a classifier using weighted cross-entropy loss, includes the following steps:

[0075] The classifier is trained using utility as the weight of the observation points.

[0076] The posterior probability provided by the classifier is used to optimize and determine the next observation point;

[0077] Evaluate new observation points and add them to the observation point set.

[0078] To achieve the above objectives, another aspect of the present invention provides an electronic device, which includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the method described above.

[0079] To achieve the above objectives, another aspect of the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the methods described above.

[0080] This invention also discloses a computer program product or computer program, which includes computer instructions stored in a computer-readable storage medium. A processor of a computer device can read the computer instructions from the computer-readable storage medium and execute the computer instructions, causing the computer device to perform the aforementioned method.

[0081] The embodiments of this invention include at least the following beneficial effects: This invention provides a multi-objective Bayesian optimization method, apparatus, electronic device, and storage medium. This scheme, during the multi-objective Bayesian optimization process, uses a dynamic threshold to classify the set of observation points, treating points located at the Pareto front as positive samples and the remaining points as negative samples, ensuring that the positive class completely covers the Pareto set. It extends density ratio estimation to multi-objective Bayesian optimization, training the classifier through weighted cross-entropy loss, making the density ratio estimation method applicable to any utility acquisition function. The multi-objective Bayesian optimization process is completed, outputting the Pareto set. Furthermore, the multi-objective Bayesian optimization process is applied to multi-object recognition in image processing tasks to obtain multi-object recognition results. The embodiments of this invention ensure that the classification results fully cover the Pareto front, while simultaneously reducing computational costs to a certain extent. Attached Figure Description

[0082] Figure 1 This is a schematic diagram of a multi-objective Bayesian optimization framework based on density ratio estimation provided in an embodiment of the present invention;

[0083] Figure 2 This is an example diagram of the classification results of observation points using a fixed threshold provided in an embodiment of the present invention;

[0084] Figure 3 This is an example of the difference between the PI and EI acquisition functions provided in the embodiments of the present invention, wherein, Figure 3 (a) represents the PI acquisition function. Figure 3 (b) represents the EI retrieval function;

[0085] Figure 4 This is a flowchart of the overall steps provided in the embodiments of the present invention;

[0086] Figure 5 This is an example diagram of the observation point classification results using dynamic thresholds provided in an embodiment of the present invention;

[0087] Figure 6 This is a comparison chart of the optimization performance of different optimization methods provided in the embodiments of the present invention for the DTLZ problem;

[0088] Figure 7 This is a schematic diagram illustrating the cumulative computation time of multiple Bayesian optimization algorithms provided in this embodiment of the invention. Detailed Implementation

[0089] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In the following description, when referring to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the embodiments of this invention; they are merely examples of apparatuses and methods consistent with some aspects of the embodiments of this invention as detailed in the appended claims.

[0090] It is understood that the terms "first," "second," "third," "fourth," etc. (if present) in the specification and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data used can be interchanged where appropriate so that embodiments of the invention described herein can be implemented 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.

[0091] It should be understood that in this invention, "at least one (item)" refers to one or more, and "more than one" refers to two or more. "And / or" describes 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.

[0092] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein is for the purpose of describing embodiments of the invention only and is not intended to limit the invention.

[0093] Before providing a detailed description of the embodiments of the present invention, the meanings of some relevant variables involved in the embodiments of the present invention are explained as follows:

[0094] Black-box functions that need optimization;

[0095] The set of observations, where (x i ,y i ) represents an observation point, and n represents the number of observation points in the set;

[0096] p(y|x,D n ): The prior probability distribution of the y-values ​​in the set of observation points with respect to x;

[0097] The function is used to calculate the benefits that different inputs x bring to the model.

[0098] U(y): Utility function, used to evaluate the merits of y values ​​in optimization problems;

[0099] τ: The threshold used in the acquisition function to evaluate the value of the observation point;

[0100] π(x): Classifier used to estimate the acquisition function;

[0101] Let x and y represent the conditional probability density of x with respect to y, respectively.

[0102] γ: The ratio of positive to negative samples among the observation points after being divided by the threshold τ;

[0103] A scalarizer is used to convert a high-dimensional point into a scalar.

[0104] P + ,P - : Represent Pareto sets and non-Pareto sets, respectively;

[0105] D′ N A newly constructed set of observation points;

[0106] z, z′: represent the classification labels of the two sets of observation points, respectively;

[0107] dr(x): Density ratio, used to represent the acquisition function;

[0108] w: Weight coefficient, used during classifier training.

[0109] The multi-objective Bayesian optimization method, apparatus, electronic device, and storage medium provided in this invention relate to the field of computer technology. The multi-objective Bayesian optimization method provided in this invention can be applied to terminals, servers, or software running on either a terminal or server. In some embodiments, the terminal can be a smartphone, tablet, laptop, desktop computer, smart speaker, smartwatch, or in-vehicle terminal, but is not limited thereto; the server can be configured as an independent physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms. The server can also be a node server in a blockchain network; the software can be an application implementing the multi-objective Bayesian optimization method, but is not limited to the above forms.

[0110] This invention can be used in a wide variety of general-purpose or special-purpose computer system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices. This invention can be described in the general context of computer-executable instructions, such as program modules, that are executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform specific tasks or implement specific abstract data types. This invention can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0111] Reference Figure 4 , Figure 4 The flowchart illustrates a multi-objective Bayesian optimization method applied to a server, as provided in this embodiment of the invention. The execution subject of this method can be any of the aforementioned computer devices (including servers or terminals). (Refer to...) Figure 4 The method may include the following steps:

[0112] In the multi-objective Bayesian optimization process, a dynamic threshold is used to classify the set of observation points. Points located at the Pareto front are considered positive samples, and the remaining points are considered negative samples, so that the positive class completely covers the Pareto set.

[0113] The density ratio estimation method is extended to multi-objective Bayesian optimization by training a classifier using weighted cross-entropy loss, making the density ratio estimation method applicable to any utility acquisition function.

[0114] Complete the multi-objective Bayesian optimization process and output the Pareto set; then apply the multi-objective Bayesian optimization process to the multi-object recognition task in image processing to obtain the multi-object recognition results;

[0115] The process of classifying the set of observation points using a dynamic threshold in the multi-objective Bayesian optimization includes the following steps:

[0116] Sample n initial observation points in the solution space to generate an initial observation point set;

[0117] Obtain the Pareto set of each observation point in the initial set of observation points;

[0118] Calculate the utility at each observation point;

[0119] Each observation point is assigned a category label based on whether it is within the Pareto set.

[0120] Extending density ratio estimation to multi-objective Bayesian optimization, and training a classifier using weighted cross-entropy loss, includes the following steps:

[0121] The classifier is trained using utility as the weight of the observation points.

[0122] The posterior probability provided by the classifier is used to optimize and determine the next observation point;

[0123] Evaluate new observation points and add them to the observation point set.

[0124] In some embodiments, the step of sampling n initial observation points in the solution space to generate an initial observation point set includes the following steps:

[0125] A set of data is sampled from the solution space using random sampling or grid sampling. The definition of the initial observation set size is:

[0126] Each point in the initial observation set is input into the black-box function F to obtain its observation value D. n :D n ←{(x i ,F(x i ))}.

[0127] In some embodiments, obtaining the Pareto set of each observation point in the initial observation point set specifically involves: determining the Pareto set and the Pareto front in the initial observation point set by judging the dominance relationship; wherein, for the min F problem, the criterion for judging the Pareto set is: for the Pareto front P + any point on There must not be a better point y such that... Where o is the dimension of y.

[0128] In some embodiments, calculating the utility of each observation point includes the following steps:

[0129] If the acquisition function is PHVI, then there is no need to perform scalarization; simply assign a 0-1 utility value to each point based on the Pareto set.

[0130] If other acquisition functions are used, including EHVI, then scalarization is performed on the observations within the Pareto set;

[0131] Among them, the observation point utility u of PHVI i And the observation point effect of EHVI i The calculation is shown in the following equation:

[0132]

[0133] Among them, P + For the obtained Pareto set, P - For non-Pareto sets; HV() represents the hypervolume constructed by a set of points and a reference point.

[0134] In some embodiments, in the step of assigning a category label to each observation point, it is not necessary to sort the utility values, classify the set of observation points, classify observation points with non-zero utility values ​​into the positive class, and classify observation points with zero utility values ​​into the negative class.

[0135] The process of training a classifier using utility as the weight of observation points includes the following steps:

[0136] A classifier is used to fit the set of observation points, where the specific acquisition function used varies.

[0137] Based on the following loss function, the posterior probability output by the classifier is used as an estimate of the density ratio, thereby estimating the acquisition function; loss function The expression is:

[0138]

[0139] Where θ represents the classifier parameters; and Let represent the conditional probability density of x with respect to y for the two values ​​of y respectively; U(s) represents the utility function independent of x; β represents the proportion of positive samples; and K represents a constant.

[0140] XGBoost, Random Forest, and Multilayer Perceptron are used as classifiers. After training, the posterior probability obtained during training is used as the estimate of the acquisition function to evaluate candidate points.

[0141] In some embodiments, the optimization using the posterior probability provided by the classifier to determine the next observation point includes the following steps:

[0142] Given a set of candidate solutions, the classifier outputs the value of the acquired function, and the point x that maximizes the acquired function is determined by optimization in the solution space. t This is used as the next observation point for the black-box function;

[0143] The evaluation of new observation points and their addition to the observation point set includes the following steps:

[0144] The optimal observation point x was evaluated using the black-box function F. t Add it to the observation point set, and expand the observation point set by acquiring the function for each new observation point.

[0145] In some embodiments, when classifying the set of observation points using a dynamic threshold, it is not necessary to perform scalarization on each observation point; it is only necessary to determine the dominance of each observation point. The dominance relationship of the observation points is determined by comparing the components y. i Size implementation of i∈(1,2,…,q);

[0146] During the training of the classifier using weighted cross-entropy loss, a scalar is first used before performing density ratio estimation. The output of the quantized black-box function F, i.e. Obtain the set of observations U(s) represents a utility function independent of x, p(s|x,D) N P represents the prior distribution provided by the surrogate model. + and P - Let these represent the Pareto set and the non-Pareto set of the function output, respectively, to obtain the function α(x; D). N ) represents the expectation of each input point x with respect to the utility function, where the utility function represents the degree to which the addition of a candidate point improves the hypervolume; the density ratio equation containing the coefficient w is modeled by maximizing the log-likelihood of dr(x) using weighted cross-entropy loss.

[0147] The implementation process of the method of the present invention in a specific application scenario is described in detail below:

[0148] To address the problems existing in the prior art, this invention proposes a multi-objective Bayesian optimization method based on dynamic threshold density ratio estimation (DR.EMO). This method first employs a dynamic threshold to ensure that the classification results fully cover the Pareto front, while simultaneously reducing computational costs to some extent. Secondly, a density ratio estimation method applicable to all types of acquisition functions is developed, and its correctness is rigorously proven theoretically.

[0149] (1) Dynamic threshold classification:

[0150] To avoid the problem of classification results failing to cover the Pareto set, DR.EMO uses a dynamic threshold to classify the observation point set. During optimization, only points located on the Pareto front have non-zero hypervolume contributions; points outside the Pareto set do not participate in hypervolume calculation. Therefore, DR.EMO treats points on the Pareto front as positive samples and the rest as negative samples. As the observation point set expands during optimization, the ratio of positive to negative samples continuously changes; therefore, this classification is based on dynamic thresholding. Figure 5 As shown, the dynamic threshold classification results can completely cover the Pareto set without being affected by the number of observation points. This allows DR.EMO to use the Pareto set as the optimization direction to improve the convergence speed.

[0151] In actual classification, DR.EMO does not require scalarization of each observation point; it only needs to determine the dominance status of each observation point. Due to the complexity of high-dimensional hypervolume computation, another advantage of dynamic thresholding is its high computational efficiency. There are no polynomial-time algorithms for high-dimensional hypervolume computation; although many estimation algorithms exist, such as the WFG algorithm, their time complexity still reaches O(n^2). q-2 The value is logn), where n and q represent the number of points and dimension of the Pareto set, respectively. Therefore, scalarization is often the main reason for the bottleneck in the efficiency of density ratio estimation.

[0152] In DR.EMO, the dominance of observation points is determined by comparing the y components. i The size of i∈(1,2,…,q) is implemented. Given an initial set of observation points, the time complexity of dynamic threshold classification is O(n^2). 2q); During the optimization process, as the set of observation points expands, when a new observation point is added, its category can be determined simply by judging its dominance relationship with each point in the Pareto set, with a time complexity of O(n′q), where n′ is the size of the Pareto set. Therefore, when using PHVI as the acquisition function, DR.EMO can avoid performing scalarization operations; when using other acquisition functions, DR.EMO can avoid performing scalarization operations on non-Pareto sets, thus improving optimization efficiency.

[0153] (2) Non-PI density ratio estimation:

[0154] by Figure 1 Inspired by the framework shown, DR.EMO extends density ratio estimation to multi-objective Bayesian optimization by training a classifier using weighted cross-entropy loss, thus avoiding the drawback of density ratio estimation not being applicable to non-PI utility functions. The theoretical derivation is given below.

[0155] Before performing density ratio estimation, DR.EMO first uses a scalar. The output of the quantized black-box function F, i.e. Obtain the set of observations U(s) represents a utility function independent of x, p(s|x,D) N P represents the prior distribution provided by the surrogate model. + and P - Let represent the Pareto set and non-Pareto set of the function output, respectively. Obtain the function α(x; D). N ) represents the expectation of each input point x with respect to the utility function, where the utility function represents the degree of improvement of the hypervolume by the addition of the candidate point, as shown in equation (7).

[0156]

[0157] Referring to equation (3), the denominator It is easy to prove that in DR.EMO, the classification ratio and probability density of observation points are expressed as: γ:=p(y∈P) + D N ),

[0158] Because U(s) changed s in D N The distribution in the numerator cannot be p(x|s,D) within the numerator integral. N The U(s) term can be directly proposed. Before calculating the molecule, as shown in equation (8), it can be transformed to eliminate the influence of the U(s) term.

[0159]

[0160] Here D′N For a newly constructed set of observation points, the following relationship exists between it and the original set of observation points:

[0161]

[0162] Where K is a constant used to maintain p(s|D′) N Normalization of ). Since x and s appear in pairs in the set of observation points, when y∈P + When x is in the set of old and new observation points, the following relationship also applies:

[0163] p(x|D′ N )=K·U(s)p(x|D N )#(10)

[0164] At the same time, due to D′ N It only changes the distribution of s, and x with respect to s and D′. N The conditional probability will remain unchanged, that is:

[0165] p(x|s,D N )=p(x|s,D′ N )#(11)

[0166] From formulas (9-11), we can obtain the following equations. Equation (12) shows that the transformation of equation (8) does not change the proportion of the Pareto set in the observation points. Equation (13) shows that this transformation will change the conditional probability of x in the Pareto set.

[0167]

[0168] Substituting equations (12-13) into the numerator of equation (7), we get:

[0169]

[0170] In summary, the acquisition function can be reconstructed into a density ratio form as shown in equation (15). Compared with the results in related prior art, the density ratio proposed in this section uses... The non-1 utility of candidate points is represented by constructing an auxiliary concept D′. N It realizes the density ratio representation of arbitrary acquisition functions.

[0171]

[0172] Building upon this, the density ratio is represented using class posterior probabilities. This section extends this method to multi-objective Bayesian optimization and corrects errors regarding the density ratio. DR.EMO uses a variable threshold for density ratio estimation, dividing observations into Pareto and non-Pareto sets, where z and z′ represent the classification labels of the two sets of observations, respectively. Naturally, we have: p(x|y∈P) + D N ) = p(x|z = 1), p(x|y ∈ P + ,D′ N )=p′(x|z=1), at the same time The following also holds true: γ = p(z = 1) = p′(z = 1). Therefore, the process of representing the density ratio dr(x) using the class posterior probability is as follows:

[0173]

[0174] According to equation (10), we have: Therefore, a coefficient can be set:

[0175]

[0176] Used to represent Furthermore, the class-conditional posterior probabilities of the two sets of observations with respect to x are equal, i.e., p′(z=1|x)=p(z=1|x), the proof of which is as follows:

[0177]

[0178] Where p(x|s,D′) N )=p(x|s,D N This always holds true when y∈P. - At that time, p(s|D′) N )=p(s|D N );at the same time Therefore:

[0179]

[0180] According to equations (16-18), the density ratio can be expressed as the conditional posterior probability of the class with respect to x:

[0181] dr(x)=w·p(z=1|x)#(19)

[0182] Equation (19) shows that the density ratio can be estimated by the conditional posterior probability. DR.EMO uses a classification function to estimate the density ratio, which is expressed as: Where θ represents the classifier parameters. To model the density ratio equation containing the coefficient w, a weighted cross-entropy loss is used to maximize the log-likelihood of dr(x), as shown below:

[0183]

[0184] Considering the potential imbalance between positive and negative samples, in practical applications, the set of observation points can be enhanced by adjusting the sample ratio. In this case:

[0185]

[0186] Where N + N - These represent the number of positive and negative samples, respectively. Finally, dr(x) can be obtained through... To make an estimate, among which

[0187] As shown below, when the acquisition function is PI, equation (22) is a regular unweighted cross-entropy. This also indicates that the original density ratio estimation method is only applicable to PI. When other acquisition functions are used, it is correct to estimate the density ratio according to equations (15) and (21).

[0188]

[0189] In summary, the specific flow of the method in this embodiment of the invention is as follows:

[0190] To address the issue that fixed threshold classification results fail to provide a good direction for optimization, DR.EMO employs dynamic thresholding for classification, ensuring that the positive class completely covers the Pareto set. To address the inability to estimate non-PI acquisition functions, DR.EMO uses weighted cross-entropy training to train the classifier, making the density ratio estimation method applicable to acquisition functions with arbitrary utility. Table 1 illustrates the algorithm flow of DR.EMO. After T optimizations, DR.EMO can obtain the Pareto set of problem F in the solution space with T+n finite observation points.

[0191] Table 1. DR.EMO Algorithm Flow

[0192]

[0193] In step 1, a certain number of observation points are sampled from the solution space to form an initial set of observation points. The specific steps include: (1) sampling a set of data from the solution space using random sampling / grid sampling or other methods. The size of the initial set of observations can be customized. (2) Input each point in the initial observation set into the black-box function F to obtain its observation value: D n ←{(x i ,F(x i ))}.

[0194] In step 2, the Pareto set and Pareto front in the initial set of observation points are determined by judging the dominance relationship. For the min F problem, the criterion for determining the Pareto set is: for the Pareto front P... + any point on There must not be a better point y such that... Where o is the dimension of y.

[0195] In step 3, if the acquisition function is PHVI, no scalarization operation is required; a 0-1 utility value is directly assigned to each point based on the Pareto set. If it is another acquisition function, such as EHVI, then only scalarization is required for the observation points within the Pareto set. The observation point utility calculations for PHVI and EHVI are shown in equations (23) and (24), where P + Let P be the Pareto set obtained in step 2. - It is a non-Pareto set.

[0196]

[0197] In step 4, without sorting the utility values, the set of observation points is classified, with observation points having non-zero utility values ​​classified as positive and observation points having zero utility values ​​classified as negative.

[0198] In step 5, a classifier is used to fit the set of observation points. Depending on the acquisition function used, the loss function shown in equation (20) is used for training. The posterior probability output by the classifier is used as an estimate of the density ratio, thereby estimating the acquisition function. DR.EMO is compatible with any advanced classifier. In subsequent experiments, this invention uses XGBoost, Random Forest (RF), and Multilayer Perceptron (MLP) as classifiers. After training, the posterior probability provided can be used as an estimate of the acquisition function to evaluate candidate points.

[0199] In step 6, given a set of candidate solutions, the classifier can output its acquired function value. Based on this, a point x that maximizes the acquired function is determined through optimization in the solution space. t This is used as the next observation point of the black-box function. DR.EMO supports various optimization methods, such as using the Covariance Matrix Adaptation Evolution Strategy (CMAES) to optimize the candidate point space.

[0200] In step 7, the black-box function F is used to evaluate the optimal observation point x obtained in step 6. tAdd the observed point to the observation point set; repeat steps 2-7, obtaining a new observation point in each round. Expand the observation point set by acquiring the function, thereby improving the fitting accuracy of the classifier and making the estimation of the acquisition function more accurate.

[0201] In step 8, based on the set of observation points, the Pareto set and Pareto front are determined as the final multi-objective optimization result.

[0202] The following describes the process of the performance evaluation experiment in an embodiment of the present invention:

[0203] DR.EMO, through its weighted classifier, can estimate the acquisition function more effectively, and therefore theoretically should offer better optimization performance. The purpose of this experiment is to demonstrate the superior optimization performance of DR.EMO by comparing it with other optimization methods on a benchmark problem.

[0204] In terms of test problem selection, the DTLZ problem was used as the benchmark problem. By setting different input and output dimensions, the performance of DR.EMO on optimization problems of different dimensions was verified. Table 2 shows the combination of benchmark problem and optimization method used in this experiment.

[0205] Table 2. Benchmark problems and optimization methods used in the experiments.

[0206]

[0207] Regarding the selection of balselines, this section selects two advanced methods from the field of multi-objective Bayesian optimization: ① MBORE, proposed in 2022, is the first method to apply density ratio estimation to multi-objective Bayesian optimization problems. It uses PHC (Pareto Hypervolumn Contribution) as a scalar, ensuring that non-Pareto points can also have non-zero scalar values. However, it still uses a fixed threshold as the partitioning criterion, resulting in the aforementioned problem of inaccurate optimization direction. ② MESMO, proposed in 2019, is a multi-objective Bayesian optimization method based on maximum entropy search. It improves the computational efficiency of PESMO by evaluating the information gain of the output space, thus increasing the evaluation efficiency. MBORE uses PHC as the utility function and XGB / RF / MLP as the classifier. In MESMO, the number of Monte Carlo samplings of the Pareto front is 3. Other parameter settings are referenced in their respective papers.

[0208] In the specific experimental setup, this section uses DR.EMO to estimate PHVI and EHVI respectively, and employs classifiers such as Xgboost, Random Forest (RF), and Multilayer Perceptron (MLP) for estimation. Relative hypervolume is used to evaluate the optimization results to avoid the influence of problem characteristics on the results. Regarding hyperparameter settings, the classifier parameters in DR.EMO are referenced from MBORE, and CMAES is used as the acquisition function optimization method. The method combinations used for comparison are shown in Table 2.

[0209] For each fixed-dimensional benchmark problem, all methods share the same initial set of observation points (n=20), and each method group undergoes two trials, with the average of the two results taken as the final result. The final result is as follows: Figure 6 As shown, the horizontal axis represents the number of iterations, and the vertical axis represents the relative hypervolume.

[0210] The results show that: (1) DREMO-EHVI+XGB / RF outperforms other methods in all dimensions and converges faster; DREMO+EHVI has a smaller standard deviation in the two experiments and is more stable than other methods; (2) Due to the underfitting problem caused by the small amount of data, MLP is not suitable for density ratio estimation and performs significantly worse than other methods in some dimensions; (3) MESMO only performs well in low-dimensional cases. In experiments with o>2 and d>2, its performance is significantly worse than other methods. The reason for this may be that the method relies on the prior likelihood assumption of Gaussian process and Monte Carlo sampling results.

[0211] To verify the computational efficiency of DR.EMO, this section statistically analyzes the computation times of DREMO (PHVI), DREMO (EHVI), MBORE (PHC), and MESMO, with the density ratio estimation classifier set to XGB and the sampling function optimization method being random sampling and taking the maximum value. The scalarization computation time and total time for each iteration are statistically analyzed, and the results are as follows: Figure 7 As shown in Table 3. The experiment was repeated twice, and the final result was the average of the two results.

[0212] Table 3. Average classification / total time for each iteration of different Bayesian optimization algorithms.

[0213]

[0214] The results show that: (1) DREMO takes the least time to estimate PHVI, and the time advantage is more obvious when the number of iterations / the problem dimension is higher; (2) When DREMO estimates EHVI, it does not need to calculate the hypervolume contribution of all observation points, so its computation time is better than MBORE. The amount of time saved depends on the proportion of the Pareto set to the observation set in each iteration. Compared with MBORE which uses a fixed threshold, it is more efficient; (3) MESMO based on maximum entropy search has the highest computation cost. At the same time, the original paper shows that its computation time is proportional to the number of Monte Carlo samplings used. When the number of samplings is 10 or higher, the computation time is longer.

[0215] Based on the above experiments, it can be concluded that DR.EMO can achieve higher optimization performance and faster convergence speed by estimating a more efficient acquisition function (EHVI); and can achieve higher computational efficiency by using a dynamic threshold.

[0216] Another aspect of this invention provides a multi-objective Bayesian optimization device, comprising:

[0217] The first module is used to classify the set of observation points using a dynamic threshold during the multi-objective Bayesian optimization process. Points located at the Pareto front are considered positive samples, and the remaining points are considered negative samples, so that the positive class completely covers the Pareto set.

[0218] The second module extends the density ratio estimation to multi-objective Bayesian optimization by training a classifier using weighted cross-entropy loss, making the density ratio estimation method applicable to any utility acquisition function.

[0219] The third module is used to complete the multi-objective Bayesian optimization process and output the Pareto set; and to apply the multi-objective Bayesian optimization process to the multi-object recognition task in image processing to obtain the multi-object recognition result;

[0220] The process of classifying the set of observation points using a dynamic threshold in the multi-objective Bayesian optimization includes the following steps:

[0221] Sample n initial observation points in the solution space to generate an initial observation point set;

[0222] Obtain the Pareto set of each observation point in the initial set of observation points;

[0223] Calculate the utility at each observation point;

[0224] Each observation point is assigned a category label based on whether it is within the Pareto set.

[0225] Extending density ratio estimation to multi-objective Bayesian optimization, and training a classifier using weighted cross-entropy loss, includes the following steps:

[0226] The classifier is trained using utility as the weight of the observation points.

[0227] The posterior probability provided by the classifier is used to optimize and determine the next observation point;

[0228] Evaluate new observation points and add them to the observation point set.

[0229] It is understood that the content of the above method embodiments is applicable to the present device embodiments. The specific functions implemented by the present device embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0230] This invention also provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the aforementioned multi-objective Bayesian optimization method. This electronic device can be any smart terminal, including tablet computers, in-vehicle computers, etc.

[0231] It is understood that the content of the above method embodiments is applicable to this device embodiment. The specific functions implemented by this device embodiment are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0232] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described multi-objective Bayesian optimization method.

[0233] It is understood that the content of the above method embodiments is applicable to this storage medium embodiment. The specific functions implemented in this storage medium embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0234] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0235] It should be noted that in various specific embodiments of the present invention, when processing data related to user identity or characteristics, such as user information, user behavior data, user historical data, and user location information, user permission or consent is obtained first. Furthermore, the collection, use, and processing of this data comply with relevant laws, regulations, and standards. In addition, when embodiments of the present invention require access to sensitive personal information of users, separate permission or consent from the user is obtained through pop-ups or redirection to a confirmation page. Only after obtaining the user's separate permission or consent is the necessary user-related data for the normal operation of the embodiments of the present invention acquired.

[0236] The embodiments described in this invention are for the purpose of more clearly illustrating the technical solutions of the embodiments of this invention, and do not constitute a limitation on the technical solutions provided by the embodiments of this invention. As those skilled in the art will know, with the evolution of technology and the emergence of new application scenarios, the technical solutions provided by the embodiments of this invention are also applicable to similar technical problems.

[0237] Those skilled in the art will understand that the technical solutions shown in the figures do not constitute a limitation on the embodiments of the present invention, and may include more or fewer steps than shown, or combine certain steps, or different steps.

[0238] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0239] Those skilled in the art will understand that all or some of the steps in the methods disclosed above, as well as the functional modules / units in the systems and devices, can be implemented as software, firmware, hardware, or suitable combinations thereof.

[0240] In the several embodiments provided by this invention, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of the units described above 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 through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0241] The units described above 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.

[0242] 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.

[0243] 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 multiple 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 of the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing programs, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0244] The preferred embodiments of the present invention have been described above with reference to the accompanying drawings, but this does not limit the scope of the claims of the present invention. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and spirit of the present invention should be within the scope of the claims of the present invention.

Claims

1. A multi-objective Bayesian optimization method, characterized in that, Includes the following steps: In the multi-objective Bayesian optimization process, a dynamic threshold is used to classify the set of observation points. Points located at the Pareto front are considered positive samples, and the remaining points are considered negative samples, so that the positive class completely covers the Pareto set. The density ratio estimation method is extended to multi-objective Bayesian optimization by training a classifier using weighted cross-entropy loss, making the density ratio estimation method applicable to any utility acquisition function. Complete the multi-objective Bayesian optimization process and output the Pareto set; then apply the multi-objective Bayesian optimization process to the multi-object recognition task in image processing to obtain the multi-object recognition results; The process of classifying the set of observation points using a dynamic threshold in the multi-objective Bayesian optimization includes the following steps: Sample n initial observation points in the solution space to generate an initial observation point set; Obtain the Pareto set of each observation point in the initial set of observation points; Calculate the utility at each observation point; Each observation point is assigned a category label based on whether it is within the Pareto set. In this step of assigning category labels to each observation point, there is no need to sort the utility values. The observation point set is classified, with observation points having non-zero utility values ​​classified as positive and observation points having zero utility values ​​classified as negative. Extending density ratio estimation to multi-objective Bayesian optimization, and training a classifier using weighted cross-entropy loss, includes the following steps: The classifier is trained using utility as the weight of the observation points. The posterior probability provided by the classifier is used to optimize and determine the next observation point; Evaluate new observation points and add them to the observation point set.

2. The multi-objective Bayesian optimization method according to claim 1, characterized in that, The process of sampling n initial observation points in the solution space to generate an initial observation point set includes the following steps: A set of data is sampled from the solution space using random sampling or grid sampling. The initial observation set size is defined as follows: ; Each point in the initial observation set is input into the black-box function. In the process, its observed values ​​are obtained. : .

3. The multi-objective Bayesian optimization method according to claim 1, characterized in that, The process of obtaining the Pareto set of each observation point in the initial observation point set specifically involves: determining the Pareto set and Pareto front in the initial observation point set by judging the dominance relationship; wherein, for The criterion for determining the Pareto set of a problem is: regarding the Pareto front... any point on There is definitely no better option. , making ,in, for Dimensions.

4. The multi-objective Bayesian optimization method according to claim 1, characterized in that, The calculation of the utility for each observation point includes the following steps: If the acquisition function is PHVI, then there is no need to perform scalarization; simply assign a 0-1 utility value to each point based on the Pareto set. If the acquisition function is EHVI, then scalarization is performed on the observations within the Pareto set; Among them, the observation point utility of PHVI The calculation equation is: EHVI observation point utility The calculation equation is: in, For the obtained Pareto set, It is a non-Pareto set; It represents the hypervolume constructed by a set of points and a reference point.

5. The multi-objective Bayesian optimization method according to claim 1, characterized in that, The process of training a classifier using utility as the weight of observation points includes the following steps: Use a classifier to fit the set of observation points; Depending on the acquisition function used, the posterior probability output by the classifier is used as an estimate of the density ratio based on the following loss function, thereby estimating the acquisition function; Loss function The expression is: in, For classifier parameters; and These represent the conditional probability density of x with respect to y for the two possible values ​​of y; This represents a utility function independent of x; This represents the proportion of positive samples; Represents a constant; XGBoost, Random Forest, and Multilayer Perceptron are used as classifiers. After training, the posterior probability obtained during training is used as the estimate of the acquisition function to evaluate candidate points.

6. The multi-objective Bayesian optimization method according to claim 1, characterized in that, The process of using the posterior probability provided by the classifier to optimize and determine the next observation point includes the following steps: Given a set of candidate solutions, the classifier outputs the acquisition function value, and the solution space is optimized to determine a point that maximizes the acquisition function. This is used as the next observation point for the black-box function; The evaluation of new observation points and their addition to the observation point set includes the following steps: Using black-box functions Evaluation of the best observation points obtained Add it to the observation point set, and expand the observation point set by acquiring the function for each new observation point.

7. The multi-objective Bayesian optimization method according to claim 1, characterized in that, In the process of classifying the set of observation points using dynamic thresholds, there is no need to scalarize each observation point; it is only necessary to determine the dominance status of each observation point. During the training of the classifier using weighted cross-entropy loss, a scalar is first used to quantize the black-box function before performing density ratio estimation. The output yields the set of observations.

8. A multi-objective Bayesian optimization device, characterized in that, include: The first module is used to classify the set of observation points using a dynamic threshold during the multi-objective Bayesian optimization process. Points located at the Pareto front are considered positive samples, and the remaining points are considered negative samples, so that the positive class completely covers the Pareto set. The second module extends the density ratio estimation to multi-objective Bayesian optimization by training a classifier using weighted cross-entropy loss, making the density ratio estimation method applicable to any utility acquisition function. The third module is used to complete the multi-objective Bayesian optimization process and output the Pareto set. The multi-object Bayesian optimization process was applied to multi-object recognition in image processing tasks to obtain multi-object recognition results. The process of classifying the set of observation points using a dynamic threshold in the multi-objective Bayesian optimization includes the following steps: Sample n initial observation points in the solution space to generate an initial observation point set; Obtain the Pareto set of each observation point in the initial set of observation points; Calculate the utility at each observation point; Each observation point is assigned a category label based on whether it is within the Pareto set. In this step of assigning category labels to each observation point, there is no need to sort the utility values. The observation point set is classified, with observation points having non-zero utility values ​​classified as positive and observation points having zero utility values ​​classified as negative. Extending density ratio estimation to multi-objective Bayesian optimization, and training a classifier using weighted cross-entropy loss, includes the following steps: The classifier is trained using utility as the weight of the observation points. The posterior probability provided by the classifier is used to optimize and determine the next observation point; Evaluate new observation points and add them to the observation point set.

9. An electronic device, characterized in that, Including the processor and memory; The memory is used to store programs; The processor executes the program to implement the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The storage medium stores a program that is executed by a processor to implement the method as described in any one of claims 1 to 7.

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