Listed company risk assessment method based on cross validation and Bayesian optimization

Abstract

The invention discloses a listed company risk assessment method based on cross validation and Bayesian optimization, and the method comprises the following steps: 1, obtaining the comprehensive factor data of a listed company, carrying out the dimension reduction of the factor data through employing a principal component analysis method, obtaining a principal component factor, carrying out the effectiveness verification of the principal component factor through an IC and IR analysis method, and carrying out the calculation of the risk of the listed company; selecting a plurality of principal component factors as input features; 2, on the basis of the multi-factor model, constructing an ensemble learning index enhancement model by taking a decision tree and an AdaBoost algorithm as cores; 3, performing system optimization on parameters of the ensemble learning index enhancement model by adopting cross validation and a Bayesian method, and finally determining an optimal parameter combination to obtain a trained ensemble learning index enhancement model; and 4, evaluating the risk of the listed company by using the trained integrated learning index enhancement model. According to the method, the calculation resource consumption of the model can be reduced, the calculation efficiency is improved, and the over-fitting risk of the model can be reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of prospect evaluation of listed companies, and in particular to a risk evaluation method for listed companies based on cross-validation and Bayesian optimization. Background Art

[0002] Risk assessment of listed companies is the focus of the current trading market, and the data disclosed by listed companies is the basis of their risk assessment. The assessment model needs to extract reliable information from a large amount of data to judge the company's future performance and risks. At present, there is machine learning based on multi-factor models to conduct risk assessment of listed companies. These factor data usually include profitability factors, valuation factors, growth factors, scale factors, technical factors, and market sentiment factors. The complexity and heterogeneity of these data make model tuning critical. At the same time, the model is prone to overfitting during the training process, that is, the model performs well on the training data, but performs poorly in actual applications. At the same time, training and running complex machine learning models requires a lot of computing resources and time. For large-scale data sets, the computing cost and time cost may be very high. Summary of the invention

[0003] The purpose of the present invention is to provide a risk assessment method for listed companies based on cross-validation and Bayesian optimization. The present invention can reduce the computing resource consumption of the model, improve computing efficiency, and reduce the overfitting risk of the model.

[0004] The technical solution of the present invention is a risk assessment method for listed companies based on cross-validation and Bayesian optimization, comprising the following steps:

[0005] Step 1: Obtain comprehensive factor data of listed companies, use principal component analysis to reduce the dimension of factor data to obtain principal component factors, and then perform IC and IR analysis to verify the effectiveness of the principal component factors, and then select multiple principal component factors as input features;

[0006] Step 2: Based on the multi-factor model, an integrated learning exponential enhancement model is constructed with decision tree and AdaBoost algorithm as the core;

[0007] Step 3: Use cross-validation and Bayesian methods to systematically optimize the parameters of the ensemble learning exponential enhancement model, and finally determine the optimal parameter combination to obtain the trained ensemble learning exponential enhancement model;

[0008] Step 4: Use the trained ensemble learning exponential enhancement model to assess the risks of listed companies.

[0009] In the above-mentioned risk assessment method for listed companies based on cross-validation and Bayesian optimization, in step 2, a multi-factor model is first established, and then based on the underlying logic of the Stacking ensemble learning framework, a decision tree algorithm is used as a base learner in the first layer, and an AdaBoost algorithm is used in the second layer to reduce the degree of overfitting of the decision tree algorithm, so as to construct an optimized ensemble learning exponential enhancement model.

[0010] In the aforementioned risk assessment method for listed companies based on cross-validation and Bayesian optimization, in step 1, the factor data includes profitability factors, valuation factors, growth capacity factors, scale factors, technical factors and sentiment factors.

[0011] In the aforementioned risk assessment method for listed companies based on cross-validation and Bayesian optimization, in step 1, after obtaining comprehensive factor data of listed companies, outliers, extreme values ​​and sample data with missing values ​​greater than 30% in the factor data are eliminated, and then the missing values ​​are filled in by using the data of the next trading day to fill the data of the previous trading day in a forward traversal manner. Finally, the factor data is standardized to ensure the accuracy and consistency of the data.

[0012] In the aforementioned risk assessment method for listed companies based on cross-validation and Bayesian optimization, in step 1, the calculation formula of the IC analysis method is as follows:

[0013] IC=corr(factor t , r t+1 );

[0014] Where: factor t represents the specific factor value of the current period t, r t+1 represents the next period rate of return; corr represents the Pearson correlation coefficient.

[0015] In the aforementioned risk assessment method for listed companies based on cross-validation and Bayesian optimization, in step 1, the calculation formula of the IR analysis method is as follows:

[0016]

[0017] Where: mean represents the multi-period mean of the IC value, and std represents the multi-period standard deviation of the IC value.

[0018] In the aforementioned risk assessment method for listed companies based on cross-validation and Bayesian optimization, in step 3, the process of systematically optimizing the parameters of the ensemble learning exponential enhancement model using cross-validation and Bayesian methods is as follows:

[0019] Step 3.1, select the K-fold cross-validation method, divide the data set into K subsets, cyclically use K-1 subsets for training, and the remaining subsets for validation;

[0020] Step 3.2: Select the parameter range, define the hyperparameter space, determine the parameters of the ensemble learning exponential enhancement model that need to be tuned and the candidate value range of the parameters;

[0021] Step 3.3: Initialize the Bayesian optimizer. Use the Bayesian optimization library to initialize the optimizer and provide the objective function and parameter space.

[0022] Step 3.4: Use the Bayesian optimizer to iteratively search in the parameter space to maximize or minimize the score of the objective function.

[0023] Step 3.5: In each iteration, the Bayesian optimizer selects the next parameter combination for evaluation based on the current proxy model and updates the proxy model.

[0024] Step 3.6: After the optimization is completed, record the optimal parameter combination.

[0025] Compared with the prior art, the present invention has the following beneficial effects:

[0026] (1) The Bayesian optimization adopted by the present invention can find a near-optimal parameter combination with fewer evaluation times and reduce computing resource consumption by using a proxy model to approximate the objective function. At the same time, compared with random search or grid search, Bayesian optimization can converge to the optimal parameters faster, improve the efficiency of parameter tuning, can be applied to high-dimensional and complex parameter spaces, can effectively handle the tuning tasks of multiple parameters, can capture the complex nonlinear relationship between parameters and model performance, and improve the optimization effect. Furthermore, by using cross-validation to evaluate model performance, each parameter combination can be evaluated more reliably, reducing the risk of overfitting and making parameter selection more robust.

[0027] (2) The present invention enables the decision tree and AdaBoost algorithms to be trained in parallel, thereby improving computational efficiency and reducing computational costs. The stacking method of the present invention can combine the prediction results of multiple base learners in parallel, further improving computational efficiency. Furthermore, the stacking method further reduces factor redundancy and improves the robustness of the model by using the output of the first-layer base learner as the input of the second-layer meta-learner, and the multi-model integration can disperse the risk of a single model being overly dependent on related factors, improve the generalization ability of the model, and make it more stable in different market environments.

[0028] (3) The present invention can flexibly adapt to different data features and has stronger adaptability. The decision tree and AdaBoost of the present invention have strong adaptability and can automatically adjust to adapt to different data features, further enhancing the flexibility and adaptability of the ensemble learning exponential boosting model.

[0029] (4) The present invention combines multiple basic learners to simplify the design and tuning of a single model. The stacking method can combine the outputs of multiple basic learners through a simple meta-learner, and by integrating the advantages of different models, the overall complexity of the model can be reduced.

[0030] (5) The decision tree of the present invention has a built-in feature selection mechanism, which automatically selects the most important features during the construction process, simplifies the model structure, and reduces the impact of irrelevant or redundant factors. Through iterative training, AdaBoost adjusts the weights of weak classifiers to make the model pay more attention to important factors, thereby reducing the complexity of the model. DETAILED DESCRIPTION

[0031] The present invention will be further described below in conjunction with the embodiments, but they are not intended to limit the present invention.

[0032] Embodiment: A risk assessment method for listed companies based on cross-validation and Bayesian optimization, comprising the following steps:

[0033] Step 1: Obtain comprehensive factor data of listed companies, use principal component analysis to reduce the dimension of factor data to obtain principal component factors, and then perform IC and IR analysis to verify the effectiveness of the principal component factors, and then select multiple principal component factors as input features;

[0034] In this step, network data sources or professional data providers are used to obtain historical transaction data and basic factor data of listed companies, including company finances, industry indicators and macroeconomic data. Among them, the industry factors can be analyzed from the product perspective to determine whether the company's products are productive resources or consumer resources. By analyzing the demand pattern, the proportion of domestic and foreign sales of the company's products can be understood. Through production pattern analysis, it can be determined whether the company is labor-intensive, capital-intensive or knowledge-technology intensive, and weights can be assigned to each factor. Therefore, the data collected in the above way constructs a factor library, including profitability factors, valuation factors, growth capacity factors, scale factors, technical factors and emotional factors, so that the value of the company can be comprehensively evaluated.

[0035] After obtaining the factor data, we remove the outliers, extreme values ​​and sample data with missing values ​​greater than 30% in the factor data, and then fill the missing values ​​by using the data of the next trading day to fill the missing values ​​of the previous trading day in a forward traversal manner. Finally, we standardize the factor data to ensure the accuracy and consistency of the data.

[0036] Then use principal component analysis to reduce the dimension of the factor data to obtain the principal component factors. Principal component analysis (PCA) is a statistical method used for dimensionality reduction. It simplifies the complexity of data analysis by retaining the main features in the data and ignoring the secondary features, converting high-dimensional data into low-dimensional data. PCA finds the principal components in the data, which are linear combinations of the original data and can explain the variation of the data to the greatest extent. The detailed steps include: 1. Select the initial analysis variables; 2. Decide whether to use the covariance matrix or the correlation matrix based on the characteristics of the variables. 3. Calculate the eigenvalues ​​and eigenvectors of the covariance matrix or the correlation matrix. 4. Determine the number of principal components: Determine the number of principal components based on the size of the eigenvalues.

[0037] Suppose the data set of listed companies is X=[X1,X2,…,X n ],in is the i-th sample, containing m factor data. These factors include profitability factor, valuation factor, growth factor, scale factor, technical factor and market sentiment factor. The total data matrix can be expressed as:

[0038]

[0039] In order to make the magnitude of factor data consistent and avoid the uneven impact of scale differences between factors on the model, the data is first standardized. The standardized data matrix is ​​X', and its element calculation formula is:

[0040]

[0041] In the formula, μ j is the mean of factor j, σ j is the standard deviation of factor j. Standardization makes all factors have a mean of zero and a standard deviation of 1.

[0042] Calculate the covariance matrix Σ of the standardized data X , used to measure the linear relationship between factors. The calculation formula of the covariance matrix is:

[0043]

[0044] In the formula, X'∈R n×m is the normalized data matrix. X∈R n×m is the covariance matrix between factors, each element in the matrix ∑ ij represents the covariance between factor i and factor j:

[0045]

[0046] The covariance matrix reflects the interrelationships and dependencies between different factors. The higher the covariance, the stronger the relationship between the factors.

[0047] By the covariance matrix Σ X Perform eigenvalue decomposition:

[0048] Σ X =VΛV T ;

[0049] Where V is the eigenvector matrix and ΛΛ is the eigenvalue matrix. Select the first K eigenvectors with the largest eigenvalues ​​and construct the principal component factor set Z = [Z1, Z2, ..., Zk], where Validity test of the principal component factors (IC and IR analysis):

[0050]

[0051] After the above steps, three main components are obtained:

[0052] Principal component 1: It combines technical factors such as MACD (exponential moving average convergence divergence) and RSI (relative strength index), and mainly reflects price trends and volatility.

[0053] Principal component 2: It combines PE (price-earnings ratio) and ROA (return on total assets) to reflect the company's fundamental financial health.

[0054] Principal component 3: It combines MFI (money flow index) and VR (volume ratio) to reflect market sentiment and capital flow.

[0055] Step 2: Based on the multi-factor model, an integrated learning exponential enhancement model is constructed with decision tree and AdaBoost algorithm as the core; in this step, based on the factors and principal components selected in step 1, on the basis of establishing the multi-factor model, based on the underlying logic of the Stacking integrated learning framework, the decision tree algorithm is used as the base learner in the first layer, giving full play to the excellent learning and feature selection capabilities of the decision tree algorithm, and the AdaBoost algorithm with lower complexity and which can significantly improve the model performance is used in the second layer to reduce the overfitting degree of the decision tree algorithm, so as to construct an optimized integrated learning exponential enhancement model (called BoostedStack Tree model).

[0056] By performing IC (information coefficient) and IR (information ratio) analysis on these principal components, the contribution of each principal component to the model prediction results was evaluated. Finally, principal components 1 and 2, which are most helpful for risk assessment, were selected as input features to form a new feature set for training the first-layer base learner.

[0057] The model is constructed using an integrated learning method. In the first layer, a decision tree is used as the base learner hi , in the second layer, the AdaBoost algorithm is used to integrate the base learners to reduce the risk of overfitting.

[0058]

[0059] Among them, α i The weight of each base learner is calculated by the AdaBoost algorithm, and the weight is adjusted iteratively to optimize the overall model for the training error. After calculation, we get the following parameters:

[0060] Maximum depth of decision tree: 5;

[0061] Minimum number of sample splits: 10;

[0062] Learning rate: 0.1;

[0063] Iterations: 50

[0064] The first layer base learner output:

[0065] h1(x): Based on these factors, decision tree 1 predicts a risk score of 0.72.

[0066] h2(x): The risk score predicted by decision tree 2 is 0.75.

[0067] h3(x): The risk score predicted by decision tree 3 is 0.68.

[0068] …

[0069] h 50 (x): The risk score predicted by the 50th decision tree is 0.70.

[0070] For company A, the feature vector input to the second-layer model is: [0.72, 0.75, 0.68, …, 0.70]. Furthermore, ensemble learning uses the Stacking framework to enhance the model. In the second layer, the AdaBoost algorithm can be used to fit these prediction results:

[0071]

[0072] Where g is a meta-learner, usually a linear regression or a lightweight classifier.

[0073] AdaBoost builds a strong learner by combining multiple weak learners (here decision trees) to improve model performance and reduce overfitting. The update rule of AdaBoost is expressed as:

[0074]

[0075] In the formula, αt is the weight of the t-th weak learner, ε t The error rate of the tth weak learner.

[0076] The final BoostedStack Tree model is a weighted combination of the first layer learners:

[0077]

[0078] T is the number of weak learners, f t (x) is the prediction of the tth weak learner.

[0079] After multiple iterations of adjusting the weights, the final combined prediction value may be 0.73, which is very close to the true risk score of 0.74.

[0080] Step 3: Use cross-validation and Bayesian methods to systematically optimize the parameters of the ensemble learning exponential enhancement model, and finally determine the optimal parameter combination to obtain the trained ensemble learning exponential enhancement model; in this step, the system optimization process is as follows:

[0081] Step 3.1, select the cross-validation method (K-fold cross-validation), divide the data set into K (such as K = 5 or 10) subsets, cyclically use K-1 subsets for training, and the remaining subsets for validation;

[0082] Step 3.2: Select the parameter range, define the hyperparameter space, determine the BoostedStack Tree parameters that need to be tuned, and their candidate value ranges.

[0083] Step 3.3: Initialize the Bayesian optimizer. Use the Bayesian optimization library to initialize the optimizer and provide the objective function and parameter space.

[0084] Step 3.4: Use the Bayesian optimizer to iteratively search in the parameter space to maximize (or minimize) the score of the objective function.

[0085] Step 3.5. In each iteration, the Bayesian optimizer selects the next parameter combination for evaluation based on the current proxy model and updates the proxy model.

[0086] Step 3.6: After the optimization is completed, record the optimal parameter combination.

[0087] Specifically, K-fold cross validation is used to divide the data set D into K subsets D1, D2, …, D K For each subset D i , use K-1 subsets for training, use the remaining subsets for validation, and calculate the average loss function value L for each fold i .

[0088]

[0089] Where, L i is the loss function value on the i-th fold validation set, which can be the mean square error (MSE) or logarithmic loss (Log-Loss).

[0090] In order to find the optimal parameter combination of the model, define the objective function f(θ), where θ is the hyperparameter of the model (such as learning rate, maximum depth, etc.). The goal is to minimize the cross-validation loss L(θ):

[0091]

[0092] Using Bayesian optimization, by building a proxy model To approximate the objective function. The proxy model is usually a Gaussian process, and the proxy model is updated based on the data of each iteration:

[0093]

[0094] Where η is the learning rate and Δf(θ) is the update of the estimated value of the objective function.

[0095] In each iteration, the hyperparameter combination for the next evaluation is selected by maximizing the Expected Improvement (EI):

[0096]

[0097] In the formula, θ + is the current optimal parameter combination. By optimizing EI(θ), Bayesian optimization can intelligently select parameter combinations for evaluation, thereby effectively reducing the number of evaluations.

[0098] Initial model parameters:

[0099] Learning Rate: 0.1

[0100] Max Depth: 5

[0101] Number of Base Learners: 50

[0102] Regularization Parameter: 0.2

[0103] Initial model performance evaluation:

[0104] Cross validation results (K=5):

[0105] Mean Square Error (MSE): 0.18

[0106] Accuracy: 72.5%

[0107] Mean square error (MSE) on the validation set: The mean square error performance of the initial model on the validation set is not ideal, indicating that the model has certain deviations when processing unknown data, which may be caused by poor parameter selection.

[0108] After optimizing the model using cross-validation (K=5) combined with Bayesian optimization, we obtained the following results:

[0109] The optimal model parameter combination obtained after Bayesian optimization:

[0110] Learning Rate: 0.05 (lowering the learning rate makes the model update more stable);

[0111] Max Depth: 6 (increased tree depth to improve the model’s ability to learn complex data patterns)

[0112] Number of Base Learners: 150 (increasing the number of base learners will improve the stability of the ensemble learning model);

[0113] Regularization Parameter: 0.3 (moderately increase regularization to prevent overfitting);

[0114] Performance evaluation of the optimized model:

[0115] Cross validation results (K=5);

[0116] Mean square error (MSE): 0.12 (down from the initial 0.18 to 0.12);

[0117] Accuracy: 78.3% (increased from 72.5% to 78.3%)

[0118] Mean squared error (MSE) of the validation set:

[0119] Each fold mean square error L i

[0120] Fold 1: MSE = 0.13

[0121] Fold 2: MSE = 0.11

[0122] Fold 3: MSE = 0.12

[0123] Fold 4: MSE = 0.11

[0124] 5th fold: MSE = 0.13

[0125] Average Mean Square Error:

[0126]

[0127] Compared with MSE=0.18 before optimization, the average mean square error after optimization is significantly reduced, indicating that the error of the model is reduced and the prediction accuracy is improved.

[0128] It can be seen that the Bayesian optimization of the present invention can find a near-optimal parameter combination with fewer evaluation times by using a proxy model to approximate the objective function, reducing the consumption of computing resources. Compared with random search or grid search, Bayesian optimization can converge to the optimal parameters faster and improve the efficiency of parameter tuning. Combined with cross-validation to evaluate model performance, each parameter combination can be evaluated more reliably and the risk of overfitting can be reduced. Cross-validation provides model evaluation results on multiple subsets, making parameter selection more robust.

[0129] Step 4: Use the trained ensemble learning index enhancement model to evaluate the risks of listed companies. This evaluation method can output the corresponding company value. According to the company value, traders or investors can evaluate the subsequent development of the company, thereby reducing the investment risk of the trading market.

[0130] In the present invention, the decision tree has the ability to select the most important features. During the construction of the tree, the decision tree will automatically select the factors that can best distinguish the data, thereby reducing factor redundancy and reducing the negative impact of correlation on the model; by training weak classifiers through multiple iterations, AdaBoost will adjust the sample weights to further reduce the negative impact of related factors on the final model, so as to solve the problem that the factors used in the multi-factor model may have correlation problems, thereby avoiding redundant information in the model and minimizing the impact of noise on the model. The BoostedStack Tree model can continuously optimize model performance during the iteration process. For example, at iteration 0, the root mean square error (RMSE) of the model is 0.5973, and in subsequent iterations, although there are fluctuations, the model performance remains at a relatively low level, such as RMSE of 0.6105 at iteration 9 and RMSE of 0.6148 at iteration 10. This shows that the BoostedStack Tree model can effectively reduce the prediction error and improve the prediction accuracy of the model.

[0131] In the present invention, the decision tree algorithm is more suitable for multi-factor models than other algorithms, and the decision tree algorithm has better adaptability to irregular data distribution when dealing with nonlinear relationships. Investors can also intuitively understand the division rules and decision-making process of decision tree nodes.

[0132] Furthermore, AdaBoost can be combined with various basic classifiers, such as decision trees, linear classifiers, etc., to make it more flexible and adaptable to different types of data, and it can combine multiple weak classifiers into a strong classifier, thereby improving the performance of the overall model.

[0133] The present invention combines decision tree and AdaBoost algorithm, which has significant advantages, such as flexibility and interpretability: the decision tree algorithm presents the decision process in a tree structure, which is easy to understand and interpret. By combining the AdaBoost algorithm, the generalization ability and accuracy of the model can be further improved while maintaining the interpretability of the model. The decision tree can adapt to complex nonlinear relationships, while AdaBoost can adapt to different market conditions by adjusting the weights of weak classifiers. This enables the model to better adapt to the dynamic changes and complexity in the financial market.

[0134] In summary, the present invention can reduce the computing resource consumption of the model, improve computing efficiency, and reduce the risk of overfitting of the model.

Claims

1. A risk assessment method for listed companies based on cross-validation and Bayesian optimization, characterized by: The steps include: Step 1: Obtain comprehensive factor data of listed companies, use principal component analysis to reduce the dimension of factor data to obtain principal component factors, and then perform IC and IR analysis to verify the effectiveness of the principal component factors, and then select multiple principal component factors as input features; Step 2: Based on the multi-factor model, an integrated learning exponential enhancement model is constructed with decision tree and AdaBoost algorithm as the core; Step 3: Use cross-validation and Bayesian methods to systematically optimize the parameters of the ensemble learning exponential enhancement model, and finally determine the optimal parameter combination to obtain the trained ensemble learning exponential enhancement model; Step 4: Use the trained ensemble learning exponential enhancement model to assess the risks of listed companies.

2. The risk assessment method for listed companies based on cross-validation and Bayesian optimization according to claim 1 is characterized by: In step 2, a multi-factor model is first established. Then, based on the underlying logic of the Stacking ensemble learning framework, the decision tree algorithm is used as the base learner in the first layer, and the AdaBoost algorithm is used in the second layer to reduce the overfitting degree of the decision tree algorithm, so as to construct an optimized ensemble learning exponential enhancement model.

3. The risk assessment method for listed companies based on cross-validation and Bayesian optimization according to claim 1 is characterized in that: In step 1, the factor data includes profitability factor, valuation factor, growth factor, scale factor, technical factor and sentiment factor.

4. The risk assessment method for listed companies based on cross-validation and Bayesian optimization according to claim 1 is characterized by: In step 1, after obtaining comprehensive factor data of listed companies, outliers, extreme values ​​and sample data with missing values ​​greater than 30% in the factor data are eliminated, and then the missing values ​​are filled in by using the data of the next trading day to fill the data of the previous trading day in a forward traversal manner. Finally, the factor data is standardized to ensure the accuracy and consistency of the data.

5. The risk assessment method for listed companies based on cross-validation and Bayesian optimization according to claim 1 is characterized in that: In step 1, the calculation formula of the IC analysis method is as follows: IC=corr(factor t ,r t+1 ) Where: factor t represents the specific factor value of the current period t, r t+1 represents the next period rate of return; corr represents the Pearson correlation coefficient.

6. The risk assessment method for listed companies based on cross-validation and Bayesian optimization according to claim 1 is characterized by: In step 1, the calculation formula of the IR analysis method is as follows: Where: mean represents the multi-period mean of the IC value, and std represents the multi-period standard deviation of the IC value.

7. The risk assessment method for listed companies based on cross-validation and Bayesian optimization according to claim 1 is characterized by: In step 3, the process of systematically optimizing the parameters of the ensemble learning exponential boosting model using cross-validation and Bayesian methods is as follows: Step 3.1, select the K-fold cross-validation method, divide the data set into K subsets, cyclically use K-1 subsets for training, and the remaining subsets for validation; Step 3.2: Select the parameter range, define the hyperparameter space, determine the parameters of the ensemble learning exponential enhancement model that need to be tuned and the candidate value range of the parameters; Step 3.3: Initialize the Bayesian optimizer. Use the Bayesian optimization library to initialize the optimizer and provide the objective function and parameter space. Step 3.4: Use the Bayesian optimizer to iteratively search in the parameter space to maximize or minimize the score of the objective function. Step 3.5: In each iteration, the Bayesian optimizer selects the next parameter combination for evaluation based on the current proxy model and updates the proxy model. Step 3.6: After the optimization is completed, record the optimal parameter combination.

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