An online credit limit pricing method, device and electronic equipment

Abstract

This application relates to the field of financial technology, and particularly to an online credit limit pricing method, device, and electronic device. The method includes: collecting customer data, environmental data, and intervention data, encoding their features to generate feature vectors; inputting the feature vectors into a multi-objective causal inference model to predict the credit target after intervention, obtaining a prediction result; constructing a constrained integer programming problem based on business objectives, business constraints, and the prediction result, generating an integer programming function; substituting Lagrange multipliers into the integer programming function, integrating the constraints into the objective function, constructing an unconstrained Lagrange function, and obtaining the optimal value of the Lagrange multipliers through alternating iterations; combining the optimal value of the Lagrange multipliers and the prediction result, determining the optimal strategy index according to a preset sorting rule, and outputting the credit limit pricing result corresponding to the optimal strategy index. This method can achieve refined, real-time, and intelligent credit limit pricing under business constraints.

Description

Technical Field

[0001] This application relates to the field of financial technology, and in particular to an online pricing method, apparatus, and electronic device for credit limits. Background Technology

[0002] Driven by both consumption upgrades and inclusive financial policies, the consumer credit market has experienced explosive growth. The deep penetration of digital technology has further propelled the booming development of the consumer finance market, and internet finance companies have gradually transformed from simple lending intermediaries into data-driven financial service providers. As a crucial link between customer needs and corporate profits, the scientific and precise pricing of credit lines directly impacts a company's sustainable development capabilities and market competitiveness. It has evolved from simple interest rate setting into a multi-dimensional, dynamic, and refined decision-making process.

[0003] Currently, financial institutions generally tend to pre-set resource constraints and then find the most profitable credit limit pricing strategy within those constraints. However, in practice, credit limit pricing systems often treat business constraints as post-conditions rather than the core of decision-making, leading to a disconnect between pricing strategies and business objectives. Simultaneously, customers exhibit significant individual differences in their sensitivity to interest rates and credit limits, and existing systems struggle to accurately capture these differences, easily resulting in a one-size-fits-all pricing model. This approach fails to fully tap into the potential of high-value customers and may miss out on valuable clients due to excessively high pricing. Against this backdrop, achieving accurate credit limit pricing under business constraints requires not only the use of advanced technologies such as big data, machine learning, and causal inference to accurately profile customers, but also the ability to quickly solve large-scale integer programming problems with business constraints.

[0004] Currently, the main technical solutions in the industry fall into two categories: one is greedy allocation based on prediction model ranking, which analyzes multidimensional customer data through machine learning or causal inference models to obtain probability scores, and allocates resources according to the scores until the constraints are met. Its advantage lies in its simplicity and strong business interpretability. The other is offline solution based on constrained integer programming, which transforms pricing decisions into a 0-1 integer programming problem and seeks the global optimal solution through a professional solver or a lookup table after bucketing. However, both of these solutions have significant limitations: greedy allocation only focuses on maximizing the marginal benefit of a single user, ignoring the synergistic effect between users, and is prone to getting trapped in local optima, and it is difficult to dynamically adapt to multidimensional business constraints; integer programming is an NP-hard problem, and the computational complexity increases exponentially with the number of customers, making it unable to handle large-scale business requests of millions, and it is also difficult to predict the situation of new customers offline. Bucketing strategies also have problems such as high sensitivity to the partitioning method and difficulty in satisfying the strong assumption that customers within a bucket are homogeneous, and they cannot adapt to dynamic changes in customer behavior.

[0005] Therefore, how to accurately capture individual customer differences, efficiently respond to large-scale real-time requests, and dynamically adapt credit line pricing to market and customer behavior changes while meeting multidimensional business constraints is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] The purpose of this application is to provide at least one online pricing method, device, and electronic device for credit limits, which accurately characterizes customer needs through multi-dimensional feature fusion and causal inference modeling, and achieves global optimal decision-making with the help of efficient optimization algorithms, thereby realizing refined, real-time, and intelligent credit limit pricing under business constraints.

[0007] To address the aforementioned technical problems, at least one embodiment of this application provides an online pricing method for credit lines, comprising: Collect customer data, environmental data, and intervention data as raw data, and perform feature encoding on the raw data to generate feature vectors; The feature vector is input into a pre-trained multi-objective causal inference model to predict the credit target after intervention, and the prediction result is obtained. Obtain preset business objectives and business constraint values, and construct a constrained integer programming problem based on the business objectives, business constraint values, and prediction results, generating an integer programming function; the integer programming function includes: an objective function and constraint conditions; Initialize the Lagrange multipliers, substitute the Lagrange multipliers into the integer programming function, integrate the constraints into the objective function, construct an unconstrained Lagrange function, and obtain the optimal value of the Lagrange multipliers through alternating iterations. Combining the optimal value of the Lagrange multiplier and the prediction result, the optimal strategy index is determined according to the preset sorting rules, and the credit limit pricing result corresponding to the optimal strategy index is output.

[0008] In one embodiment, the step of substituting the Lagrange multipliers into the integer programming function, integrating the constraints into the objective function to construct an unconstrained Lagrange function, and obtaining the optimal value of the Lagrange multipliers through alternating iterations includes: Substitute the Lagrange multipliers into the integer programming function, and then incorporate the weighted calculation of the constraints and the Lagrange multipliers into the objective function to construct an unconstrained Lagrange function. Based on the predicted loan probability values ​​of customers under each intervention strategy, the optimal solution of the decision variables is obtained under the current Lagrange multipliers to obtain the customer decision set. Calculate the candidate values ​​of the Lagrange multipliers based on the customer decision set; Determine whether the preset termination condition is met; If not satisfied, the candidate value of the Lagrange multiplier is used as the new current Lagrange multiplier, and the process jumps to the step of solving for the optimal solution of the decision variable under the current Lagrange multiplier based on the loan probability value of the customer under each intervention strategy in the prediction result. If the conditions are met, the final candidate value of the Lagrange multiplier is taken as the optimal value of the Lagrange multiplier.

[0009] In one embodiment, calculating the candidate values ​​of the Lagrange multipliers based on the customer decision set includes: Based on the customer decision set, combined with the prediction results, the business constraint values, and the interest rate / quota parameters corresponding to each intervention strategy, the objective optimization function of the Lagrange multiplier is constructed. The objective optimization function is solved using the ternary search method to obtain candidate values ​​for the Lagrange multipliers.

[0010] In one embodiment, the online pricing method for credit lines further includes: Based on the latest historical loan disbursement data, calculate the current actual value of business constraints; Calculate the error between the business constraint value and the current actual value; Calculate the Lagrange multiplier adjustment based on the error value, and update the Lagrange multipliers based on the Lagrange multiplier adjustment. Before obtaining the optimal value of the Lagrange multiplier through alternating iteration, the method further includes replacing the current Lagrange multiplier with the updated Lagrange multiplier.

[0011] In one embodiment, calculating the Lagrange multiplier adjustment based on the error value includes: Calculate the proportional term, integral term, and differential term respectively; wherein, the proportional term is the product of a preset proportional coefficient and the error value, the integral term is the product of a preset integral coefficient and the historical cumulative error value, and the differential term is the product of a preset differential coefficient and the error change rate. The summation of the proportional term, the integral term, and the differential term is used as the adjustment amount of the Lagrange multiplier.

[0012] In one embodiment, the online pricing method for credit lines further includes: Obtain random, unbiased experimental data; the experimental data includes: the actual credit strategy tiers accepted by customers and the corresponding business results; Based on the pricing strategy decision results, the actual credit strategy tiers in the experimental data are grouped. Select the group whose pricing strategy decision result is consistent with the actual credit strategy level as the target group; The business results of each target group are aggregated and calculated to obtain the simulation evaluation results of the overall pricing strategy.

[0013] In one embodiment, feature encoding is performed on the original data to generate a feature vector, including: Based on the data type, the original data is divided into discrete feature data and numerical feature data; The discrete feature data is then densely vectorized to obtain a dense vector; The numerical feature data is normalized to obtain a normalized vector; The dense vector and the normalized vector are concatenated and merged according to a preset dimension to form the feature vector.

[0014] In one embodiment, the step of inputting the feature vector into a pre-trained multi-objective causal inference model for intervention-based credit target prediction includes: Extract the user feature vector, environment feature vector, and intervention feature vector from the feature vector; The user feature vector and the environment feature vector are concatenated and input into a self-attention network. The self-attention network is then invoked to estimate the credit prediction target based on the correlation between the features, resulting in an intervention-free baseline result. The user feature vector, the environment feature vector, and the intervention feature vector are concatenated and then input into the intervention perception attention network. The intervention perception attention network is then invoked to estimate the impact of the intervention on the credit prediction target, thus obtaining the intervention increment result. The baseline results without intervention and the incremental results with intervention are combined, and the combined result is used as the prediction result.

[0015] At least one embodiment of this application also provides an online pricing device for credit lines, comprising: The feature encoding module is used to collect customer data, environmental data, and intervention data as raw data, and to perform feature encoding on the raw data to generate feature vectors. The credit prediction module is used to input the feature vector into a pre-trained multi-objective causal inference model to predict the credit target after intervention, and obtain the prediction result. The function construction module is used to obtain preset business objectives and business constraint values, and construct a constrained integer programming problem based on the business objectives, the business constraint values, and the prediction results, generating an integer programming function; the integer programming function includes: an objective function and constraint conditions; The iterative solution module is used to initialize the Lagrange multipliers, substitute the Lagrange multipliers into the integer programming function, integrate the constraints into the objective function, construct an unconstrained Lagrange function, and obtain the optimal value of the Lagrange multipliers through alternating iterative solutions. The pricing generation module is used to combine the optimal value of the Lagrange multiplier and the prediction result, determine the optimal strategy index according to the preset sorting rules, and output the credit limit pricing result corresponding to the optimal strategy index.

[0016] At least one embodiment of this application also provides an electronic device, including: at least one processor; and a memory communicatively connected to said at least one processor; The memory stores instructions that can be executed by the at least one processor, which, when executed, enable the at least one processor to perform the online pricing method for the credit line.

[0017] The online credit pricing method provided in this application uses customer data, environmental data, and intervention data as its core collection points, comprehensively covering the individual, external, and strategic dimensions of credit pricing. Then, through attention-aware multi-intervention, multi-objective causal inference modeling, it accurately captures the complex interactive relationships between users, the environment, and intervention strategies, achieving unified and efficient prediction of multiple business objectives. Simultaneously, this method innovatively introduces Lagrange dual optimization and alternating iterative solving, transforming the constrained integer programming problem into an efficiently solvable dual problem, overcoming the bottleneck of solving discontinuous variables in large-scale scenarios and ensuring online real-time decision response. Finally, it integrates the optimal value of Lagrange multipliers with multi-dimensional prediction results, quantifying the comprehensive value of each intervention strategy through preset ranking rules. This ensures both personalized optimization for individual customers and alignment with global business objectives and constraint boundaries, avoiding a one-size-fits-all pricing approach.

[0018] This method, through integer programming modeling and Lagrange duality solution, coordinates the combination optimization of all customers and intervention strategies, which can fully explore the synergistic value among users, achieve a dual balance between maximizing business objectives and complying with business constraints, and significantly improve overall decision-making efficiency. Attached Figure Description

[0019] One or more embodiments are illustrated by way of example with reference to the accompanying drawings, and these illustrative descriptions do not constitute a limitation on the embodiments.

[0020] Figure 1 This is a flowchart illustrating an online pricing method for credit lines, as provided in one embodiment of this application. Figure 2 This is a schematic diagram of the module division of an online pricing device for credit limits provided in one embodiment of this application; Figure 3 This is a schematic diagram of the module division of an online pricing device for a credit limit provided in one embodiment of this application; Figure 4 This is a schematic diagram of the structure of an electronic device provided in one embodiment of this application. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the various embodiments of this application will be described in detail below with reference to the accompanying drawings. However, those skilled in the art will understand that many technical details have been provided in the various embodiments of this application to help readers better understand this application. However, the technical solutions claimed in this application can be implemented even without these technical details and various changes and modifications based on the following embodiments. The division of the various embodiments below is for the convenience of description and should not constitute any limitation on the specific implementation of this application. The various embodiments can be combined with and referenced by each other without contradiction.

[0022] The following is a detailed description of the implementation details of the online pricing method for credit limits in this embodiment. The following content is only for the convenience of understanding and is not necessary for implementing this solution.

[0023] Example 1: The specific process of the online pricing method for credit limits in this embodiment can be as follows: Figure 1 As shown, it includes: Step 101: Collect customer data, environmental data, and intervention data as raw data, and perform feature encoding on the raw data to generate feature vectors.

[0024] The data collected serves three categories of data for credit line pricing: customer data, environmental data, and intervention data.

[0025] Customer data refers to core data that can characterize a customer's creditworthiness, repayment ability, and behavioral preferences, including but not limited to: basic customer information (age, occupation, education, region), economic status (income level, debt-to-asset ratio, employment stability), credit history (overdue records, credit card usage rate, changes in credit limit), and behavioral characteristics (APP activity, application frequency, repayment channel preference), which are used to accurately depict individual customer profiles.

[0026] Environmental data refers to external macroeconomic and scenario data that affect customers' credit decisions and repayment ability, including but not limited to: industry prosperity index, regional economic indicators, application time (such as holidays, end of quarter), etc., used to capture the potential impact of the external environment on credit business.

[0027] Intervention data refers to pre-set credit strategy options that can be applied to customers. Specifically, it can be a combination of different credit limits and loan interest rates (such as a combination of 3 credit limits and 5 interest rates), which serves as the core basis for intervention actions in subsequent causal inferences.

[0028] This embodiment does not limit the data collection method. Relevant data can be retrieved from business systems, credit databases, and external environmental data platforms via preset data interfaces to ensure automated and real-time data collection. After data collection, further data verification can be performed to remove invalid records with missing data or abnormal formats, ensuring the integrity of the original data.

[0029] The verified raw data is feature-encoded to form standardized feature vectors with a unified structure and fixed dimensions, ensuring that subsequent models can directly read and process them. It should be noted that this embodiment does not limit the specific feature encoding method used. An appropriate encoding scheme can be flexibly selected based on the type and characteristics of the raw data, the input requirements of the subsequent model, and the needs of the business scenario. The key requirement is that the encoded feature vectors have a unified structure, fixed dimensions, and retain the core information of the original data. This adapts to the input requirements of the self-attention network and intervention perception attention network in the multi-objective causal inference model, providing standardized data support for subsequent credit target prediction.

[0030] To deepen understanding, a feature encoding method is introduced here, which can be implemented by following these steps: Step 11: Based on the data type, divide the original data into discrete feature data and numerical feature data.

[0031] Identify the type of each field in the original data one by one. Discrete feature data refers to non-numerical data with limited categories and no continuous quantitative meaning (such as customer gender, occupation, city level, application channel, intervention strategy level, etc.); numerical feature data refers to numerical data with continuous or quantifiable values ​​(such as customer income, age, debt-to-asset ratio, credit score, industry prosperity index, loan interest rate, etc.). According to the above criteria, all original data fields are classified into discrete feature datasets or numerical feature datasets respectively.

[0032] Step 12: Perform dense vector encoding on the discrete feature data to obtain a dense vector.

[0033] For each discrete feature field (e.g., occupation includes categories such as white-collar, blue-collar, and self-employed), a mapping relationship between categories and vectors is constructed; a unique low-dimensional dense vector is assigned to each category (e.g., the dimension is set to 16 or 32), where each element in the vector is a continuous real number, and the vectors corresponding to semantically similar categories are closer in distance (e.g., the vector similarity between white-collar and gold-collar workers is higher than that between white-collar workers and farmers); all fields in the discrete feature dataset are traversed, and each category is replaced with the corresponding dense vector, ultimately forming a set of dense vectors corresponding to the discrete features.

[0034] Step 13: Normalize the numerical feature data to obtain a normalized vector.

[0035] By employing standardization or normalization algorithms, numerical feature data are mapped to a uniform numerical range (such as [0,1] or [-1,1]), eliminating the influence of numerical features of different magnitudes on model training and forming a set of normalized vectors corresponding to the numerical features.

[0036] Step 14: Concatenate and merge the dense vector and the normalized vector according to the preset dimensions to obtain the feature vector.

[0037] The concatenation dimension rules (such as sorting by feature importance or field category order) ensure consistent concatenation logic; all discrete feature dense vectors corresponding to a single customer are sequentially concatenated into a comprehensive dense vector, and all numerical feature normalized vectors are sequentially concatenated into a comprehensive normalized vector; the two comprehensive vectors are then further concatenated to form a single feature vector containing full-dimensional information on customers, environment, and interventions (e.g., the comprehensive dense vector has 256 dimensions, the comprehensive normalized vector has 64 dimensions, and the concatenated feature vector has 320 dimensions); after concatenation, the vector dimensions are verified to be consistent with the preset values ​​to ensure no data loss or dimension errors.

[0038] This method categorizes data types for processing. Discrete features are processed through dense vector encoding to uncover semantic relationships, while numerical features are processed through normalization to eliminate magnitude interference, enabling accurate adaptation to different data types. It should be noted that this embodiment only uses the above feature encoding method as an example, but it is not limited to this. Other feature encoding methods can be referred to in this embodiment, and will not be elaborated further here.

[0039] Step 102: Input the feature vector into the pre-trained multi-objective causal inference model to predict the credit target after intervention, and obtain the prediction result.

[0040] The feature vectors with uniform structure and fixed dimensions generated in step 101 are input into the pre-trained multi-objective causal inference model. This model has been trained using historical data and has the ability to identify the inherent causal relationship between customer characteristics, environmental characteristics, and intervention strategies, making it suitable for the prediction needs of multiple interventions and multiple objectives in credit scenarios.

[0041] After receiving the feature vectors, the model calculates the multi-dimensional credit target results corresponding to each preset intervention strategy (different credit limits / interest rate tiers) after the intervention strategy is applied. Among them, the credit target covers the core dimensions required for business decision-making, including customer loan probability (whether they will accept the credit plan), default probability (whether they will default after acceptance), and loan amount (if accepted, the expected actual loan amount), etc.

[0042] The model outputs a set of structured prediction results, which is based on the core mapping relationship of intervention strategy, credit target, and predicted value. For example, intervention strategy A (credit limit of 30,000 + interest rate of 4.5%): loan probability 78%, default probability 2.1%, loan amount 28,000; intervention strategy B (credit limit of 60,000 + interest rate of 5.0%): loan probability 63%, default probability 3.5%, loan amount 57,000.

[0043] The prediction results need to cover all preset intervention strategies, ensuring that each potential credit pricing scheme has corresponding effect prediction data, so as to provide a complete basis for subsequent selection of the optimal strategy.

[0044] Step 103: Obtain the preset business objectives and business constraint values, and construct a constrained integer programming problem based on the business objectives, business constraint values, and prediction results, and generate an integer programming function.

[0045] Obtain the pre-set business objectives and business constraints from the business side. Business objectives refer to the core decision-making direction that credit pricing needs to achieve. These are quantifiable maximization goals, such as maximizing the number of loan customers, maximizing the net profit of credit business, and maximizing the effective loan amount, thus clarifying the core direction of decision-making. Business constraints refer to the boundary conditions that cannot be broken in business operations. These are specific numerical restrictions, such as the upper limit of the average loan interest rate (e.g., not exceeding 5.5%), the total default rate threshold (e.g., not exceeding 3%), and the maximum credit limit per customer (e.g., not exceeding 200,000), to limit the feasible scope of decision-making.

[0046] Taking the decision of whether to allocate a certain type of intervention strategy (a specific credit limit + interest rate combination) to a customer as the core decision object, we define 0-1 type integer decision variables (e.g., variable z_ij=1 indicates that the j-th intervention strategy is allocated to customer i, and z_ij=0 indicates that it is not allocated). Based on the prediction results output in step 102, we associate each decision variable (allocating a certain intervention strategy) with the corresponding prediction results (e.g., loan probability, default probability, loan amount). For example, when customer i is allocated the j-th intervention strategy, its loan probability is p_ij in the prediction results and its default probability is q_ij. This provides data support for the construction of the objective function and constraints, transforming the credit limit pricing decision into a constrained integer programming problem at the mathematical level, and generating an integer programming function.

[0047] Step 104: Initialize the Lagrange multipliers, substitute the Lagrange multipliers into the integer programming function, integrate the constraints into the objective function, construct an unconstrained Lagrange function, and obtain the optimal value of the Lagrange multipliers through alternating iteration.

[0048] Initial Lagrange multipliers (with values ​​≥ 0) are randomly generated according to preset rules. These multipliers are the key bridge connecting the objective function and the constraints, and their values ​​directly reflect the strength of the influence of the constraints on the objective function.

[0049] Substitute the initialized Lagrange multipliers into the integer programming function generated in step 103, and embed the constraints in the integer programming function (such as the upper limit of the average loan interest rate and the total default rate threshold) into the objective function (such as maximizing the number of loan customers and maximizing net profit). This eliminates the direct restriction of the constraints on the decision variables, forming an unconstrained Lagrange function that only contains decision variables and Lagrange multipliers. This transforms the originally complex constrained optimization problem into an easier-to-solve unconstrained optimization problem.

[0050] Then, by using an alternating iterative logic of finding the optimal solution for decision variables with fixed multipliers and finding the optimal solution for multipliers based on decision variables, the optimal value of the Lagrange multipliers that can balance business objectives and constraints can be efficiently obtained.

[0051] The integer programming problem constructed in step 103 has extremely high complexity when solved directly, especially when facing a customer scale of millions in a credit scenario, which is difficult to meet the needs of online real-time decision-making. This step uses Lagrange dual transformation to decompose it into subproblems that can be solved efficiently, avoiding the exponential complexity of directly solving integer programming and keeping the solution time within an acceptable range for online decision-making (such as milliseconds), thereby meeting the real-time pricing needs of a large number of customers in a credit scenario.

[0052] Furthermore, business objectives (such as maximizing profits) and constraints (such as controlling risk) often conflict. In this step, the Lagrange multipliers quantify the weight of the constraints on the objective. Through iterative solving, a function that maximizes the objective is found, ensuring that the transformed unconstrained function is equivalent to the original constrained problem. The alternating iterative process gradually approaches the optimal solution, ensuring that the final optimal value of the Lagrange multipliers accurately balances the business objective and constraints. Regardless of whether the business constraint is single-dimensional (such as only restricting the interest rate) or multi-dimensional (such as simultaneously restricting the interest rate and default rate), the function construction and iterative solution can be completed by expanding the dimensions of the Lagrange multipliers without refactoring the modeling logic. Therefore, this method can be adapted to the business needs of different credit products.

[0053] Step 105: Combining the optimal value of the Lagrange multiplier and the prediction results, determine the optimal strategy index according to the preset sorting rules, and output the credit limit pricing result corresponding to the optimal strategy index.

[0054] The optimal value of the Lagrange multiplier has balanced the global business objectives and constraints. By combining the optimal value of the Lagrange multiplier with the credit target prediction results corresponding to each intervention strategy, the contribution of the strategy to the business objectives and the fit of the constraints are quantified. This ensures that the optimal strategy for a single customer not only conforms to its individual characteristics but also fits the global business objectives and constraint boundaries, avoiding the impact of local optima on overall returns. The intervention strategy with the highest score is the optimal strategy for that customer, and its corresponding unique identifier (such as strategy number, tier index) is the optimal strategy index. Based on the optimal strategy index, the corresponding credit limit and loan interest rate are extracted to form a structured pricing result, such as customer ID: XXX, credit limit: 50,000 yuan, loan interest rate: 4.5%.

[0055] Based on the above introduction, the online credit limit pricing method provided in this embodiment takes customer data, environmental data, and intervention data as the core of collection, comprehensively covering the individual, external, and strategic dimensions of credit pricing. Then, through attention-aware multi-intervention, multi-objective causal inference modeling, it accurately captures the complex interaction relationship between users, environment, and intervention strategies, achieving unified and efficient prediction of multiple business objectives. At the same time, this method innovatively introduces Lagrange dual optimization and alternating iterative solution, transforming the constrained integer programming problem into an efficiently solvable dual problem, breaking through the bottleneck of solving non-continuous variables in large-scale scenarios, and ensuring online real-time decision response. Finally, it integrates the optimal value of Lagrange multipliers and multi-dimensional prediction results, and quantifies the comprehensive value of each intervention strategy through preset ranking rules, ensuring both personalized optimization for individual customers and conformity with global business objectives and constraint boundaries, avoiding one-size-fits-all pricing.

[0056] Unlike traditional greedy allocation strategies that rely on a first-come, first-served, locally optimal logic, this method uses integer programming modeling and Lagrange duality to optimize the combination of all customers and intervention strategies. This approach can fully tap into the collaborative value among users, achieving a dual balance between maximizing business objectives and complying with business constraints, thus significantly improving overall decision-making efficiency.

[0057] Example 2: In online credit pricing scenarios, efficiently solving constrained integer programming problems is a core bottleneck for achieving real-time decision-making. Lagrange duality can transform constrained problems into unconstrained functions. However, the specific execution logic of iterative solution is not limited in the above embodiments. The computational complexity can be reduced by simplifying the solution logic, and the consistency and reliability of the solution results can be ensured by standardizing the process. In order to overcome the timeliness bottleneck of traditional solution methods in large-scale scenarios and ensure that the optimal value of Lagrange multipliers can accurately balance business objectives and constraints, this embodiment proposes an alternating iterative step-by-step solution method, which can realize the rapid solution of non-continuous 0-1 decision variables and adapt to the needs of online real-time decision-making.

[0058] Specifically, step 104 involves substituting the Lagrange multipliers into the integer programming function, integrating the constraints into the objective function, constructing an unconstrained Lagrange function, and obtaining the optimal values ​​of the Lagrange multipliers through alternating iterations. This can be performed according to the following steps: Step 41: Substitute the Lagrange multipliers into the integer programming function, and then incorporate the weighted calculation of the constraints and Lagrange multipliers into the objective function to construct an unconstrained Lagrange function.

[0059] By leveraging the constraint transformation effect of Lagrange multipliers, business constraints such as the upper limit of per capita interest rate and the threshold of total default rate in the integer programming function are embedded into objective functions such as maximizing the number of loan customers and maximizing net profit through weighted fusion. This eliminates the direct restriction of the constraints on the decision variables, transforming the originally complex constrained optimization problem into an unconstrained optimization problem containing only decision variables and Lagrange multipliers, laying the foundation for subsequent step-by-step solution.

[0060] Step 42: Based on the loan probability values ​​of customers under each intervention strategy in the prediction results, solve for the optimal solution of the decision variables under the current Lagrange multipliers to obtain the customer decision set.

[0061] Among them, the decision variable is defined as a 0-1 variable (z_ij=1 indicates allocation, z_ij=0 indicates no allocation) for whether to allocate the j-th intervention strategy (specific amount + interest rate combination) to customer i. The loan probability value is the core predictive indicator output by the multi-objective causal inference model, which directly reflects the customer's expected response to the intervention strategy.

[0062] For each customer, the function contribution value corresponding to each intervention strategy is calculated by combining the loan probability value under all intervention strategies with the current Lagrange multiplier. The intervention strategy with the best contribution value is selected as the optimal choice for the customer. Finally, the optimal strategy choices of all customers are integrated to form a customer decision set containing the customer-optimal intervention strategy mapping relationship. This ensures that the solution of decision variables is highly consistent with the customer's actual credit response expectations, while also adapting to the business reality of 0-1 non-continuous variables.

[0063] Step 43: Calculate the candidate values ​​of the Lagrange multipliers based on the customer decision set.

[0064] The initial values ​​of the Lagrange multipliers are randomly generated and cannot accurately match the balance between business objectives and constraints. This step is based on the customer decision set obtained in step 42 (i.e., the optimal intervention strategy selection results for all customers), combined with the preset business constraint values ​​and the core parameters of each intervention strategy. By quantifying the degree of fit between the current decision set and business constraints, the intermediate value of the Lagrange multipliers that can more accurately balance business objectives and constraints is obtained. The calculation based on the business performance of the actual customer decision set allows the multipliers to be dynamically adjusted according to the decision effect, gradually approaching the optimal value.

[0065] Step 44: Determine whether the preset termination condition is met; if not, take the candidate value of the Lagrange multiplier as the new current Lagrange multiplier, and jump to the step of solving the optimal solution of the decision variable under the current Lagrange multiplier based on the loan probability value of the customer under each intervention strategy in the prediction results; if satisfied, take the finally obtained candidate value of the Lagrange multiplier as the optimal value of the Lagrange multiplier.

[0066] The specific type of the preset termination condition is not limited in this embodiment. For example, it can be set as follows: the number of iterations reaches a preset threshold (e.g., 10 rounds) to avoid excessive iteration consuming computing resources; the absolute difference between two consecutive candidate Lagrange multiplier values ​​is less than a set error range (e.g., 0.001), indicating that the multiplier has stabilized; the actual constraint satisfaction calculated based on the current customer decision set (e.g., the deviation between the actual per capita interest rate and the constraint value) is less than the business allowable error to ensure compliance with the constraint conditions. This embodiment only uses the above condition types as examples for introduction. The setting of other conditions can refer to the introduction of this embodiment and will not be repeated here.

[0067] If the termination condition is not met, it means that the current candidate value of the Lagrange multiplier has not accurately balanced the business objectives and constraints. The candidate value should be used as the new current Lagrange multiplier, and the process should jump to the step of solving the optimal solution of the decision variables under the current Lagrange multiplier based on the loan probability value of each customer intervention strategy in the prediction results. A new customer decision set should be generated, and then the new candidate value of the multiplier should be calculated to start the next round of iteration.

[0068] If the termination condition is met, it indicates that the current candidate value of the Lagrange multiplier has achieved the optimal balance between business objectives and constraints. At this point, the candidate value is determined as the final optimal value of the Lagrange multiplier and used for the calculation of the subsequent optimal credit limit pricing strategy, thus terminating the iteration process.

[0069] In this embodiment, the specific calculation method for step 43 is not limited. For example, the multiplier value can be directly adjusted by statistically analyzing the constraint satisfaction deviation of the customer decision set, or the correlation between the multiplier and the decision effect can be solved by constructing a linear regression model. To deepen understanding, a method for calculating the candidate value of the Lagrange multiplier is further introduced here. Through a combination of objective optimization function construction and efficient algorithm solution, the candidate value of the multiplier can be solved accurately and quickly, ensuring that it can effectively balance business objectives and constraints.

[0070] Specifically, step 43, which calculates the candidate values ​​of the Lagrange multipliers based on the customer decision set, can be performed as follows: Step 431: Based on the customer decision set, combined with the prediction results, business constraint values ​​and the interest rate / quota parameters corresponding to each intervention strategy, construct the objective optimization function of the Lagrange multiplier.

[0071] Based on the customer decision set as the core, this approach integrates forecast results, business constraints, and interest rate / credit line parameters for various intervention strategies. It establishes a mathematical function with Lagrange multipliers as the optimization object, clarifying the quantitative relationship between the multiplier value and the degree of achievement of business objectives plus the degree of constraint satisfaction. The deviations in achieving business objectives and satisfying constraints are transformed into mathematical expressions related to the Lagrange multipliers. For example, when the business objective is to maximize the number of loan customers and the constraint is that the average interest rate per customer ≤ R, the function quantifies the degree to which the expected number of loan customers deviates from the actual average interest rate per customer under the current multiplier, forming a single-objective optimization function with the Lagrange multiplier as the sole variable. This clarifies the impact of the multiplier value on the overall decision-making effect.

[0072] Step 432: Solve the objective optimization function using the ternary search method to obtain candidate values ​​for the Lagrange multipliers.

[0073] Based on the mathematical definition of Lagrange multipliers (non-negative), an initial search interval (such as [0,1]) is set, and the boundary is adjusted according to the characteristics of the business scenario (such as the strictness of the constraints) to ensure that the search range covers the potential optimal value.

[0074] Divide the initial search interval into three equal parts to obtain two intermediate nodes. Calculate the target optimization function value corresponding to the two nodes. Compare the function values ​​to narrow the search range. Keep the sub-interval with the better function value and discard the sub-interval without the optimal value. Repeat the above process of dividing into three parts, calculating, comparing and narrowing until the length of the search interval is less than the preset error threshold (e.g., 0.001).

[0075] When the search interval meets the error requirements, the node value with the best intermediate value or function value within the interval is taken as the candidate value of the Lagrange multiplier to ensure that the accuracy of the candidate value meets the business requirements.

[0076] The objective optimization function has a unimodal characteristic. The three-way search method can be used to quickly lock the optimal value through a logarithmic number of iterations, avoiding the efficiency loss caused by blind search.

[0077] Based on the above introduction, this embodiment solves the decision variables based on the loan probability value of the customer intervention strategy, so that the decision set is highly consistent with the actual credit response expectation. Then, by integrating the core business parameters to construct the objective optimization function, and combining the three-way search method to efficiently search for the optimal solution, it not only adapts to the business characteristics of 0-1 non-continuous decision variables, but also controls the computational complexity within the acceptable range of online real-time decision-making. It breaks through the bottleneck of low efficiency of traditional integer programming in solving large-scale scenarios, and provides stable and efficient core parameter support for the global optimal decision of subsequent credit quota pricing.

[0078] Example 3: In online credit pricing scenarios, market conditions (such as economic cycle fluctuations and interest rate policy adjustments) and customer behavioral preferences are constantly changing. Traditional Lagrange multiplier solutions rely solely on iterative optimization using historical data, making it difficult to respond quickly to real-time environmental changes. This can easily lead to a disconnect between the optimal multiplier value and the actual needs of the current business, thus affecting the adaptability and effectiveness of the pricing strategy. To achieve dynamic adaptive adjustment of the multiplier parameters, this embodiment further proposes a real-time data feedback mechanism. Based on the latest historical loan disbursement data, it calibrates the actual execution of business constraints. Through error calculation and multiplier adjustment, it ensures that the Lagrange multiplier always aligns with the current business scenario, avoiding decision-making biases caused by static parameters in a dynamic environment.

[0079] Specifically, in addition to the steps mentioned above, the following steps may be performed: Step 106: Based on the latest historical loan disbursement data, calculate the current actual value of business constraints.

[0080] Determine the statistical dimensions corresponding to the business constraints. For example, the average loan interest rate per person should be calculated as total interest income / total number of loan customers, and the total default rate should be calculated as the number of defaulting customers / total number of loan customers. Then, filter the latest historical loan disbursement data from the real business data of recently completed loans, and remove invalid or abnormal records (such as loan cancellations or records with missing data). Finally, summarize and calculate the valid data according to the statistical dimensions to obtain the current actual value corresponding to each business constraint, such as the actual value of the average loan interest rate per person being 4.9% and the actual value of the total default rate being 2.8%.

[0081] Step 107: Calculate the error between the business constraint value and the current actual value.

[0082] The preset business constraint values ​​(such as the upper limit of the average loan interest rate of 5.5% and the total default rate threshold of 3%) are quantitatively compared with the current actual values ​​obtained in step 106. The error value is calculated by using the calculation logic of error value = business constraint value - current actual value to calculate the degree of deviation between the two and obtain the error value, thereby clarifying the gap between the current business operation status and the preset target.

[0083] Step 108: Calculate the Lagrange multiplier adjustment based on the error value, and update the Lagrange multipliers based on the Lagrange multiplier adjustment.

[0084] Using the error value obtained in step 107 as the core input, combined with the preset adjustment coefficient, the adjustment range (adjustment amount) of the Lagrange multiplier is solved through the proportional-integral-derivative (PID) calculation logic. Then, the adjustment amount is superimposed with the current Lagrange multiplier to obtain the updated Lagrange multiplier, thereby realizing the dynamic adaptive correction of the parameters.

[0085] By dynamically correcting the Lagrange multiplier through error feedback, the multiplier can be adapted to the current business operation status. If the actual value exceeds the constraint (the error value is negative), the multiplier is increased to strengthen the influence of the constraint on the objective function; if the constraint satisfies redundancy (the error value is positive), the multiplier is appropriately reduced to focus on maximizing the business objective, ensuring that the multiplier always fits the actual business needs.

[0086] Before obtaining the optimal value of the Lagrange multipliers through alternating iterations, the process includes replacing the current Lagrange multipliers with the updated ones. Before entering the alternating iteration process in step 104, the initial or previous multipliers are replaced with the Lagrange multipliers updated in step 108. The updated multipliers are used as the starting parameters for alternating iterations to ensure that the starting point of the iteration solution aligns with the current business reality, making the starting point of the iteration solution closer to the current optimal solution range, shortening the iteration convergence time, and ensuring that the final optimal value of the multipliers can balance real-time business constraints and objectives, avoiding decision-making biases of static parameters in dynamic environments.

[0087] It should be noted that this embodiment does not limit the specific calculation method of the adjustment coefficient in step 108. For example, a fixed coefficient can be set directly based on business scenario experience, or a machine learning model can be trained using historical error data to fit the optimal coefficient. In order to achieve a precise match between the adjustment coefficient and the error characteristics, improve the stability of the Lagrange multiplier adjustment, and avoid adjustment lag or excessive fluctuation caused by setting a single coefficient, a method for calculating the adjustment coefficient that integrates proportional, integral, and differential characteristics is proposed. By separating the immediate impact of the error, the historical cumulative effect, and the trend of change, the scientific quantification of the multiplier adjustment can be achieved, ensuring that parameter updates can respond to real-time business deviations and resist the impact of environmental fluctuations.

[0088] Specifically, the calculation of the Lagrange multiplier adjustment based on the error value in step 108 can be performed according to the following steps: Step 81: Calculate the proportional term, integral term, and differential term respectively.

[0089] Based on the different dimensions of the error's impact, three types of components are calculated to quantify the error's immediate response, historical cumulative effect, and future trend.

[0090] Specifically, a preset proportional coefficient (calibrated based on historical data, reflecting the strength of the response to the current error) is extracted and directly multiplied by the error value obtained in step 107. The formula is: Proportional term = Preset proportional coefficient × Error value. For example, when the error value is 0.3% and the proportional coefficient is 0.2, the proportional term = 0.2 × 0.3% = 0.06%, directly quantifying the immediate impact of the current deviation on the multiplier adjustment. A preset integral coefficient (reflecting the strength of the correction to historical accumulated errors) is extracted and multiplied by the historical accumulated error value within a specified period (such as the sum of all error values ​​in the last 7 days). The formula is: Integral term = Preset integral coefficient × Historical accumulated error value. For example, when the historical accumulated error value is 1.2% and the integral coefficient is 0.1, the integral term = 0.1 × 1.2% = 0.12%, used to offset long-term accumulated systematic deviations. Extract the preset differential coefficient (reflecting the strength of the prediction of the error change trend), and multiply it by the error change rate (the difference between the current error and the error of the previous period divided by the time interval). The formula is: differential term = preset differential coefficient × error change rate. For example, when the current error increases by 0.1% compared with the previous period, the time interval is 1 day, and the differential coefficient is 0.15, the differential term = 0.15 × (0.1% / 1) = 0.015%, which predicts the future direction of error change and adjusts it in advance.

[0091] By using three types of components to cover current deviation, historical accumulation, and future trend respectively, the limitations of a single coefficient in responding only to immediate errors can be overcome, ensuring comprehensive capture of the impact of errors.

[0092] Step 82: Sum the proportional term, integral term, and differential term to obtain the Lagrange multiplier adjustment.

[0093] The proportional, integral, and differential terms calculated in step 81 are summed. For example, when the proportional term is 0.06%, the integral term is 0.12%, and the differential term is 0.015%, the adjustment amount is 0.06% + 0.12% + 0.015% = 0.195%. By integrating the effects of multi-dimensional errors, the final adjustment magnitude of the Lagrange multiplier is obtained.

[0094] This embodiment uses the above adjustment calculation method as an example, but it is not limited to this. Other calculation methods can be referred to the description in this embodiment, and will not be repeated here.

[0095] Based on the above introduction, this embodiment breaks the traditional static parameter dependence by statistically analyzing the current actual value of business constraints based on the latest historical loan disbursement data, making error calculation closely follow the real-time business status. On the other hand, this embodiment proposes a multi-dimensional calculation logic of proportional-integral-differential. The proportional term quickly responds to the current error, the integral term offsets the historical accumulated deviation, and the differential term predicts the error change trend. The three work together to make the adjustment of the Lagrange multiplier take into account immediacy, stability and foresight, avoiding excessive fluctuations or lags caused by single-dimensional adjustment, shortening the solution convergence time, improving the efficiency of online decision-making, and ensuring that the final optimal value of the multiplier can accurately balance the real-time business objectives and constraints, further strengthening the global optimality and robustness of credit pricing decisions.

[0096] Example 4: In online credit line pricing scenarios, traditional evaluation methods neglect the correlation between model prediction accuracy and the effectiveness of decision-making strategies, easily leading to excellent model metrics but actual business returns falling short of expectations. To achieve accurate pre-validation of pricing strategy effectiveness, this embodiment further proposes a simulation evaluation method based on random unbiased experimental data. By matching the consistency grouping of decision results with actual business scenarios, the true effect of the overall pricing strategy is quantified, providing an objective basis for strategy optimization and model iteration, and avoiding business risks caused by blind deployment.

[0097] Specifically, in addition to the steps mentioned above, the following steps may be performed further: Step 109: Obtain random unbiased experimental data.

[0098] Extract unbiased business data obtained through methods such as randomized controlled trials (RCTs). The data must include the credit strategy tiers actually accepted by customers (such as the specific tiers of a certain credit limit + interest rate combination), as well as the actual business results generated after the strategy is implemented (such as whether a loan is granted, whether there is a default, the loan amount, etc.). Filter valid data that meets the random allocation strategy to ensure that the credit strategy tiers accepted by customers are randomly allocated and to avoid selection bias.

[0099] Step 110: Based on the pricing strategy decision results, group the actual credit strategy tiers in the experimental data.

[0100] Identify all the strategy tiers (e.g., tier 1 to tier m) included in the pricing strategy decision results and use them as group labels; then iterate through each customer in the experimental data and classify them into the corresponding group according to the credit strategy tier they actually accept, such as classifying customers who actually accept tier 2 into group 2.

[0101] After grouping, the validity of each group's data can be verified to ensure that each group contains a sufficient sample size, avoiding evaluation bias caused by insufficient samples. Of course, this verification step can also be omitted, and this embodiment does not limit this.

[0102] Step 111: Select the group whose pricing strategy decision results are consistent with the actual credit strategy level as the target group.

[0103] Iterate through each group and compare the actual strategy tier corresponding to the group with the optimal strategy tier recommended for that group in the pricing strategy decision results. If the two are completely consistent (e.g., the actual tier 3 corresponding to group 3 matches the recommended optimal tier 3), then the group is determined as the target group. If there are multiple matching groups, they can all be included in the target group set to ensure that the evaluation object is only the customer group whose pricing strategy has actually been implemented, avoid misjudgment of the effect due to the strategy not being actually implemented, and improve the accuracy of the evaluation results.

[0104] Step 112: Aggregate and calculate the business results of each target group to obtain the simulation evaluation results of the overall pricing strategy.

[0105] First, identify the core evaluation metrics for business results (such as loan conversion rate, average loan amount, default rate, net profit, etc.). Then, for each target group, calculate the average of each evaluation metric for all customers within that group (e.g., loan conversion rate for target group 1 = number of loan customers in the group / total number of customers in the group). Finally, weight and aggregate the average metrics for all target groups (weighted by the sample size ratio of each group) to obtain the simulation evaluation metrics for the overall pricing strategy (such as overall loan conversion rate, average net profit, etc.), forming a complete evaluation results report. This transforms the dispersed business results of the target groups into globally unified evaluation metrics, quantifying the overall effectiveness of the pricing strategy.

[0106] The simulation evaluation method provided in this embodiment relies on random, unbiased experimental data for evaluation. This avoids the selection bias and confounding factors of traditional observational data, ensuring that the evaluation results accurately reflect the actual implementation effect of the pricing strategy. Simultaneously, it precisely matches the pricing strategy decision results with the credit tiers actually accepted by customers, achieving end-to-end effect verification from multi-objective causal prediction to online decision output, rather than just evaluating the performance of a single model component. This method is adaptable to multi-intervention and multi-business objective scenarios, eliminating the need to reconstruct the evaluation framework due to adjustments in strategy tiers or changes in business objectives. Furthermore, it allows for flexible adjustment of business constraints to generate multi-dimensional effect curves, providing comprehensive data support for strategy optimization. The evaluation process is computationally efficient and the results are highly interpretable, enabling pre-emptive verification of the global effectiveness of the pricing strategy and reducing the business risks associated with blind deployment.

[0107] Example 5: Traditional multi-objective causal inference models often directly integrate user, environment, and intervention features for overall prediction, making it difficult to accurately separate the basic business performance without intervention from the incremental impact of intervention. This can easily lead to distorted descriptions of intervention effects and fail to fully explore the complex interaction relationships between features. To achieve refined modeling of intervention effects and basic performance, this embodiment proposes a prediction method that uses a hierarchical attention network architecture to capture the inherent relationship between users and the environment, as well as the interactive relationship between users, the environment, and intervention. This accurately separates the basic results without intervention from the incremental results of intervention, making the prediction results more consistent with the actual business logic and providing a more reliable quantitative basis for subsequent pricing decisions.

[0108] Specifically, step 102, which involves inputting the feature vector into a pre-trained multi-objective causal inference model for post-intervention credit target prediction, can be performed as follows: Step 21: Extract the user feature vector, environment feature vector, and intervention feature vector from the feature vector.

[0109] From the feature vector, three core vectors are separated according to data attributes to separate the feature information related to users, environment and intervention, and user feature vector, environment feature vector and intervention feature vector are extracted.

[0110] User feature vectors encompass customer basic information (age, occupation, education), economic status (income, debt-to-equity ratio), and credit history (overdue records, credit card usage rate)—features strongly correlated with the customer themselves. Environmental feature vectors include external scenario features such as industry prosperity index, regional economic indicators, and application time. Intervention feature vectors focus on features related to the customer's available credit strategy tiers (e.g., different credit limits and interest rate combinations). Decomposing the mixed features according to the subject-scenario-strategy logic allows the subsequent network model to specifically learn the relationships between features across different dimensions. This avoids insufficient interaction information mining caused by feature mixing and provides a prerequisite for accurately separating basic results from intervention incremental results.

[0111] Step 22: The user feature vector and the environment feature vector are concatenated and input into the self-attention network. The self-attention network is then invoked to estimate the credit prediction target based on the correlation between the features, thus obtaining the basic result without intervention.

[0112] User feature vectors and environment feature vectors are concatenated in dimensional order to form a comprehensive user + environment feature vector. This vector is then input into a pre-trained self-attention network. The network captures hidden correlations (such as the loan caution of high-income customers in an economic downturn) by calculating the attention weights between features. At the same time, independent output branches are constructed according to credit prediction objectives (loan probability, default probability, loan amount, etc.). By removing interference from intervention factors and relying solely on the customer's own attributes and the external environment, the natural performance expectation of the business objective is obtained. Each branch corresponds to the non-intervention prediction result of one objective, and the results are finally integrated to form a set of non-intervention basic results.

[0113] Step 23: After concatenating the user feature vector, environmental feature vector, and intervention feature vector, input them into the intervention perception attention network, call the intervention perception attention network to estimate the impact of the intervention on the credit prediction target, and obtain the intervention increment result.

[0114] The feature vectors of users, environment, and intervention are concatenated in a predefined dimensional order to form a comprehensive vector containing information across all dimensions of subject, scenario, and strategy. This vector is then input into an intervention perception attention network. The network uses a targeted attention mechanism to focus on the interaction logic between intervention features and user and environmental features (e.g., the effect of a low-interest-rate strategy on increasing the loan willingness of young, high-income customers). Similarly, independent output branches are constructed according to credit prediction objectives. Each branch outputs the incremental value brought by the intervention strategy under the corresponding objective (e.g., the increase in loan probability, the change in default probability). These are then integrated to form a set of incremental intervention results. The specific impact of intervention strategies is modeled separately, eliminating interference from inherent user attributes and environmental factors, and accurately characterizing the heterogeneous causal effects of different intervention strategies on different customer groups.

[0115] Step 24: Combine the baseline results without intervention and the incremental results with intervention, and use the combined results as the prediction results.

[0116] For each credit forecast target (such as loan probability, default probability, loan amount), a fusion logic of basic results + incremental results is used for calculation.

[0117] Based on the above introduction, the credit target prediction method provided in this embodiment uses a self-attention network to mine the hidden correlation between user and environmental features, ensuring the objectivity of the results without intervention; at the same time, it uses an intervention-aware attention network to focus on the specific impact of intervention on business objectives, improving the accuracy of incremental effect prediction. This hierarchical modeling logic is adaptable to multi-intervention and multi-objective scenarios and can be flexibly extended to various credit prediction objectives (such as loan probability, default rate, and loan amount).

[0118] Example 6: This embodiment relates to an online credit limit pricing device. A schematic diagram of the online credit limit pricing device in this embodiment can be seen as follows: Figure 2 As shown, it includes: feature encoding module 201, credit prediction module 202, function construction module 203, iterative solution module 204, and pricing generation module 205.

[0119] Among them, the feature encoding module 201 is used to collect customer data, environmental data and intervention data as raw data, and to perform feature encoding on the raw data to generate feature vectors; The credit prediction module 202 is used to input the feature vector into the pre-trained multi-objective causal inference model for intervention credit target prediction and obtain the prediction result. The function construction module 203 is used to obtain the preset business objectives and business constraint values, and to construct a constrained integer programming problem based on the business objectives, business constraint values ​​and prediction results, and generate an integer programming function; the integer programming function includes: objective function and constraint conditions; The iterative solution module 204 is used to initialize the Lagrange multipliers, substitute the Lagrange multipliers into the integer programming function, integrate the constraints into the objective function, construct an unconstrained Lagrange function, and obtain the optimal value of the Lagrange multipliers through alternating iterative solution; The pricing generation module 205 is used to combine the optimal value of the Lagrange multiplier and the prediction results, determine the optimal strategy index according to the preset sorting rules, and output the credit limit pricing result corresponding to the optimal strategy index.

[0120] In the online pricing device for credit limits provided in this embodiment, the feature encoding module classifies and encodes multi-dimensional raw data to accurately mine the semantic association of discrete features and the quantitative value of numerical features; the credit prediction module adopts a pre-trained multi-objective causal inference model, which can effectively capture the complex interaction relationship between users, environment and intervention, separate the basic results from the intervention increment, and improve the causal accuracy of multi-objective prediction; the iterative solution module introduces Lagrange dual optimization, transforms the constrained integer programming problem into an unconstrained dual problem, and efficiently solves discontinuous variables through alternating iteration, breaking through the bottlenecks of traditional methods such as difficulty in finding the global optimum and insufficient real-time performance.

[0121] This device is adaptable to scenarios with multiple interventions, multiple business objectives, and dynamic business constraints. It can quickly respond to online pricing needs and provide an extended foundation for subsequent dynamic parameter adjustments and end-to-end simulation evaluation, enabling refined, globally optimal, and real-time implementation of credit pricing.

[0122] Additionally, it should be noted that all modules involved in this embodiment are logical modules. In practical applications, a logical module can be a physical module, a part of a physical module, or a combination of multiple physical modules.

[0123] Furthermore, in order to highlight the innovative aspects of this application, this embodiment does not introduce modules that are not closely related to solving the technical problems proposed in this application, but this does not mean that there are no other modules in this embodiment.

[0124] Example 7: This embodiment introduces another method for dividing the online credit limit pricing device. A schematic diagram of the online credit limit pricing device provided in this embodiment can be seen as follows: Figure 3 As shown, it includes: a business target prediction module, an offline parameter solving module, an online decision-making module, a dynamic control feedback module, and an offline simulation evaluation module.

[0125] The business objective prediction module, serving as the foundational data support module for pricing decisions, has its core function of accurately quantifying the impact of different credit strategies on customer business outcomes through a multi-objective causal inference model. This provides high-quality predictive basis for subsequent constraint optimization and decision output. The module is logically designed in a hierarchical manner: data input, feature processing, hierarchical modeling, and result output. The specific implementation is as follows: Data Input Layer: Responsible for collecting and integrating three types of core data to form a complete modeling data source. This includes intervention characteristics (customer-selectable credit strategy tiers, such as different combinations of credit limits and interest rates), environmental characteristics (external scenario variables such as industry prosperity index, regional economic indicators, and application time), and user characteristics (basic information: age, occupation, education, region; economic status: income level, debt-to-asset ratio, employment stability; credit history: overdue records, credit card usage rate, changes in credit limit; behavioral characteristics: APP activity, application frequency, repayment channel preferences, and other customer-related data), ensuring that data dimensions cover the entire strategy-scenario-customer journey.

[0126] Feature encoding layer: This layer addresses the specific characteristics of different data types to enhance feature representation capabilities. Discrete features (such as categorical data like gender, city, and occupation) are transformed into low-dimensional dense vectors using hash embedding and pre-trained embedding techniques to uncover semantic relationships between categories. Numerical features (such as quantitative data like income, age, and credit scores) are normalized to eliminate interference from features of different magnitudes, ensuring a unified modeling scale for all features and laying the foundation for subsequent network learning.

[0127] Self-interaction layer: Focuses on basic business performance prediction in non-intervention scenarios, constructing a user + environment correlation modeling logic. User feature vectors and environment feature vectors are concatenated according to preset dimensions and input into a self-attention network. The network adaptively calculates attention weights between features to capture hidden correlations (such as the loan caution of high-income customers in an economic downturn, and the increased loan demand of young customers during peak consumption seasons). Simultaneously, based on the core prediction objectives of credit business (loan probability, default probability, loan amount, etc.), independent output branches are established. Each branch corresponds to a non-intervention basic prediction result for one objective, ensuring the relevance and independence of multi-objective predictions.

[0128] Intervention Perception Interaction Layer: This layer specifically models the incremental impact of intervention strategies on business objectives, accurately depicting the three-way interaction effect between users, environment, and intervention. User feature vectors, environment feature vectors, and intervention feature vectors are concatenated and input into the intervention perception attention network. This network uses a dedicated attention mechanism to focus on the fit between intervention strategies and customers / scenarios (e.g., the effect of low-interest rate strategies on increasing loan willingness among young, high-income customers, and the attractiveness of high-amount strategies to small and micro-enterprise owners). Similarly, independent output branches are set according to the prediction target, with each branch outputting the incremental value brought by the intervention strategy under the corresponding target (e.g., the increase in loan probability, the change in default probability, and the increase in loan amount), achieving refined quantification of the intervention effect.

[0129] Prediction Output Layer: This layer organically integrates the basic and incremental results to generate the final prediction result. For each business objective, it employs a calculation logic of uninterrupted basic results + intervened incremental results to obtain the final estimated result of the objective after applying a specific credit strategy (e.g., final loan probability = uninterrupted loan probability + loan probability increase due to intervention). This provides direct data input for subsequent constraint optimization modeling.

[0130] The offline constraint control module, as the core optimization module for pricing strategies, is primarily responsible for solving for the globally optimal parameters that satisfy business constraints in offline scenarios, providing a stable and reliable optimization benchmark for online real-time decision-making. The module includes two core functions: offline parameter solving and offline simulation evaluation, specifically: Offline parameter solving module: For constrained optimization problems in credit pricing, a Lagrange dual optimization framework is introduced to achieve efficient solving of discontinuous variables. Taking maximizing the number of loan customers as the business objective and the upper limit of the average loan price interest rate as the business constraint, the specific module implementation logic is as follows: Define decision variables: Let This indicates whether to assign the j-th price / interest rate strategy to customer i, where n is the number of customers to be decided, and m is the number of strategy tiers. Construct the original optimization problem: The objective function is:

[0131] in, Indicates to the customer No. The probability score for whether a certain price interest rate strategy constitutes a loan is represented by... No. The price interest rate of a price interest rate strategy.

[0132] The constraints are:

[0133] Where R represents the per capita interest rate constraint. (where the interest rate is for the j-th strategy). Construct the Lagrangian function: ,in It is a Lagrange multiplier.

[0134] Incorporating the constraints into the objective function, we obtain:

[0135]

[0136]

[0137] Transformation dual problem: through The original problem is transformed into a dual problem that is easier to solve, and the optimal Lagrange multipliers are found using the alternating iterative method. ,

[0138] When λ is fixed, by

[0139]

[0140]

[0141] To obtain the optimal strategy for customer i .

[0142] When Z is fixed, the optimal λ is solved in O(n) complexity by using the three-way search method, and the process is iterated until the termination condition (fixed number of rounds or constraint error threshold) is met.

[0143] Offline simulation evaluation module: Breaking through the limitations of traditional single-intervention evaluation indicators, this module constructs an end-to-end strategy effectiveness verification system. Based on random unbiased experimental data (the actual credit strategy tiers accepted by customers and the corresponding business results), the experimental data is grouped according to the pricing decision results. Target groups whose decision results are consistent with the actual strategy tiers are selected. The business results (loan rate, default rate, loan amount, etc.) of each group are aggregated and calculated to obtain the overall pricing strategy simulation evaluation results. This method can effectively verify the end-to-end effect of model prediction and decision optimization in multi-intervention scenarios. By adjusting business constraints, it can also plot multi-dimensional effect curves, providing comprehensive data support for strategy optimization.

[0144] The online decision feedback module, serving as the real-time execution and dynamic optimization module for pricing strategies, primarily enables online millisecond-level pricing decisions based on offline-solved optimal parameters. It also adapts to market environment changes through a dynamic feedback mechanism, ensuring the timeliness and robustness of the strategy. The module comprises two core functions: online decision-making and dynamic control feedback, specifically including: Online decision-making module: Receives real-time customer characteristic data and, through the business target prediction module, determines the customer's performance at each strategy level. The value, combined with the optimal Lagrange multiplier obtained by the offline parameter solving module. According to the sorting rules:

[0145] The system determines the optimal strategy index and outputs the corresponding credit limit and interest rate pricing results. The entire process is computationally efficient and adaptable to the online real-time decision-making needs of millions of customers.

[0146] Dynamic control feedback module: Addressing the dynamic changes in market environment (economic cycles, interest rate policies) and customer behavior, this module introduces a PID (Proportional-Integral-Derivative) control mechanism to achieve adaptive updates of the Lagrange multiplier λ. The specific working logic of the dynamic control feedback module is as follows: Calculate the error value: Based on the latest historical loan disbursement data, the current actual value of the business constraint is statistically analyzed, and the error e(t) is defined as: business constraint target value - current actual value; Calculate the adjustment component: proportional term (Fast response to current error), integral term (Offsetting historical cumulative bias), differential term (Predicting the trend of error change), where , and These are coefficients calibrated based on historical data; Update multipliers: Calculate adjustment amount Proportional term + integral term + differential term, new =old +Δ At the same time, set reasonable boundaries for λ (such as 0.01≤λ≤0.5) to prevent over-adjustment; Frequency control: Update the λ parameter at hourly or daily frequency, input the new parameter into the online decision module, and ensure that the strategy can quickly adapt to environmental changes.

[0147] It should be noted that the specific algorithm in the online credit limit pricing device provided in this embodiment can be adjusted according to the actual use scenario, and this embodiment is not limited to this.

[0148] Example 8: Another embodiment of this application relates to an electronic device, such as... Figure 4 As shown, it includes: at least one processor 301; and a memory 302 communicatively connected to at least one processor 301; wherein the memory 302 stores instructions executable by at least one processor 301, which are executed by at least one processor 301 to enable at least one processor 301 to perform the steps of the online pricing method for credit limits in the above embodiments.

[0149] The memory and processor are connected via a bus, which can include any number of interconnecting buses and bridges, connecting various circuits of one or more processors and memories. The bus can also connect various other circuits, such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and will not be described further herein. A bus interface provides an interface between the bus and the transceiver. The transceiver can be a single component or multiple components, such as multiple receivers and transmitters, providing modules for communicating with various other devices over a transmission medium. Data processed by the processor is transmitted over the wireless medium via an antenna, which further receives data and transmits it to the processor.

[0150] The processor manages the bus and general processing, and also provides various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory is used to store data used by the processor during operation.

[0151] Those skilled in the art will understand that the above embodiments are specific embodiments for implementing this application, and in practical applications, various changes can be made to them in form and detail without departing from the spirit and scope of this application.

Claims

1. An online pricing method for credit lines, characterized in that, include: Collect customer data, environmental data, and intervention data as raw data, and perform feature encoding on the raw data to generate feature vectors; The feature vector is input into a pre-trained multi-objective causal inference model to predict the credit target after intervention, and the prediction result is obtained. Obtain preset business objectives and business constraint values, and construct a constrained integer programming problem based on the business objectives, business constraint values, and prediction results, and generate an integer programming function; The integer programming function includes: an objective function and constraints; Initialize the Lagrange multipliers, substitute the Lagrange multipliers into the integer programming function, integrate the constraints into the objective function, construct an unconstrained Lagrange function, and obtain the optimal value of the Lagrange multipliers through alternating iterations. Combining the optimal value of the Lagrange multiplier and the prediction result, the optimal strategy index is determined according to the preset sorting rules, and the credit limit pricing result corresponding to the optimal strategy index is output.

2. The online pricing method for credit lines according to claim 1, characterized in that, The step of substituting the Lagrange multipliers into the integer programming function, integrating the constraints into the objective function, constructing an unconstrained Lagrange function, and obtaining the optimal values ​​of the Lagrange multipliers through alternating iterations includes: Substitute the Lagrange multipliers into the integer programming function, and then incorporate the weighted calculation of the constraints and the Lagrange multipliers into the objective function to construct an unconstrained Lagrange function. Based on the predicted loan probability values ​​of customers under each intervention strategy, the optimal solution of the decision variables is obtained under the current Lagrange multipliers to obtain the customer decision set. Calculate the candidate values ​​of the Lagrange multipliers based on the customer decision set; Determine whether the preset termination condition is met; If not satisfied, the candidate value of the Lagrange multiplier is used as the new current Lagrange multiplier, and the process jumps to the step of solving for the optimal solution of the decision variable under the current Lagrange multiplier based on the loan probability value of the customer under each intervention strategy in the prediction result. If the conditions are met, the final candidate value of the Lagrange multiplier is taken as the optimal value of the Lagrange multiplier.

3. The online pricing method for credit lines according to claim 2, characterized in that, The step of calculating candidate Lagrange multiplier values ​​based on the customer decision set includes: Based on the customer decision set, combined with the prediction results, the business constraint values, and the interest rate / quota parameters corresponding to each intervention strategy, the objective optimization function of the Lagrange multiplier is constructed. The objective optimization function is solved using the ternary search method to obtain candidate values ​​for the Lagrange multipliers.

4. The online pricing method for credit lines according to claim 1, characterized in that, Also includes: Based on the latest historical loan disbursement data, calculate the current actual value of business constraints; Calculate the error between the business constraint value and the current actual value; Calculate the Lagrange multiplier adjustment based on the error value, and update the Lagrange multipliers based on the Lagrange multiplier adjustment. Before obtaining the optimal value of the Lagrange multiplier through alternating iteration, the method further includes replacing the current Lagrange multiplier with the updated Lagrange multiplier.

5. The online pricing method for credit lines according to claim 4, characterized in that, The calculation of the Lagrange multiplier adjustment based on the error value includes: Calculate the proportional term, integral term, and differential term respectively; wherein, the proportional term is the product of a preset proportional coefficient and the error value, the integral term is the product of a preset integral coefficient and the historical cumulative error value, and the differential term is the product of a preset differential coefficient and the error change rate. The summation of the proportional term, the integral term, and the differential term is used as the adjustment amount of the Lagrange multiplier.

6. The online pricing method for credit lines according to claim 1, characterized in that, Also includes: Obtain random unbiased experimental data; The experimental data includes: the actual credit strategy tiers accepted by customers and the corresponding business results; Based on the pricing strategy decision results, the actual credit strategy tiers in the experimental data are grouped. Select the group whose pricing strategy decision result is consistent with the actual credit strategy level as the target group; The business results of each target group are aggregated and calculated to obtain the simulation evaluation results of the overall pricing strategy.

7. The online pricing method for credit lines according to claim 1, characterized in that, The original data is subjected to feature encoding to generate a feature vector, including: Based on the data type, the original data is divided into discrete feature data and numerical feature data; The discrete feature data is then densely vectorized to obtain a dense vector; The numerical feature data is normalized to obtain a normalized vector; The dense vector and the normalized vector are concatenated and merged according to a preset dimension to form the feature vector.

8. The online pricing method for credit lines according to any one of claims 1 to 7, characterized in that, The step of inputting the feature vector into a pre-trained multi-objective causal inference model for intervention-based credit target prediction includes: Extract the user feature vector, environment feature vector, and intervention feature vector from the feature vector; The user feature vector and the environment feature vector are concatenated and input into a self-attention network. The self-attention network is then invoked to estimate the credit prediction target based on the correlation between the features, resulting in an intervention-free baseline result. The user feature vector, the environment feature vector, and the intervention feature vector are concatenated and then input into the intervention perception attention network. The intervention perception attention network is then invoked to estimate the impact of the intervention on the credit prediction target, thus obtaining the intervention increment result. The baseline results without intervention and the incremental results with intervention are combined, and the combined result is used as the prediction result.

9. An online pricing device for credit lines, characterized in that, include: The feature encoding module is used to collect customer data, environmental data, and intervention data as raw data, and to perform feature encoding on the raw data to generate feature vectors. The credit prediction module is used to input the feature vector into a pre-trained multi-objective causal inference model to predict the credit target after intervention, and obtain the prediction result. The function construction module is used to obtain preset business objectives and business constraint values, and to construct a constrained integer programming problem based on the business objectives, the business constraint values ​​and the prediction results, and generate an integer programming function. The integer programming function includes: an objective function and constraints; The iterative solution module is used to initialize the Lagrange multipliers, substitute the Lagrange multipliers into the integer programming function, integrate the constraints into the objective function, construct an unconstrained Lagrange function, and obtain the optimal value of the Lagrange multipliers through alternating iterative solutions. The pricing generation module is used to combine the optimal value of the Lagrange multiplier and the prediction result, determine the optimal strategy index according to the preset sorting rules, and output the credit limit pricing result corresponding to the optimal strategy index.

10. An electronic device, characterized in that, include: At least one processor; And, a memory communicatively connected to the at least one processor; The memory stores instructions executable by the at least one processor, which, when executed by the at least one processor, enables the at least one processor to perform the online pricing method for credit lines as described in any one of claims 1 to 8.

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