Intelligent bidding optimization method and system in real-time bidding

Abstract

This invention provides an intelligent bidding optimization method and system for real-time bidding, relating to the field of real-time bidding technology. It includes constructing bidding behavior characteristics by analyzing historical and market data, and analyzing competitor bidding probabilities based on Bayesian inference and clustering. The mutual information matrix of features and competition probabilities is dimensionality-reduced to obtain strategy coordinates, thereby constructing and solving a profit-maximizing equilibrium model under resource constraints. Finally, market volatility indicators are combined to generate real-time bid values. This invention can adapt to the competitive environment, achieving dynamic optimization of bidding strategies and improved returns.

Description

Technical Field

[0001] This invention relates to the field of real-time bidding technology, and in particular to a method and system for intelligent bidding optimization in real-time bidding. Background Technology

[0002] In real-time bidding (RTB) systems, traditional bidding optimization methods suffer from technical problems such as insufficient utilization of decision information, inadequate perception of the competitive environment, limited strategy expression capabilities, and weak dynamic adaptability. Current mainstream methods mainly rely on a single prediction model and simple rule adjustments, which cannot effectively capture the market competition structure and price fluctuation patterns.

[0003] Existing technologies typically use click-through rate (CTR) and conversion rate (CTR) prediction models to directly calculate expected value, lacking modeling and analysis of competitor behavior patterns. This approach struggles to accurately determine the optimal bidding strategy in complex and ever-changing bidding environments, particularly performing poorly in highly competitive high-value traffic. Furthermore, traditional methods do not delve deeply enough into historical bidding data, failing to fully extract temporal features and competitive landscape information, resulting in a lack of foresight in bidding decisions. Common bidding optimization algorithms, such as linear bidding and ROI-based proportional bidding, rely heavily on human experience for parameter adjustments, making it difficult to automatically adapt to market changes. While reinforcement learning methods introduce a sequential decision-making framework, they face challenges such as the curse of dimensionality in the state space and sparse reward signals, limiting their practical application effectiveness.

[0004] Furthermore, existing systems generally lack sensitive analysis and rapid response mechanisms for market price fluctuations, making it impossible to adjust strategies in a timely manner to cope with sudden changes in traffic and changes in competitors' strategies. Under resource constraints, traditional methods struggle to achieve a good balance between global optimization and real-time response. Therefore, this solution provides a new intelligent bidding optimization method for real-time bidding. Summary of the Invention

[0005] This invention provides a method and system for intelligent bidding optimization in real-time bidding, which can solve the problems in the prior art.

[0006] A first aspect of the present invention provides a smart bidding optimization method for real-time bidding, comprising:

[0007] Obtain its own bidding history and market aggregated data, and statistically analyze the frequency distribution of bids, the rate of change of bid magnitude, and the success rate in segments according to the bidding cycle, and splice them together to form a bidding behavior feature vector;

[0008] Based on the aggregated market data, Bayesian inference is used to calculate the bidding probability distribution of competitors. Competitors are clustered using behavioral heterogeneity indicators. The bidding probabilities of each group are weighted and averaged to form an aggregated distribution. The mutual information matrix is ​​calculated in combination with the bidding behavior feature vector.

[0009] Singular value decomposition is performed on the mutual information matrix, and the singular values ​​are sorted by size. The left singular vectors whose cumulative contribution reaches the retention threshold are selected as the basis of the subspace. The bidding behavior feature vectors are projected onto the subspace to obtain the dimensionality reduction strategy coordinates.

[0010] Using the reduced coordinates as decision variables, an objective function is constructed to be the sum of the product of the winning probability and the unit revenue in each cycle. After introducing resource constraints, an equilibrium equation system is established by the Lagrange multiplier method. Fixed-point iteration is used to update the equations round by round. When the difference between adjacent solutions is lower than the convergence threshold, the equilibrium strategy parameters are output.

[0011] Extract the transaction price sequence of continuous bidding cycles from the market aggregated data, calculate the time-series change rate of the transaction price sequence as a market volatility indicator, and use the market volatility indicator to perform nonlinear mapping on the equilibrium strategy parameters to generate real-time output value.

[0012] Based on the aggregated market data, Bayesian inference is used to calculate the bidding probability distribution of competitors. Competitors are clustered using behavioral heterogeneity indicators. A weighted average of the bidding probabilities for each cluster is taken to form an aggregated distribution. The mutual information matrix is ​​then calculated using the bidding behavior feature vectors, including:

[0013] Extract the price range width and median of each bidding period, and calculate their ratio as a price dispersion index. Map the price dispersion index to the variance parameter of the Bayesian likelihood function.

[0014] The market transaction price distribution is divided into multiple non-overlapping sub-intervals. The transaction frequency of each sub-interval is counted to construct an observation vector. Combined with the conjugate prior distribution, Bayesian inference is used to calculate the bidding probability of the competitors in each sub-interval. The vectors are then spliced ​​together to form the bidding probability distribution of the competitors.

[0015] The information entropy and skewness coefficient of the competitor's bid probability distribution are calculated as behavioral heterogeneity indicators. In the two-dimensional feature space composed of the information entropy and the skewness coefficient, each competitor is clustered. The mode position of the competitor's bid probability distribution in each cluster is extracted. The reciprocal distance from the mode position to the cluster center is used as the weight to perform a weighted average of the bid probability distribution within the cluster. The average distribution of each cluster is then weighted twice according to the cluster size proportion to obtain the competitor aggregate distribution.

[0016] The aggregated distribution of the competitors and the feature vector of the bidding behavior are aligned in a grid along the price dimension. The joint distribution entropy and the marginal distribution entropy after alignment are calculated, and a mutual information matrix is ​​constructed based on the difference in entropy.

[0017] The market transaction price distribution is divided into multiple non-overlapping sub-intervals. The transaction frequency of each sub-interval is statistically analyzed to construct an observation vector. Combined with the conjugate prior distribution, Bayesian inference is used to calculate the bidding probability of competitors in each sub-interval. These vectors are then concatenated to form the competitor bidding probability distribution, including:

[0018] Quantile analysis is performed on the market transaction price distribution to extract multiple quantile points and divide the price space into multiple non-overlapping sub-intervals, ensuring that each sub-interval is connected end to end on the price axis and there is no overlapping area. The interval identifier and interval boundary value of each sub-interval are stored.

[0019] Based on the transaction price sequence in the market transaction price distribution, each transaction price is compared with the interval boundary value of each sub-interval to determine the attribution relationship. The number of transactions in each sub-interval is accumulated to obtain the transaction frequency. The transaction frequency of each sub-interval is associated with the corresponding interval identifier to construct an observation vector.

[0020] Select a conjugate prior distribution type that matches the probability distribution form of the observed vector, set the initial value of the hyperparameter of the conjugate prior distribution based on historical market data, input the observed vector into the Bayesian inference framework, and obtain the estimated bid probability of the competitor in each sub-interval through posterior probability calculation.

[0021] The normalization constraints of the bid probability estimates are tested. Bid probability estimates that do not meet the normalization conditions are normalized and corrected. The corrected bid probability estimates are then concatenated into a one-dimensional vector according to the increasing order of price in each sub-interval, forming the bid probability distribution of the competitors.

[0022] Singular value decomposition is performed on the mutual information matrix, and the singular values ​​are sorted by size. Left singular vectors whose cumulative contribution reaches the retention threshold are selected as the basis of the subspace. The bidding behavior feature vectors are projected onto the subspace to obtain the dimensionality reduction strategy coordinates, including:

[0023] Perform singular value decomposition on the mutual information matrix to obtain a left singular vector matrix and a singular value diagonal matrix. Extract the singular value sequence from the main diagonal of the singular value diagonal matrix. Arrange the singular value sequence in descending order of value. Record the mapping relationship between the original index and the new index of each singular value. Adjust the column vector arrangement order of the left singular vector matrix synchronously according to the mapping relationship.

[0024] Calculate the square of each singular value after sorting, and use the ratio of each square value to the sum of all square values ​​as the variance contribution. Calculate the cumulative value of the variance contribution. When the cumulative value reaches the retention threshold, extract the corresponding column vectors from the sorted left singular vector matrix to form a subspace basis matrix. Calculate the inner product between the bidding behavior feature vector and each column vector of the subspace basis matrix, and arrange the inner product values ​​in column vector order to form the dimensionality reduction strategy coordinates.

[0025] Using the reduced coordinates as decision variables, an objective function is constructed to be the sum of the products of the winning probability and the unit revenue in each cycle. After introducing resource constraints, an equilibrium equation system is established using the Lagrange multiplier method. Fixed-point iteration is used to update the equations round by round. When the difference between adjacent solutions is lower than the convergence threshold, the equilibrium strategy parameters are output, including:

[0026] Calculate the covariance matrix of the coordinates of the dimensionality reduction strategy and the aggregate distribution of the competitors, perform eigenvalue decomposition on the covariance matrix to extract the maximum eigenvalue and construct a risk measurement function, express the winning probability of each period as a composite function of the decision variables mapped by the risk measurement function, and calculate the cumulative sum of the composite function and the unit return in each period to form the objective function.

[0027] By introducing nonnegative slack variables, the resource total inequality constraint is transformed into an equality constraint. An augmented Lagrangian function containing penalty terms for decision variables and slack variables is constructed, and Lagrangian multipliers are assigned to the equality constraint. The partial derivatives of the augmented Lagrangian function with respect to the decision variables and slack variables are calculated and set to zero, and the partial derivative equation is rewritten as an implicit mapping relationship of the decision variables. A compression mapping operator is constructed and the Lipshitz constant is calculated to verify the compressibility.

[0028] Initialize decision variables, slack variables, and penalty coefficients. Substitute the current decision variables into the compression mapping operator to obtain the mapping value. Calculate the residual vector between the mapping value and the current value. Extract the infinite norm of the residual vector as the convergence index. Adaptively adjust the penalty coefficient according to the magnitude of the convergence index.

[0029] Update the mapping value to the current value and repeat the iteration. When the convergence index is lower than the threshold, terminate the iteration and output the final decision variable as the equilibrium strategy parameter.

[0030] By introducing nonnegative slack variables, the resource total inequality constraint is transformed into an equality constraint. An augmented Lagrangian function is constructed, including penalty terms for decision variables and slack variables. Lagrange multipliers are assigned to the equality constraint, including:

[0031] Calculate the residual value of the resource total inequality constraint. For constraints with residual values ​​below the tightness threshold, introduce non-negative relaxation variables to transform them into equations. For constraints with residual values ​​above the tightness threshold, establish complementary relaxation conditions where the product of the relaxation variable and the residual is zero.

[0032] Calculate the difference vector between the decision variable and the center point of the feasible region, construct the covariance matrix of the difference vector, calculate the quadratic form of the difference vector with respect to the inverse of the covariance matrix to obtain the Mahalanobis distance, and apply an exponential mapping to construct a penalty term for the decision variable. Take the logarithm of each component of the slack variable vector, sum the logarithms, and take the negative value to construct a logarithmic barrier penalty term.

[0033] Add the original objective function to the penalty term of the decision variable, subtract the logarithmic obstacle penalty term and multiply by the obstacle parameter to obtain the obstacle objective function. Assign Lagrange multiplier vectors to the equality constraints and complementary relaxation conditions. Construct the inner product of the multiplier vector and the constraint residual vector to form a bilinear constraint term. Add the bilinear constraint term to the obstacle objective function to form the augmented Lagrange function.

[0034] We establish the primal optimality condition by taking the partial derivatives of the augmented Lagrange function with respect to the decision variable and the slack variable, and establish the dual feasibility condition by taking the partial derivatives with respect to the Lagrange multiplier vector.

[0035] Calculating the time-series rate of change of the transaction price series as a market volatility indicator, and using the market volatility indicator to perform a nonlinear mapping of the equilibrium strategy parameters to generate a real-time exit value, including:

[0036] Calculate the price difference scores for multiple consecutive moments in the transaction price sequence, sum the absolute values ​​of the price difference scores to obtain the cumulative volatility, calculate the price range of the transaction price sequence within the same time period, and divide the cumulative volatility by the price range to obtain the normalized market volatility index.

[0037] Construct a mapping table between the market volatility index and the adjustment intensity. When the market volatility index increases, the corresponding adjustment intensity increases non-linearly. Based on the current market volatility index, find the corresponding adjustment intensity value in the mapping table and extract the reference bid corresponding to the current market state from the equilibrium strategy parameters.

[0038] The initial bid value is obtained by multiplying the reference bid price by the adjustment intensity value. The deviation between the latest price and the historical average price of the transaction price sequence is calculated. The initial bid value is corrected based on the deviation. The corrected bid value is smoothed. The difference between the bid value and the bid value at the previous moment is calculated. When the absolute value of the difference exceeds the jump threshold, peak shaving is performed. The processed value is output as the real-time bid value.

[0039] A second aspect of the present invention provides an intelligent bidding optimization system for real-time bidding, comprising:

[0040] The feature extraction unit is used to obtain its own bidding history and market aggregated data, and to statistically analyze the frequency distribution of bids, the rate of change of the magnitude of the bid, and the winning rate in segments according to the bidding cycle, and to splice them to form a bidding behavior feature vector.

[0041] The competition modeling unit is used to calculate the bidding probability distribution of competitors based on the aggregated market data using Bayesian inference, perform clustering of competitors through behavioral heterogeneity indicators, take a weighted average of the bidding probabilities of each group to form an aggregated distribution, and calculate the mutual information matrix in combination with the bidding behavior feature vector.

[0042] The dimension reduction projection unit is used to perform singular value decomposition on the mutual information matrix, sort the singular values ​​by size, select the left singular vector whose cumulative contribution reaches the retention threshold as the subspace basis, and project the bidding behavior feature vector onto the subspace to obtain the dimension reduction strategy coordinates.

[0043] The equilibrium solution unit is used to construct an objective function that uses the reduced coordinates as decision variables to construct the sum of the products of the winning probability and the unit revenue in each cycle. After introducing resource constraints, the equilibrium equation system is established by the Lagrange multiplier method. The system is updated round by round using fixed-point iteration. When the difference between adjacent solutions is lower than the convergence threshold, the equilibrium strategy parameters are output.

[0044] The volatility mapping unit is used to extract the transaction price sequence of continuous bidding cycles from the market aggregated data, calculate the time-series change rate of the transaction price sequence as a market volatility indicator, and use the market volatility indicator to perform nonlinear mapping on the equilibrium strategy parameters to generate real-time output value.

[0045] A third aspect of the present invention provides an electronic device, comprising:

[0046] processor;

[0047] Memory used to store processor-executable instructions;

[0048] The processor is configured to invoke instructions stored in the memory to execute the aforementioned method.

[0049] A fourth aspect of the present invention provides a computer-readable storage medium having stored thereon computer program instructions that, when executed by a processor, implement the aforementioned method.

[0050] This method significantly improves the quality of bidding decisions and resource utilization efficiency in real-time bidding. It calculates the probability distribution of competitors' bids based on Bayesian inference and performs cluster analysis using behavioral heterogeneity indicators, effectively characterizing the heterogeneity of the market competition landscape. By weighted averaging of the probability distributions of each group to form an aggregated distribution and calculating its mutual information matrix with its own behavioral characteristics, it can accurately identify the key correlations and dependencies between its own bidding strategy and market dynamics, thereby gaining insight into potential market opportunities and risks. Singular value decomposition of the mutual information matrix and selection of left singular vectors with sufficient cumulative contribution to construct a subspace effectively reduces the dimensionality of high-dimensional bidding behavior feature vectors. Projecting the original features into this subspace yields the dimensionality-reduced strategy coordinates, significantly reducing the complexity of the decision-making problem while preserving core information, thus clearing obstacles for subsequent optimization calculations.

[0051] Using reduced-dimensional coordinates as decision variables, an optimization problem constrained by resources is constructed with the objective of maximizing the sum of the products of the probability of winning a bid and the unit revenue in each cycle. An equilibrium equation system is established using the Lagrange multiplier method and solved using a fixed-point iterative algorithm. This approach efficiently approximates the global or local optimal equilibrium point of resource allocation and bidding strategies while satisfying the constraints, ensuring the stability and executability of the strategy.

[0052] By analyzing the time-series rate of change of market transaction prices to quantify market volatility indicators and applying a nonlinear mapping to the equilibrium strategy parameters, a real-time bid value is generated. This mechanism enables the bidding strategy to dynamically respond to short-term fluctuations in the market environment, transforming the static equilibrium strategy into a highly adaptable and responsive real-time bid order, thereby maintaining a competitive advantage and stable returns in a volatile market. Attached Figure Description

[0053] Figure 1 This is a flowchart illustrating the intelligent bidding optimization method in real-time bidding according to an embodiment of the present invention.

[0054] Figure 2 This is a flowchart illustrating the method for calculating the bidding probability distribution and mutual information matrix of competitors according to an embodiment of the present invention. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] The technical solution of the present invention will be described in detail below with reference to specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments.

[0057] Figure 1 This is a flowchart illustrating the intelligent bidding optimization method in real-time bidding according to an embodiment of the present invention, as shown below. Figure 1 As shown, the method includes:

[0058] Obtain its own bidding history and market aggregated data, and statistically analyze the frequency distribution of bids, the rate of change of bid magnitude, and the success rate in segments according to the bidding cycle, and splice them together to form a bidding behavior feature vector;

[0059] Based on the aggregated market data, Bayesian inference is used to calculate the bidding probability distribution of competitors. Competitors are clustered using behavioral heterogeneity indicators. The bidding probabilities of each group are weighted and averaged to form an aggregated distribution. The mutual information matrix is ​​calculated in combination with the bidding behavior feature vector.

[0060] Singular value decomposition is performed on the mutual information matrix, and the singular values ​​are sorted by size. The left singular vectors whose cumulative contribution reaches the retention threshold are selected as the basis of the subspace. The bidding behavior feature vectors are projected onto the subspace to obtain the dimensionality reduction strategy coordinates.

[0061] Using the reduced coordinates as decision variables, an objective function is constructed to be the sum of the product of the winning probability and the unit revenue in each cycle. After introducing resource constraints, an equilibrium equation system is established by the Lagrange multiplier method. Fixed-point iteration is used to update the equations round by round. When the difference between adjacent solutions is lower than the convergence threshold, the equilibrium strategy parameters are output.

[0062] Extract the transaction price sequence of continuous bidding cycles from the market aggregated data, calculate the time-series change rate of the transaction price sequence as a market volatility indicator, and use the market volatility indicator to perform nonlinear mapping on the equilibrium strategy parameters to generate real-time output value.

[0063] Figure 2 This is a flowchart illustrating the method for calculating the bidding probability distribution and mutual information matrix of competitors according to an embodiment of the present invention. Based on the aggregated market data, Bayesian inference is used to calculate the bidding probability distribution of competitors. Competitors are clustered using behavioral heterogeneity indicators. A weighted average of the bidding probabilities of each cluster is taken to form an aggregated distribution. The mutual information matrix is ​​then calculated in conjunction with the bidding behavior feature vectors, including:

[0064] Extract the price range width and median of each bidding period, and calculate their ratio as a price dispersion index. Map the price dispersion index to the variance parameter of the Bayesian likelihood function.

[0065] The market transaction price distribution is divided into multiple non-overlapping sub-intervals. The transaction frequency of each sub-interval is counted to construct an observation vector. Combined with the conjugate prior distribution, Bayesian inference is used to calculate the bidding probability of the competitors in each sub-interval. The vectors are then spliced ​​together to form the bidding probability distribution of the competitors.

[0066] The information entropy and skewness coefficient of the competitor's bid probability distribution are calculated as behavioral heterogeneity indicators. In the two-dimensional feature space composed of the information entropy and the skewness coefficient, each competitor is clustered. The mode position of the competitor's bid probability distribution in each cluster is extracted. The reciprocal distance from the mode position to the cluster center is used as the weight to perform a weighted average of the bid probability distribution within the cluster. The average distribution of each cluster is then weighted twice according to the cluster size proportion to obtain the competitor aggregate distribution.

[0067] The aggregated distribution of the competitors and the feature vector of the bidding behavior are aligned in a grid along the price dimension. The joint distribution entropy and the marginal distribution entropy after alignment are calculated, and a mutual information matrix is ​​constructed based on the difference in entropy.

[0068] In this specific embodiment, it is necessary to obtain its own historical bidding data and market aggregated data. The own historical bidding data includes information such as the bid amount, whether the bid was successful, the number of ad impressions obtained and their effects within a certain period of time. The market aggregated data includes information such as the transaction price of each bidding cycle, the number of advertisers participating in the competition, and traffic characteristics. The data is segmented according to the bidding cycle (such as hour, day or custom time period), and feature extraction and statistical analysis are performed on each segment.

[0069] Based on data segmentation, the frequency distribution of bids for each bidding cycle is statistically analyzed. The price range is divided into several intervals, such as dividing the percentage of the highest historical transaction price of an ad slot into ten equidistant intervals. The number of bids within each interval is counted to obtain a frequency distribution vector. The rate of change in bid amplitude between consecutive bidding cycles is calculated, which is the percentage change in the number of bids for the same price range between two consecutive cycles. The success rate for each price range is calculated, which is the proportion of bidders who obtain ad display opportunities within that range. The three feature vectors—bid frequency distribution, rate of change in amplitude, and success rate—are concatenated to form a bidding behavior feature vector.

[0070] After acquiring aggregated market data, the upper and lower boundaries of the transaction prices recorded in each bidding period are extracted, and the interval width and median are calculated. Dividing the interval width by the median yields the price dispersion index, which reflects the degree of dispersion in market bids. When the price dispersion is large, it indicates significant differences in bids among competitors. This index is used as an estimate of the variance parameter of the Bayesian likelihood function, and is used to characterize the intensity of uncertainty in subsequent probability inference.

[0071] The market transaction price range is divided into several non-overlapping sub-intervals at equal intervals. The transaction frequency in each sub-interval is counted to construct an observation vector. The Dirichlet distribution is selected as the conjugate prior distribution, and its hyperparameters are set according to the long-term transaction frequency ratio of historical bidding data. The observation vector is combined with the prior distribution, and the posterior distribution is updated through Bayesian inference to obtain the bidding probability of the competitors in each sub-interval. The probability values ​​corresponding to all sub-intervals are concatenated in price order to form the bidding probability distribution vector of the competitors.

[0072] Calculate the information entropy for the bidding probability distribution of each competitor. The skewness coefficient is used to measure the uncertainty of the probability distribution and to calculate the distribution's skewness coefficient, obtained by dividing the third central moment by the cube of the standard deviation, to characterize the distribution's asymmetric properties. A two-dimensional feature space is constructed using information entropy as the x-axis and skewness coefficient as the y-axis. In this space, a clustering algorithm is performed on all competitors, using the K-means method to divide them into different groups, each representing a typical bidding behavior pattern.

[0073] For the bidding probability distribution of competitors within each category, the price corresponding to the sub-interval with the highest probability value is extracted as the mode position. The Euclidean distance between this mode position and the category center in the price dimension is calculated, and the reciprocal of the distance is taken as the weight of that competitor. The bidding probability distributions of all competitors within the category are weighted and averaged to obtain the category average distribution. The number of competitors included in each category is counted, and the proportion of each category to the total number of competitors is calculated as the category size proportion. The average distributions of each category are then weighted and averaged again according to the category size proportion to obtain the competitor aggregation distribution, which comprehensively reflects the overall bidding tendency of the market.

[0074] Align the competitor's aggregated distribution with its own bidding behavior feature vector in a gridded manner along the price dimension. Specifically, map the bid frequency distribution in the bidding behavior feature vector to the same price sub-interval grid as the competitor's aggregated distribution, and fill in the frequency values ​​at corresponding positions using interpolation methods, ensuring both distributions have the same discretization granularity. Calculate the joint distribution entropy of the two distributions after alignment, i.e. The joint probability is obtained by normalizing the product of the corresponding positions of the two distributions. The marginal entropy H(X) of the competitor's aggregation distribution and the marginal entropy H(Y) of the bidding behavior feature vector are calculated respectively. The mutual information value is obtained through... The mutual information values ​​corresponding to different price range combinations are calculated and filled into a matrix to form the final mutual information matrix. This matrix quantifies the correlation between the bidder's bidding behavior and the market competition situation.

[0075] The market transaction price distribution is divided into multiple non-overlapping sub-intervals. The transaction frequency of each sub-interval is statistically analyzed to construct an observation vector. Combined with the conjugate prior distribution, Bayesian inference is used to calculate the bidding probability of competitors in each sub-interval. These vectors are then concatenated to form the competitor bidding probability distribution, including:

[0076] Quantile analysis is performed on the market transaction price distribution to extract multiple quantile points and divide the price space into multiple non-overlapping sub-intervals, ensuring that each sub-interval is connected end to end on the price axis and there is no overlapping area. The interval identifier and interval boundary value of each sub-interval are stored.

[0077] Based on the transaction price sequence in the market transaction price distribution, each transaction price is compared with the interval boundary value of each sub-interval to determine the attribution relationship. The number of transactions in each sub-interval is accumulated to obtain the transaction frequency. The transaction frequency of each sub-interval is associated with the corresponding interval identifier to construct an observation vector.

[0078] Select a conjugate prior distribution type that matches the probability distribution form of the observed vector, set the initial value of the hyperparameter of the conjugate prior distribution based on historical market data, input the observed vector into the Bayesian inference framework, and obtain the estimated bid probability of the competitor in each sub-interval through posterior probability calculation.

[0079] The normalization constraints of the bid probability estimates are tested. Bid probability estimates that do not meet the normalization conditions are normalized and corrected. The corrected bid probability estimates are then concatenated into a one-dimensional vector according to the increasing order of price in each sub-interval, forming the bid probability distribution of the competitors.

[0080] Acquire all transaction price records from multiple recent bidding cycles to form a price series dataset. This dataset includes the final transaction price of each bidding session, along with corresponding timestamps, traffic characteristics, and other related information. Extract this data from the real-time bidding platform's log system, ensuring data integrity and representativeness. Typically, bidding records from the most recent 7 or 30 days are selected, with the time window length adjusted according to the market's rate of change. Sort the obtained price series by numerical value, calculate key quantiles, and dynamically select the granularity of the division based on the degree of market price volatility. Specifically, calculate the coefficient of variation (standard deviation divided by mean) of the price series. When the coefficient of variation is greater than a preset threshold (e.g., 0.3), use quartiles; when the coefficient of variation is in a moderate range (e.g., 0.1 to 0.3), use quintiles; and when the coefficient of variation is small (less than 0.1), use quartiles.

[0081] Based on the selected quantiles, non-overlapping sub-intervals are divided. Taking the 10-tenths as an example, the 1st, 2nd to 9th quantiles of the dataset are calculated to obtain nine quantile values, P10, P20 to P90. The minimum price is set as the lower limit of the interval L0 (which can be the minimum value of the dataset or the theoretical minimum value 0), and the maximum price is set as the upper limit of the interval U9 (which can be the maximum value of the dataset or the theoretical upper limit), forming 10 price sub-intervals: [L0, P10), [P10, P20), ..., [P80, P90), [P90, U9]. A unique identifier code is assigned to each sub-interval, such as an integer from 0 to 9, for easy reference and calculation later.

[0082] Traverse each record in the transaction price sequence and perform interval mapping operations. For the price value p, starting from the first interval, check whether the condition Li ≤ p < Ui is satisfied in sequence. Once a matching interval is found, classify the price record into the corresponding interval and interrupt the retrieval. For the maximum value, ensure that it is correctly classified into the last closed interval [Pn, Un]. Optimize the interval positioning process through algorithms such as binary search, especially when the number of sub-intervals is large, to improve processing efficiency.

[0083] Accumulatively count the occurrence times of price records in each sub-interval. Create an integer array with a length equal to the number of sub-intervals, and the initial values are all 0. Whenever a price value is classified into a certain interval, the corresponding array element is incremented by 1. After processing all price records, the element values in the array are the transaction frequencies of each interval. Bind the frequency array with the interval identifiers to form a structured observation vector. This vector reflects the distribution of the activity levels in different price intervals in the bidding market. In the mobile application advertising bidding scenario, for example, for a certain application startup page ad slot, it is observed that there are 120 transactions in the price interval [0.5 million yuan, 1 million yuan), 180 transactions in the interval [1 million yuan, 1.5 million yuan), and 50 transactions in the interval [1.5 million yuan, 2 million yuan). This distribution indicates that the market competition is concentrated in the medium and low price intervals, providing a reference for formulating bidding strategies.

[0084] Based on the discrete distribution characteristics of the observation vector, select the Dirichlet distribution as the conjugate prior distribution for Bayesian inference. The Dirichlet distribution is the conjugate prior of the multinomial distribution and is very suitable for processing categorical count data, and can naturally express the uncertainty of the bidding probabilities in different price intervals. Construct the prior hyperparameter vector of the Dirichlet distribution, and extract the average transaction proportion of each price interval in a relatively long time period (such as the recent 3 months) from the historical bidding data. To enhance the model stability, introduce the prior intensity coefficient α, whose general value range is from 1 to 50. A larger α value indicates a higher degree of trust in the prior information. Multiply the historical transaction proportions of each interval by α to obtain the prior hyperparameter vector [α1, α2,..., αn], where n is the number of price sub-intervals. In the highly competitive e-commerce promotion season advertising bidding, it is observed that the historical transaction proportions in different price intervals are [, 0.3, 0.4, 0.2]. Select the prior intensity coefficient α = 10, then the prior hyperparameter vector is [1, 3, 4, 2], which reflects a moderate trust in the historical data and an openness to new observations.

[0085] The observed transaction frequency vector for the current period is added to the corresponding elements of the prior hyperparameter vector, and the posterior update formula of the Dirichlet-Multinomial model is applied to calculate the bidding probability of each sub-interval. Specifically, the estimated bidding probability of the i-th sub-interval is equal to (current interval transaction frequency + prior hyperparameter αi) / (sum of transaction frequencies of all intervals + sum of all prior hyperparameters). The sum of the calculated bidding probability estimates of all sub-intervals is then checked to ensure it equals 1. Due to the limitations of floating-point arithmetic precision, the accumulated result may have slight deviations. A tolerance threshold ε (e.g., 0.0001) is set. When the absolute value of the accumulated sum deviating from 1 exceeds ε, normalization is performed. The normalization process divides the probability estimate of each sub-interval by the sum of probabilities to ensure that the final distribution meets the basic requirement that the probability sum is 1.

[0086] Following the ascending order of the sub-intervals on the price axis, the corrected bid probability estimates are sequentially written into a one-dimensional array, forming a complete competitor bid probability distribution vector. The length of this vector equals the number of sub-intervals, and the k-th element corresponds to the competitor bid probability of the k-th price interval. This representation method preserves the order information of the price intervals while quantifying the relative importance of each interval.

[0087] Singular value decomposition is performed on the mutual information matrix, and the singular values ​​are sorted by size. Left singular vectors whose cumulative contribution reaches the retention threshold are selected as the basis of the subspace. The bidding behavior feature vectors are projected onto the subspace to obtain the dimensionality reduction strategy coordinates, including:

[0088] Perform singular value decomposition on the mutual information matrix to obtain a left singular vector matrix and a singular value diagonal matrix. Extract the singular value sequence from the main diagonal of the singular value diagonal matrix. Arrange the singular value sequence in descending order of value. Record the mapping relationship between the original index and the new index of each singular value. Adjust the column vector arrangement order of the left singular vector matrix synchronously according to the mapping relationship.

[0089] Calculate the square of each singular value after sorting, and use the ratio of each square value to the sum of all square values ​​as the variance contribution. Calculate the cumulative value of the variance contribution. When the cumulative value reaches the retention threshold, extract the corresponding column vectors from the sorted left singular vector matrix to form a subspace basis matrix. Calculate the inner product between the bidding behavior feature vector and each column vector of the subspace basis matrix, and arrange the inner product values ​​in column vector order to form the dimensionality reduction strategy coordinates.

[0090] After obtaining the mutual information matrix, singular value decomposition (SVD) is performed on the matrix. SVD decomposes the mutual information matrix into a product of three matrices: the left singular vector matrix, the singular value diagonal matrix, and the transpose of the right singular vector matrix. Each column vector of the left singular vector matrix represents an orthogonal basis direction in the original feature space. The diagonal elements of the singular value diagonal matrix reflect the importance of each basis direction. Values ​​are read sequentially from the diagonal positions of the singular value diagonal matrix to form a singular value sequence. The length of this sequence is equal to the rank of the mutual information matrix, and each element corresponds to a latent feature dimension.

[0091] The extracted singular value sequences are sorted in descending order of numerical value. During the sorting process, the position index of each singular value in the original sequence and its new position index after sorting are recorded, creating an index mapping table. Based on this mapping table, the column vectors of the left singular vector matrix are synchronously adjusted, moving the column vector corresponding to the k-th singular value to the k-th column position after sorting, ensuring that the singular value maintains its association with its corresponding basis vector. Each sorted singular value is squared to obtain the variance contribution of each dimension. Each squared value is divided by the sum of all squared values ​​to calculate the percentage variance contribution of that dimension. Starting from the first singular value, the variance contribution is accumulated for each singular value, stopping when the accumulated sum first reaches or exceeds a preset retention threshold. The retention threshold is typically set between 0.85 and 0.95, indicating that dimensions sufficient to explain most of the variability of the original data are retained. The number of singular values ​​to be retained is determined based on the stopping position. The first few column vectors corresponding to these values ​​are extracted from the sorted left singular vector matrix and concatenated column-wise to form the subspace basis matrix.

[0092] The original bidding behavior feature vector is projected onto a low-dimensional space spanned by the subspace basis matrix. This projection operation is achieved by calculating the inner product of the bidding behavior feature vector with each column vector of the subspace basis matrix. For the i-th basis vector, the product of each element in the bidding behavior feature vector with the corresponding element of that basis vector is calculated. The sum of all products yields the i-th reduced-dimensional coordinate component. The inner product with all retained basis vectors is then calculated sequentially, and the inner product values ​​are arranged according to the column order of the basis vectors in the subspace basis matrix to form the reduced-dimensional strategy coordinate vector. The dimension of this reduced-dimensional coordinate vector is equal to the number of retained singular values, significantly lower than the dimension of the original bidding behavior feature vector. Simultaneously, it retains the main variation information in the original feature space, providing a compact representation of decision variables for subsequent optimization calculations. Essentially, the projection process maps the high-dimensional bidding behavior features onto a low-dimensional manifold spanned by the main variation directions, filtering out noise interference and highlighting the core strategy dimensions that significantly influence the bidding results.

[0093] Using the reduced coordinates as decision variables, an objective function is constructed to be the sum of the products of the winning probability and the unit revenue in each cycle. After introducing resource constraints, an equilibrium equation system is established using the Lagrange multiplier method. Fixed-point iteration is used to update the equations round by round. When the difference between adjacent solutions is lower than the convergence threshold, the equilibrium strategy parameters are output, including:

[0094] Calculate the covariance matrix of the coordinates of the dimensionality reduction strategy and the aggregate distribution of the competitors, perform eigenvalue decomposition on the covariance matrix to extract the maximum eigenvalue and construct a risk measurement function, express the winning probability of each period as a composite function of the decision variables mapped by the risk measurement function, and calculate the cumulative sum of the composite function and the unit return in each period to form the objective function.

[0095] By introducing nonnegative slack variables, the resource total inequality constraint is transformed into an equality constraint. An augmented Lagrangian function containing penalty terms for decision variables and slack variables is constructed, and Lagrangian multipliers are assigned to the equality constraint. The partial derivatives of the augmented Lagrangian function with respect to the decision variables and slack variables are calculated and set to zero, and the partial derivative equation is rewritten as an implicit mapping relationship of the decision variables. A compression mapping operator is constructed and the Lipshitz constant is calculated to verify the compressibility.

[0096] Initialize decision variables, slack variables, and penalty coefficients. Substitute the current decision variables into the compression mapping operator to obtain the mapping value. Calculate the residual vector between the mapping value and the current value. Extract the infinite norm of the residual vector as the convergence index. Adaptively adjust the penalty coefficient according to the magnitude of the convergence index. Update the mapping value to the current value and repeat the iteration. When the convergence index is lower than the threshold, terminate the iteration and output the final decision variable as the equilibrium strategy parameter.

[0097] After obtaining the coordinates for the dimensionality reduction strategy, the coordinate sequence is represented as a d-dimensional vector X, where d is the dimension of the retained subspace. The bidding probability aggregation distribution of each competitive group is extracted, and the quantile values ​​of the distribution are sampled at fixed intervals to form a sample set. The covariance matrix between the sample set and the dimensionality reduction coordinate sequence is calculated. Eigenvalue decomposition is performed on the covariance matrix to obtain... Extract the diagonal matrix The largest eigenvalue in the middle Construct a risk measurement function This function characterizes the degree to which a decision deviates from mainstream market behavior. The probability of winning a bid in period t is modeled as... , where k is the sensitivity coefficient, determined through maximum likelihood estimation of historical winning bids. Let r be the unit return for period t. t The objective function is calculated as the ratio of the target value to the bidding cost. It is defined as the sum of expected revenues for each period, where T is the planning time domain length. The expression is:

[0098] .

[0099] Total resource constraints are represented by a budget or display limit, denoted as ,in For the resource consumption in period t corresponding to the decision variable, a nonnegative slack variable is introduced. Rewrite the inequality as Constructing the augmented Lagrangian function:

[0100] ,

[0101] in It is a Lagrange multiplier. This is the penalty coefficient.

[0102] Regarding L and Taking the partial derivatives separately, we get and Rewrite the above equation in implicit form The step size Based on the adaptive selection of the gradient norm, the Lipshitz constant of the mapping is verified to be less than 1, ensuring the existence of the fixed point and the convergence of the iteration.

[0103] Initialize decision variables The mean vector of the dimension-reduced coordinates, slack variables Set the penalty coefficient to 10% of the total resources. Set it to 0.1, and in the k-th iteration, Substitution mapping operator calculation Synchronously update slack variables Calculate the residual vector. Extract its infinite norm As a convergence metric, when this metric exceeds twice the convergence threshold, the penalty coefficient is updated to... When the indicator is less than 0.5 times the threshold, update to Repeat the iteration until ,in Set to 10 -4 .

[0104] By introducing nonnegative slack variables, the resource total inequality constraint is transformed into an equality constraint. An augmented Lagrangian function is constructed, including penalty terms for decision variables and slack variables. Lagrange multipliers are assigned to the equality constraint, including:

[0105] Calculate the residual value of the resource total inequality constraint. For constraints with residual values ​​below the tightness threshold, introduce non-negative relaxation variables to transform them into equations. For constraints with residual values ​​above the tightness threshold, establish complementary relaxation conditions where the product of the relaxation variable and the residual is zero.

[0106] Calculate the difference vector between the decision variable and the center point of the feasible region, construct the covariance matrix of the difference vector, calculate the quadratic form of the difference vector with respect to the inverse of the covariance matrix to obtain the Mahalanobis distance, and apply an exponential mapping to construct a penalty term for the decision variable. Take the logarithm of each component of the slack variable vector, sum the logarithms, and take the negative value to construct a logarithmic barrier penalty term.

[0107] Add the original objective function to the penalty term of the decision variable, subtract the logarithmic obstacle penalty term and multiply by the obstacle parameter to obtain the obstacle objective function. Assign Lagrange multiplier vectors to the equality constraints and complementary relaxation conditions. Construct the inner product of the multiplier vector and the constraint residual vector to form a bilinear constraint term. Add the bilinear constraint term to the obstacle objective function to form the augmented Lagrange function.

[0108] We establish the primal optimality condition by taking the partial derivatives of the augmented Lagrange function with respect to the decision variable and the slack variable, and establish the dual feasibility condition by taking the partial derivatives with respect to the Lagrange multiplier vector.

[0109] In establishing the equilibrium equations using the Lagrange multiplier method, the total resource constraint needs to be transformed into a canonical form for numerical solution. The original resource constraint states that the sum of the bidding decision variables in each period does not exceed the total budget limit. This inequality constraint can lead to instability in the iteration direction during numerical optimization. A constraint transformation mechanism is used to address this issue. The residual value of the inequality constraint is calculated, which is equal to the difference between the right-hand side and the left-hand side. When this difference is lower than a preset tightness threshold, it indicates that the current iteration point is close to the constraint boundary. At this point, a non-negative slack variable is introduced so that the residual value plus the slack variable equals zero, thus transforming the inequality into an equality constraint. For constraints with residual values ​​higher than the tightness threshold, it indicates that the constraint is in a non-tight state, and complementary slack conditions need to be established, i.e., the product of the slack variable and the residual value is always equal to zero, ensuring that the slack variable only takes a positive value when the constraint is activated.

[0110] To prevent decision variables from deviating from a reasonable range during iteration, a penalty term is constructed to impose constraints on abnormal deviations. The difference vector between the current value of the decision variable and the center point of the feasible region is calculated. This center point can be determined by the mean of historical optimal solutions. A covariance matrix is ​​constructed for the difference vector. The diagonal elements of the covariance matrix reflect the variance of each dimension, while the off-diagonal elements reflect the correlation between dimensions. The transpose of the difference vector is multiplied by the inverse of the covariance matrix, and then multiplied again by the difference vector to obtain the square of the Mahalanobis distance. This distance metric considers the correlation structure between variables. An exponential function is applied to the Mahalanobis distance to form a penalty term for the decision variables. When the decision variable deviates far from the center point, the penalty term grows exponentially, thus generating a strong constraint. For the slack variable vector, to prevent its excessive value from causing the equality constraint to fail, the natural logarithm of each component is taken, summed, and negative to construct a logarithmic barrier penalty term. This penalty term tends towards positive infinity as the slack variable approaches zero, forcing the slack variable to remain strictly non-negative.

[0111] The original objective function, which is the sum of the product of the winning probability and the unit profit in each period, is added to the penalty term of the decision variable. This reflects the pursuit of maximizing profits while controlling the degree of decision deviation. The logarithmic obstacle penalty term multiplied by the obstacle parameter is subtracted from this sum. The obstacle parameter is initially set to a large positive value and gradually decreases with iterations to weaken the obstacle effect. After construction, the obstacle objective function is obtained, which includes both the profit term and the constraint penalty term. Lagrange multiplier vectors are assigned to the equality constraints and complementary relaxation conditions. The multiplier dimension of the equality constraints is equal to the number of equality constraints, and the multiplier dimension of the complementary relaxation conditions is equal to the number of non-tight constraints. The inner product of the multiplier vector and the constraint residual vector is calculated to form the bilinear constraint term. The constraint residual vector is formed by subtracting the right side from the left side of the equation. The obstacle objective function is added to the bilinear constraint term to form the augmented Lagrange function, which includes both the original variable and the dual variable.

[0112] Partial derivatives of the augmented Lagrange function with respect to both decision and slack variables are calculated. Setting these partial derivatives to zero establishes the initial optimality conditions. The partial derivatives of the decision variables include the derivative of the objective function with respect to that variable, the product of the penalty term's derivative with respect to the Mahalanobis distance and the Mahalanobis distance's derivative with respect to the decision variable, and the product of the multipliers in the bilinear term and the corresponding rows of the constraint Jacobian matrix. The partial derivatives of the slack variables include the product of the derivative of the logarithmic barrier term and the barrier parameter, and the corresponding multiplier component in the bilinear term. Taking the partial derivative with respect to the Lagrange multiplier vector is equivalent to extracting the constraint residual vector; setting this to zero establishes the dual feasibility conditions. This set of optimality conditions, together with the complementary slack conditions, constitutes a complete system of equilibrium equations. This system of equations is solved iteratively using fixed-point iterations, updating the decision variables, slack variables, and multiplier vectors until all variables converge to stable values, thereby determining the equilibrium strategy parameters that meet resource constraints.

[0113] Calculating the time-series rate of change of the transaction price series as a market volatility indicator, and using the market volatility indicator to perform a nonlinear mapping of the equilibrium strategy parameters to generate a real-time exit value, including:

[0114] Calculate the price difference scores for multiple consecutive moments in the transaction price sequence, sum the absolute values ​​of the price difference scores to obtain the cumulative volatility, calculate the price range of the transaction price sequence within the same time period, and divide the cumulative volatility by the price range to obtain the normalized market volatility index.

[0115] Construct a mapping table between the market volatility index and the adjustment intensity. When the market volatility index increases, the corresponding adjustment intensity increases non-linearly. Based on the current market volatility index, find the corresponding adjustment intensity value in the mapping table and extract the reference bid corresponding to the current market state from the equilibrium strategy parameters.

[0116] The initial bid value is obtained by multiplying the reference bid price by the adjustment intensity value. The deviation between the latest price and the historical average price of the transaction price sequence is calculated. The initial bid value is corrected based on the deviation. The corrected bid value is smoothed. The difference between the bid value and the bid value at the previous moment is calculated. When the absolute value of the difference exceeds the jump threshold, peak shaving is performed. The processed value is output as the real-time bid value.

[0117] After obtaining the equilibrium strategy parameters, the value needs to be adjusted according to real-time market fluctuations. This involves extracting the transaction price sequence from the most recent several bidding periods (e.g., the most recent 10 periods) from the aggregated market data, denoted as... Calculate the price difference between adjacent time points. Where i ranges from 1 to n-1, the absolute values ​​of each difference are summed to obtain the cumulative volatility, which reflects the severity of price fluctuations. Simultaneously, the highest and lowest transaction prices within this period are calculated; the difference between them is the price range, used to measure the overall range of price changes. Dividing the cumulative volatility by the price range eliminates the influence of price dimensions, resulting in the normalized market volatility index. A larger index value indicates more frequent and uneven market price changes.

[0118] A pre-established mapping table between market volatility indicators and adjustment strength is used. This table employs a piecewise nonlinear mapping rule. When the market volatility indicator is in a low-level range, a smaller adjustment strength corresponds to maintaining relatively stable pricing. When the volatility indicator enters a medium-level range, the adjustment strength increases exponentially, enabling pricing to respond quickly to market changes. When the volatility indicator exceeds a high threshold, the rate of increase in adjustment strength is limited to avoid overly aggressive pricing adjustments. Based on the currently calculated normalized market volatility indicator, its corresponding range is located in the mapping table. The corresponding adjustment strength value is obtained through linear interpolation or direct table lookup. A reference pricing value matching the current market state (such as the current time period and competition density) is extracted from the equilibrium strategy parameters. This reference pricing reflects the theoretically optimal pricing level under equilibrium conditions.

[0119] Multiplying the reference bid by the adjustment strength value yields the initial bid value, which already includes an initial response to market fluctuations. To further capture price trend anomalies, the difference between the latest price in the transaction price series and the historical average price (such as the arithmetic mean of the last 5 periods) is calculated. Dividing this difference by the historical average price yields the price deviation. When the deviation is positive and large, it indicates that the current market price is significantly higher than the average, requiring an appropriate increase in the bid to maintain competitiveness; when the deviation is negative, the bid is reduced to avoid wasting resources. The initial bid value is then linearly adjusted based on the deviation, with the adjustment coefficient typically set as a function of the deviation. The adjusted bid value reflects both volatility response and trend following.

[0120] The corrected bid value is smoothed by a moving average method using an exponentially weighted moving average. The current bid value is summed with the bid values ​​from previous bid times using exponentially decaying weights to suppress bid fluctuations caused by high-frequency noise. The difference between the smoothed bid value and the bid value from the previous bid time is calculated. When the absolute value of this difference exceeds a preset jump threshold (e.g., 15% of the bid value from the previous bid time), it is judged as an abnormal jump and triggers a peak-shaving mechanism. Peak-shaving reduces the portion exceeding the threshold proportionally, keeping the bid change within a reasonable range and preventing the bidding strategy from becoming unstable due to sudden data disturbances. After peak-shaving, the final value is output as the real-time bid value for the current bidding period. This bid value achieves a balance between responding to market fluctuations, tracking price trends, and maintaining strategy stability.

[0121] This invention also provides an intelligent bidding optimization system for real-time bidding, including:

[0122] The feature extraction unit is used to obtain its own bidding history and market aggregated data, and to statistically analyze the frequency distribution of bids, the rate of change of the magnitude of the bid, and the winning rate in segments according to the bidding cycle, and to splice them to form a bidding behavior feature vector.

[0123] The competition modeling unit is used to calculate the bidding probability distribution of competitors based on the aggregated market data using Bayesian inference, perform clustering of competitors through behavioral heterogeneity indicators, take a weighted average of the bidding probabilities of each group to form an aggregated distribution, and calculate the mutual information matrix in combination with the bidding behavior feature vector.

[0124] The dimension reduction projection unit is used to perform singular value decomposition on the mutual information matrix, sort the singular values ​​by size, select the left singular vector whose cumulative contribution reaches the retention threshold as the subspace basis, and project the bidding behavior feature vector onto the subspace to obtain the dimension reduction strategy coordinates.

[0125] The equilibrium solution unit is used to construct an objective function that uses the reduced coordinates as decision variables to construct the sum of the products of the winning probability and the unit revenue in each cycle. After introducing resource constraints, the equilibrium equation system is established by the Lagrange multiplier method. The system is updated round by round using fixed-point iteration. When the difference between adjacent solutions is lower than the convergence threshold, the equilibrium strategy parameters are output.

[0126] The volatility mapping unit is used to extract the transaction price sequence of continuous bidding cycles from the market aggregated data, calculate the time-series change rate of the transaction price sequence as a market volatility indicator, and use the market volatility indicator to perform nonlinear mapping on the equilibrium strategy parameters to generate real-time output value.

[0127] A third aspect of the present invention provides an electronic device, comprising:

[0128] processor;

[0129] Memory used to store processor-executable instructions;

[0130] The processor is configured to invoke instructions stored in the memory to execute the aforementioned method.

[0131] A fourth aspect of the present invention provides a computer-readable storage medium having stored thereon computer program instructions that, when executed by a processor, implement the aforementioned method.

[0132] This invention can be a method, apparatus, system, and / or computer program product. The computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for performing various aspects of the invention.

[0133] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for intelligent bid optimization in real-time bidding, characterized in that, include: Obtain its own bidding history and market aggregated data, and statistically analyze the frequency distribution of bids, the rate of change of bid magnitude, and the success rate in segments according to the bidding cycle, and splice them together to form a bidding behavior feature vector; Based on the aggregated market data, Bayesian inference is used to calculate the bidding probability distribution of competitors. Competitors are clustered using behavioral heterogeneity indicators. The bidding probabilities of each group are weighted and averaged to form an aggregated distribution. The mutual information matrix is ​​calculated in combination with the bidding behavior feature vector. Singular value decomposition is performed on the mutual information matrix, and the singular values ​​are sorted by size. The left singular vectors whose cumulative contribution reaches the retention threshold are selected as the basis of the subspace. The bidding behavior feature vectors are projected onto the subspace to obtain the dimensionality reduction strategy coordinates. Using the reduced coordinates as decision variables, an objective function is constructed to be the sum of the product of the winning probability and the unit revenue in each cycle. After introducing resource constraints, an equilibrium equation system is established by the Lagrange multiplier method. Fixed-point iteration is used to update the equations round by round. When the difference between adjacent solutions is lower than the convergence threshold, the equilibrium strategy parameters are output. Extract the transaction price sequence of continuous bidding cycles from the market aggregated data, calculate the time-series change rate of the transaction price sequence as a market volatility indicator, and use the market volatility indicator to perform nonlinear mapping on the equilibrium strategy parameters to generate real-time output value.

2. The method according to claim 1, characterized in that, Based on the aggregated market data, Bayesian inference is used to calculate the bidding probability distribution of competitors. Competitors are clustered using behavioral heterogeneity indicators. A weighted average of the bidding probabilities for each cluster is taken to form an aggregated distribution. The mutual information matrix is ​​then calculated using the bidding behavior feature vectors, including: Extract the price range width and median of each bidding period, and calculate their ratio as a price dispersion index. Map the price dispersion index to the variance parameter of the Bayesian likelihood function. The market transaction price distribution is divided into multiple non-overlapping sub-intervals. The transaction frequency of each sub-interval is counted to construct an observation vector. Combined with the conjugate prior distribution, Bayesian inference is used to calculate the bidding probability of the competitors in each sub-interval. The vectors are then spliced ​​together to form the bidding probability distribution of the competitors. The information entropy and skewness coefficient of the competitor's bid probability distribution are calculated as behavioral heterogeneity indicators. In the two-dimensional feature space composed of the information entropy and the skewness coefficient, each competitor is clustered. The mode position of the competitor's bid probability distribution in each cluster is extracted. The reciprocal distance from the mode position to the cluster center is used as the weight to perform a weighted average of the bid probability distribution within the cluster. The average distribution of each cluster is then weighted twice according to the cluster size proportion to obtain the competitor aggregate distribution. The aggregated distribution of the competitors and the feature vector of the bidding behavior are aligned in a grid along the price dimension. The joint distribution entropy and the marginal distribution entropy after alignment are calculated, and a mutual information matrix is ​​constructed based on the difference in entropy.

3. The method according to claim 2, characterized in that, The market transaction price distribution is divided into multiple non-overlapping sub-intervals. The transaction frequency of each sub-interval is statistically analyzed to construct an observation vector. Combined with the conjugate prior distribution, Bayesian inference is used to calculate the bidding probability of competitors in each sub-interval. These vectors are then concatenated to form the competitor bidding probability distribution, including: Quantile analysis is performed on the market transaction price distribution to extract multiple quantile points and divide the price space into multiple non-overlapping sub-intervals, ensuring that each sub-interval is connected end to end on the price axis and there is no overlapping area. The interval identifier and interval boundary value of each sub-interval are stored. Based on the transaction price sequence in the market transaction price distribution, each transaction price is compared with the interval boundary value of each sub-interval to determine the attribution relationship. The number of transactions in each sub-interval is accumulated to obtain the transaction frequency. The transaction frequency of each sub-interval is associated with the corresponding interval identifier to construct an observation vector. Select a conjugate prior distribution type that matches the probability distribution form of the observed vector, set the initial value of the hyperparameter of the conjugate prior distribution based on historical market data, input the observed vector into the Bayesian inference framework, and obtain the estimated bid probability of the competitor in each sub-interval through posterior probability calculation. The normalization constraints of the bid probability estimates are tested. Bid probability estimates that do not meet the normalization conditions are normalized and corrected. The corrected bid probability estimates are then concatenated into a one-dimensional vector according to the increasing order of price in each sub-interval, forming the bid probability distribution of the competitors.

4. The method according to claim 1, characterized in that, Singular value decomposition is performed on the mutual information matrix, and the singular values ​​are sorted by size. Left singular vectors whose cumulative contribution reaches the retention threshold are selected as the basis of the subspace. The bidding behavior feature vectors are projected onto the subspace to obtain the dimensionality reduction strategy coordinates, including: Perform singular value decomposition on the mutual information matrix to obtain a left singular vector matrix and a singular value diagonal matrix. Extract the singular value sequence from the main diagonal of the singular value diagonal matrix. Arrange the singular value sequence in descending order of value. Record the mapping relationship between the original index and the new index of each singular value. Adjust the column vector arrangement order of the left singular vector matrix synchronously according to the mapping relationship. Calculate the square of each singular value after sorting, and use the ratio of each square value to the sum of all square values ​​as the variance contribution. Calculate the cumulative value of the variance contribution. When the cumulative value reaches the retention threshold, extract the corresponding column vectors from the sorted left singular vector matrix to form a subspace basis matrix. Calculate the inner product between the bidding behavior feature vector and each column vector of the subspace basis matrix, and arrange the inner product values ​​in column vector order to form the dimensionality reduction strategy coordinates.

5. The method according to claim 1, characterized in that, Using the reduced coordinates as decision variables, an objective function is constructed to be the sum of the products of the winning probability and the unit revenue in each cycle. After introducing resource constraints, an equilibrium equation system is established using the Lagrange multiplier method. Fixed-point iteration is used to update the equations round by round. When the difference between adjacent solutions is lower than the convergence threshold, the equilibrium strategy parameters are output, including: Calculate the covariance matrix of the coordinates of the dimensionality reduction strategy and the aggregate distribution of the competitors, perform eigenvalue decomposition on the covariance matrix to extract the maximum eigenvalue and construct a risk measurement function, express the winning probability of each period as a composite function of the decision variables mapped by the risk measurement function, and calculate the cumulative sum of the composite function and the unit return in each period to form the objective function. By introducing nonnegative slack variables, the resource total inequality constraint is transformed into an equality constraint. An augmented Lagrangian function containing penalty terms for decision variables and slack variables is constructed, and Lagrange multipliers are assigned to the equality constraint. The partial derivatives of the augmented Lagrangian function with respect to the decision variables and slack variables are calculated and set to zero, and the partial derivative equation is rewritten as an implicit mapping relationship of the decision variables. A compression mapping operator is constructed and the Lipshitz constant is calculated to verify the compressibility. Initialize decision variables, slack variables, and penalty coefficients. Substitute the current decision variables into the compression mapping operator to obtain the mapping value. Calculate the residual vector between the mapping value and the current value. Extract the infinite norm of the residual vector as the convergence index. Adaptively adjust the penalty coefficient according to the magnitude of the convergence index. Update the mapping value to the current value and repeat the iteration. When the convergence index is lower than the threshold, terminate the iteration and output the final decision variable as the equilibrium strategy parameter.

6. The method according to claim 5, characterized in that, By introducing nonnegative slack variables, the resource total inequality constraint is transformed into an equality constraint. An augmented Lagrangian function is constructed, including penalty terms for decision variables and slack variables. Lagrange multipliers are assigned to the equality constraint, including: Calculate the residual value of the resource total inequality constraint. For constraints with residual values ​​below the tightness threshold, introduce non-negative relaxation variables to transform them into equations. For constraints with residual values ​​above the tightness threshold, establish complementary relaxation conditions where the product of the relaxation variable and the residual is zero. Calculate the difference vector between the decision variable and the center point of the feasible region, construct the covariance matrix of the difference vector, calculate the quadratic form of the difference vector with respect to the inverse of the covariance matrix to obtain the Mahalanobis distance, and apply an exponential mapping to construct a penalty term for the decision variable. Take the logarithm of each component of the slack variable vector, sum the logarithms, and take the negative value to construct a logarithmic barrier penalty term. Add the original objective function to the penalty term of the decision variable, subtract the logarithmic obstacle penalty term and multiply by the obstacle parameter to obtain the obstacle objective function. Assign Lagrange multiplier vectors to the equality constraints and complementary relaxation conditions. Construct the inner product of the multiplier vector and the constraint residual vector to form a bilinear constraint term. Add the bilinear constraint term to the obstacle objective function to form the augmented Lagrange function. We establish the primal optimality condition by taking the partial derivatives of the augmented Lagrange function with respect to the decision variable and the slack variable, and establish the dual feasibility condition by taking the partial derivatives with respect to the Lagrange multiplier vector.

7. The method according to claim 1, characterized in that, Calculating the time-series rate of change of the transaction price series as a market volatility indicator, and using the market volatility indicator to perform a nonlinear mapping of the equilibrium strategy parameters to generate a real-time exit value, including: Calculate the price difference scores for multiple consecutive moments in the transaction price sequence, sum the absolute values ​​of the price difference scores to obtain the cumulative volatility, calculate the price range of the transaction price sequence within the same time period, and divide the cumulative volatility by the price range to obtain the normalized market volatility index. Construct a mapping table between the market volatility index and the adjustment intensity. When the market volatility index increases, the corresponding adjustment intensity increases non-linearly. Based on the current market volatility index, find the corresponding adjustment intensity value in the mapping table and extract the reference bid corresponding to the current market state from the equilibrium strategy parameters. The initial bid value is obtained by multiplying the reference bid price by the adjustment intensity value. The deviation between the latest price and the historical average price of the transaction price sequence is calculated. The initial bid value is corrected according to the deviation. The corrected bid value is smoothed. The difference between the bid value and the bid value at the previous moment is calculated. When the absolute value of the difference exceeds the jump threshold, peak shaving is performed. The processed value is output as the real-time bid value.

8. An intelligent bidding optimization system for real-time bidding, used to implement the method as described in any one of claims 1-7, characterized in that, include: The feature extraction unit is used to obtain its own bidding history and market aggregated data, and to statistically analyze the frequency distribution of bids, the rate of change of the magnitude of the bid, and the success rate in segments according to the bidding cycle, and to splice them together to form a feature vector of bidding behavior. The competition modeling unit is used to calculate the bidding probability distribution of competitors based on the aggregated market data using Bayesian inference, perform clustering of competitors through behavioral heterogeneity indicators, take a weighted average of the bidding probabilities of each group to form an aggregated distribution, and calculate the mutual information matrix in combination with the bidding behavior feature vector. The dimension reduction projection unit is used to perform singular value decomposition on the mutual information matrix, sort the singular values ​​by size, select the left singular vector whose cumulative contribution reaches the retention threshold as the subspace basis, and project the bidding behavior feature vector onto the subspace to obtain the dimension reduction strategy coordinates. The equilibrium solution unit is used to construct an objective function that uses the reduced coordinates as decision variables to construct the sum of the products of the winning probability and the unit revenue in each cycle. After introducing resource constraints, the equilibrium equation system is established by the Lagrange multiplier method. The system is updated round by round using fixed-point iteration. When the difference between adjacent solutions is lower than the convergence threshold, the equilibrium strategy parameters are output. The volatility mapping unit is used to extract the transaction price sequence of continuous bidding cycles from the market aggregated data, calculate the time-series change rate of the transaction price sequence as a market volatility indicator, and use the market volatility indicator to perform nonlinear mapping on the equilibrium strategy parameters to generate real-time output value.

9. An electronic device, characterized in that, include: processor; Memory used to store processor-executable instructions; The processor is configured to invoke instructions stored in the memory to execute the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having computer program instructions stored thereon, characterized in that, When the computer program instructions are executed by the processor, they implement the method described in any one of claims 1 to 7.

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