How to calculate the decision variables

Abstract

To provide a calculation method of a decision variable, capable of calculating a decision variable which can achieve an effect of reverse estimation of the decision variable, without training in common, a shared model by combination learning, by members of the combination learning.SOLUTION: A reverse estimation request person can calculate, a desired decision variable by reverse estimation, according to a target result, by a learned prediction model provided from some members of combination learning, in a calculation method of the decision variable, the method includes: reverse estimation of an input parameter by providing a target result to the learned prediction model related to the method; formation of a loss function, from a difference between each learned prediction model and the target result; integration of all input parameters subjected to reverse estimation, to an integrated input parameter, integration of all loss functions to an integrated loss function, construction of an optimized problem, by the integrated input parameter and integrated loss function for determining a solution thereof, the solution determined from the optimized problem is a desired decision variable.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a method for calculating decision variables, and more particularly to a method for inversely estimating decision variables that match a target outcome using multiple trained artificial intelligence prediction models provided by members of federated learning. [Background technology]

[0002] With advances in medical engineering technology, the applications of regenerative medicine in clinical disease treatment have become increasingly diverse, and its research and applications have attracted increasing attention from various fields. Currently, regenerative medicine is mainly applied to organ repair, immune cell therapy, and stem cell therapy. Cell therapy involves culturing or processing human cells ex vivo, then transplanting the cultured cells into an individual's body. Therefore, effective cell cultivation is a crucial element in regenerative medicine. Previous research has shown that each individual's cells have unique characteristics, making it necessary to customize cells suitable for each individual's treatment, increasing the complexity and difficulty of cellular processes. On the other hand, with the availability of large amounts of cell and bioprocess data, machine learning can generate predictive models to evaluate the effects of individual cell culture conditions and process parameters. Therefore, machine learning can reduce the complexity and difficulty of customizing cellular processes. However, most of this cell and bioprocess data, such as patient cell data from various hospitals or laboratories, is highly sensitive and confidential personal data. When using conventional aggregated machine learning methods, all bioprocess data must be aggregated on a central server for analysis and training, which may be impractical due to constraints such as regulations, privacy protection, and commercial considerations. Furthermore, aggregated machine learning methods may face similar problems not only in biomedical engineering but also in any technical field where data is highly sensitive and confidential.

[0003] Federated learning, also known as collaborative learning, is a type of machine learning technique that trains algorithms on multiple distributed edge devices or servers with local data samples. This approach differs significantly from traditional centralized machine learning techniques, which upload all local datasets to a single server for machine learning training. In contrast, federated learning is performed by multiple members. Each member individually trains its own dataset to generate a trained predictive model and uploads the trained predictive model parameters to a central server. The central server then weights and aggregates all the trained predictive model parameters to form a federated model. This federated model can then be redistributed to each member for use. The central server only aggregates the trained predictive model parameters; it does not directly analyze or process each member's dataset for machine learning. This prevents sensitive and confidential data samples and information from each member's dataset from being leaked, protecting the confidentiality of the data.

[0004] The federated model formed by the above-mentioned federated aggregation algorithm can not only generate prediction results for input decision variables, but also, conversely, inversely estimate the decision variables that should be input to a target result. However, compared to developing an inverse estimation function for a jointly trained and shared unified model, although members participating in the federated learning method can individually develop inverse estimation functions using predictive models trained on their own local datasets, the inverse estimation results may not be as ideal. In addition, when a unit other than a federated member wants to collaborate with a member with good predictive or inverse estimation results, it is not possible to determine which federated member's predictive model best meets the needs of that unit by simply testing the effectiveness of the jointly developed federated model.

[0005] In addition, while federated learning prevents highly sensitive and confidential data samples in each member's dataset from leaking to the outside, it does require the central server and each member to exchange model parameters. Therefore, the method of obtaining decision variables by performing inverse estimation using a jointly developed federated model not only involves a complex process, but also requires the members to exchange model parameters directly or indirectly.

[0006] Therefore, in order to solve the problems of complexity and model confidentiality when inversely estimating decision variables using a federated model, it is necessary to develop a method that allows federated learning members to inversely estimate decision variables without jointly calculating a shared predictive model using a federated learning algorithm. Summary of the Invention [Problem to be solved by the invention]

[0007] In view of the above, the present invention provides a method for calculating decision variables to solve the above-mentioned conventional problems. [Means for solving the problem]

[0008] According to a specific embodiment of the present invention, a method for calculating decision variables includes the steps of: providing a plurality of trained predictive models, each of which is obtained by machine learning a plurality of local datasets using a machine learning method; providing a target result and inversely estimating a plurality of input parameters for the target result using the trained predictive models; configuring a plurality of loss functions corresponding to the trained predictive models, each of which is assigned a first weight value and then summed to generate a comprehensive loss function, wherein each of the loss functions is defined as the absolute value, square of the difference between the function value of an objective function representing each of the trained predictive models and the target result, or a function having a monotonically increasing characteristic with respect to the difference value; generating comprehensive input parameters by assigning second weight values ​​to the input parameters and then summing them, and formulating an optimization problem using the comprehensive input parameters and the comprehensive loss function; and solving the optimization problem to obtain the second weight value for each of the input parameters and calculate the comprehensive input parameters as the decision variables.

[0009] The method for calculating decision variables further includes the steps of: calculating derivatives of the overall loss function for each of the second weight values; combining the derivatives to form a direction; and inputting the overall input parameters into the trained predictive model after increasing the step size along the direction to determine whether the function value of the overall loss function decreases.

[0010] The trained predictive models are each provided by multiple members of a federated learning model.

[0011] In the method for calculating decision variables, the step of inversely estimating the input parameters for each of the target outcomes using the trained predictive model further includes a step by a first member of the members comparing the target outcome with all samples in a corresponding first local dataset among the local datasets, and selecting samples in the first local dataset that match the target outcome as reference samples for inversely estimating the input parameters.

[0012] In the method for calculating decision variables, the step of inversely estimating the input parameters for each of the target results using the trained predictive model further includes the steps of: a second member of the members comparing the target result with all samples in a corresponding second local dataset among the local datasets to obtain multiple anchor samples and forming a multidimensional subspace using the anchor samples; determining an initial sample within the multidimensional subspace; obtaining a direction of the initial sample within the multidimensional subspace and forming relay samples by increasing a step size along the direction for the initial sample; and inputting the relay samples into a second trained predictive model provided by the second member to confirm whether the generated prediction result is close to the target result; continuing to perform the operations of determining the direction and inputting the relay samples with the increased step size into the second trained predictive model until the prediction result generated by the second trained predictive model matches the target result, and setting the final relay sample as the input parameter corresponding to the second trained predictive model.

[0013] In the method for calculating decision variables, the step of inversely estimating the input parameters for each of the target results using the trained predictive models further includes the steps of: a third member among the members setting a dummy layer connected to an input terminal of a corresponding third trained predictive model to form a parameter predictive model, the dummy layer becoming the input terminal of the parameter predictive model; setting the output of the parameter predictive model to the target result; inputting a training dataset including at least one all-ones vector into the parameter predictive model to train the parameter predictive model; and adjusting multiple arc weight values ​​between the dummy layer and the third trained predictive model using an optimizer in a machine learning method that trained the third trained predictive model, and setting the arc weight values ​​as the input parameters corresponding to the third trained predictive model.

[0014] In the method for calculating decision variables, the step of inversely estimating the input parameters for the target result using the trained predictive model further includes a step in which a fourth member of the members compares the target result with all samples of a corresponding fourth local dataset among the local datasets to obtain a plurality of anchor samples, and forms a multidimensional subspace using the anchor samples; a step in which the fourth member determines an initial sample in the multidimensional subspace; and a step in which the fourth member obtains a gradient by performing a minimization operation on the objective function of the fourth trained predictive model using an optimizer used to generate the fourth trained predictive model. and setting the opposite direction of the gradient as the direction of the initial sample; forming relay samples by increasing the step size along the direction of the initial sample and inputting the relay samples into the fourth trained prediction model to check whether the generated prediction result is close to the target result; continuing to perform the operations of determining the direction and inputting the relay samples with the increased step size into the fourth trained prediction model until the prediction result generated by the fourth trained prediction model matches the target result, and setting the final relay sample as the input parameter corresponding to the fourth trained prediction model.

[0015] In the method for calculating decision variables, the step of inversely estimating the input parameters for the target outcome using the trained predictive model further includes the steps of: providing a plurality of confirmed decision variables and calculating a first vector of the confirmed decision variables; obtaining a plurality of corresponding sample parameters from sample parameters in all samples of the fourth local dataset based on the confirmed decision variables and calculating a second vector of the corresponding sample parameters; comparing the first vector with the second vector, and obtaining a reference sample by comparing the predicted results generated by the fourth trained predictive model for all samples of the fourth local dataset with the target outcome, wherein the second vector of the reference sample is close to or identical to the first vector, and the predicted result of the reference sample is close to or identical to the target outcome; and setting the reference sample as the initial sample.

[0016] The method for calculating a decision variable further includes the steps of providing a first test sample, the first test sample including a plurality of confirmed test input parameters and a test target result, and inputting the test input parameters into a plurality of candidate trained predictive models, and determining the candidate trained predictive model whose output result matches the target test result as the trained predictive model.

[0017] The method for calculating a decision variable further includes the steps of: providing a first test sample, the first test sample including a plurality of confirmed first test input parameters and a first test target result; inputting the first test input parameters into a plurality of candidate trained prediction models, and designating the candidate trained prediction models whose output results match the first test target result as a plurality of first candidate trained prediction models; providing a second test sample, the second test sample including a plurality of confirmed second test input parameters and a second target test result; and providing the second target test results to the first candidate trained prediction models, respectively, to have the first candidate trained prediction models inversely estimate a plurality of candidate first input parameters, and designating the first candidate trained prediction models whose first candidate input parameters match or are close to the second test input parameters or whose first candidate input parameters satisfy a validation process as the trained prediction models. [Effects of the Invention]

[0018] In summary, the decision variable calculation method of the present invention allows input parameters (i.e., decision variables) that match a specific target result to be inversely estimated using trained predictive models provided by multiple members of the federated learning, without the need to jointly calculate a shared model through federated learning. The method of the present invention allows a specific member of the federated learning or a unit outside the federated learning to request inverse estimation. Furthermore, since collaborators can be directly sought and selected without going through the federated model generated by federated learning, complex machine learning and inverse estimation processes can be avoided. Furthermore, the decision variable calculation method of the present invention does not require members of the federated learning to exchange highly sensitive and confidential data samples and information in the training dataset, nor does it require the exchange of model parameters of each member's trained predictive model. This not only reduces the complexity of the process, but also further protects the confidentiality of the data. [Brief explanation of the drawings]

[0019] [Figure 1]FIG. 1 shows a flow chart of the steps of a method for calculating decision variables according to an illustrative embodiment of the present invention. [Figure 2] FIG. 2 shows a flow chart of the further steps of step S18 in the method of calculating the decision variables of FIG. [Figure 3] FIG. 3 shows a flow chart of the steps of a method for calculating decision variables according to another embodiment of the present invention. [Figure 4] FIG. 4 shows a flow chart of the steps of a method for calculating decision variables according to another exemplary embodiment of the present invention. [Figure 5] FIG. 5 shows a flow chart of the steps of a method for calculating decision variables according to another exemplary embodiment of the present invention. [Figure 6] FIG. 6 shows a flow chart of the steps of a method for calculating decision variables according to another exemplary embodiment of the present invention. [Figure 7] FIG. 7 shows a flow chart of the steps of a method for calculating decision variables according to another exemplary embodiment of the present invention. [Figure 8] FIG. 8 shows a flow chart of the steps of a method for calculating decision variables according to another exemplary embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0020] To make the advantages, spirit, and features of the present invention more easily and clearly understandable, the present invention will be described and discussed in detail below using specific examples and with reference to the drawings. It should be noted that these specific examples are merely representative examples of the present invention, and the specific methods, devices, conditions, materials, etc. exemplified do not limit the present invention or the corresponding specific examples. Furthermore, the components in the drawings are used only to represent their relative positions and are not drawn to actual scale. Furthermore, the step numbers of the present invention are used only to distinguish different steps and do not represent the order of the steps. The above will be explained in advance.

[0021] Please refer to Figure 1. Figure 1 shows a flowchart of the steps of the calculation method for decision variables according to a specific embodiment of the present invention. As shown in Figure 1, the calculation method for decision variables in this specific embodiment includes the following steps:

[0022] Step S10: Providing a plurality of trained prediction models, each of which is obtained by machine learning the local dataset using a machine learning method.

[0023] Step S12: Provide a target result, and use the trained prediction model to inversely estimate a plurality of input parameters for the target result.

[0024] Step S14: A plurality of loss functions corresponding to the trained prediction model are set, and different first weight values ​​are set for these loss functions, and then the loss functions are summed to generate an overall loss function.

[0025] Step S16: A second weight value is assigned to each of the input parameters, and then the input parameters are summed to generate a comprehensive input parameter, and an optimization problem is constructed using the comprehensive input parameter and a comprehensive loss function.

[0026] Step S18: By solving the optimization problem, the second weight value of each input parameter is obtained, and the overall input parameter is calculated as the decision variable.

[0027] In this specific embodiment, the trained predictive models in step S10 are provided by each of the federated learning members. Specifically, each of the federated learning members may have its own AI model training device and its own local dataset. Therefore, each member can independently train its own AI predictive model. For example, in the field of regenerative medicine, each member's AI model training device may be a computer device capable of running machine learning algorithms in a hospital or laboratory. The local dataset is a sample dataset for training, validation, and testing held by the hospital or laboratory. In practice, each of the federated learning members can obtain its own trained predictive model by machine learning the local dataset using artificial neural networks (ANNs), convolutional neural networks (CNNs), recurrent neural networks (RNNs), or any other machine learning or neural network algorithms. The machine learning algorithm is selected according to the needs of each member. In addition, the trained prediction model in step S10 is a selected trained prediction model and is provided by only some of the members of the federated learning. In practice, each member of the federated learning has a different local data set, machine learning algorithm used, model parameter adjustment ability, and inverse estimation ability of the decision variables using the trained prediction model, so the trained prediction models of all members may not necessarily meet the requirements. The selection of the trained prediction model will be described in a specific example below.

[0028] In step S12, the members of the federated learning who provided the trained predictive models can inversely estimate input parameters based on the target results. Specifically, each member can use the same or different inverse estimation algorithm to match the target results with the output results of their respective trained predictive models, thereby inversely estimating input parameters such that the output results of the trained predictive models match the target results. The inverse estimation algorithms used by each member will be described in the specific examples below.

[0029] In step S14, a loss function can be set for each trained prediction model. The loss function can be defined as the absolute value or square of the difference between the function value of the objective function representing each trained prediction model and the target result, or any function that has a monotonically increasing characteristic with respect to the difference (e.g., the fourth or sixth power of the difference). In other words, the loss function represents the degree of approximation between the output result of each trained prediction model and the target result. The overall loss function is formed by weighting and then summing the loss functions corresponding to each trained prediction model. In practice, the weighting of each loss function (i.e., the first weight value) is determined based on the reliability or performance of each trained prediction model. For example, if a requester of inverse estimation selects and identifies one trained prediction model that has a high influence on the provided target result, or if the trained prediction model is identified as having a relatively accurate prediction rate and inverse estimation rate in testing, the first weight value of the loss function corresponding to that trained prediction model can be set higher than the loss functions corresponding to other trained prediction models.

[0030] Similarly, in step S16, a second weight value can be assigned to each input parameter that each trained predictive model has previously inversely estimated for the same target result. Unlike the first weight value in step S14, the second weight value is not a preset value but must be determined by calculation in a subsequent step. In steps S14 and S16, a comprehensive loss function and comprehensive input parameters corresponding to each trained predictive model are generated, and the optimal input parameters can be obtained by constructing an optimization problem and solving it.

[0031] In step S18, the method for solving the optimization problem is simply to find the overall input parameters with the smallest overall loss function. Since the input parameters of each trained predictive model in the overall input parameters are known, the second weight values ​​are obtained by solving the optimization problem. After obtaining all the second weight values, the overall input parameters can be calculated and used as the desired decision variables.

[0032] The method for solving the optimization problem described above can be performed by a numerical analysis method. Reference is now made to Fig. 2, which shows a flowchart of further steps of step S18 in the method for calculating the decision variables of Fig. 1. As shown in Fig. 2, the above step S18 may further include the following steps:

[0033] Step S180: Calculate the derivative of the overall loss function for each second weight value.

[0034] Step S182: The derivatives are combined to form a direction.

[0035] Step S184: After increasing the step size of the overall input parameters along the above direction, input the step size to all trained prediction models to determine whether the function value of the overall loss function decreases.

[0036] As described above, the overall input parameters are calculated by multiplying the multiple input parameters inversely estimated in step S12 by the second weights and then summing them. In other words, each second weight has a different effect on the final function value of the overall loss function. Therefore, in step S180 of the decision variable calculation method in this specific embodiment, the derivative of the overall loss function with respect to each second weight is calculated. That is, the change in the function value of the overall loss function formed with a small change in each second weight is calculated. Each derivative is the rate of change of the overall loss function with respect to each different second weight. Therefore, as shown in step S182, the above direction can be obtained by multiplying each derivative by the unit vector formed by each second weight and summing them. After the direction is determined in step S182, in step S184, an appropriate step size is set for this direction, and the overall input parameters after increasing the step size are substituted into the overall loss function to obtain an appropriate reduction value. Therefore, a new overall input parameter (advanced by one step) can obtain a function value of the overall loss function that is smaller than that of the previous overall input parameter. In other words, it is possible to get closer to the solution of the optimization problem. Steps S180 to S184 can be repeatedly executed until the smallest function value of the overall loss function is found, and the overall input parameter found becomes the solution to the optimization problem. In other words, this can be used as a decision variable.

[0037] For example, in a method for calculating decision variables, if trained prediction models provided by two members of federated learning are selected, a target result T is first provided to these two members. Then, using each trained prediction model, input parameters I1 and I2 that match the target result T are inversely estimated, and two loss functions L1 and L2 corresponding to these two trained prediction models are set. The loss functions L1 and L2 are the absolute values ​​|f1-T| and |f2-T| of the difference between the functions f1 and f2 representing each trained prediction model and the target result, respectively. Next, first weights α and 1-α are assigned to the two loss functions, respectively, and then summed to generate an overall loss function L = α × |f1-T| + (1-α) × |f2-T|. Second weights β and γ are assigned to the two input parameters I1 and I2, respectively, and then summed to generate an overall input parameter S 1 = β × I1 + γ × I2. The optimization problem constructed by the overall input parameters and the overall loss function is to minimize the overall loss function L by finding the optimal β, γ and overall input parameters when α, T, I1, and I2 are all fixed.

[0038] In the method for solving the optimization problem described above, first, the derivatives d1 and d2 of the overall loss function L with respect to the second weight values ​​β and γ are calculated, respectively. Next, a direction g = (d1 × (1,0) + d2 × (0,1)) is set. Note that (1,0) and (0,1) are unit vectors of β and γ, respectively. After the direction is found, a step size t is set along this direction, and the overall input parameter is advanced by the step size t in that direction to obtain a new overall input parameter S 2 =S 1 -t×g can be generated. Note that the derivatives d1 and d2 represent the gradient of the overall loss function with respect to β and γ, and the direction of the step size is opposite to the gradient. By adjusting the appropriate step size t, the new overall input parameter S after the step size is calculated. 2 After substituting into the overall loss function L, the reduced function value (the original overall input parameter S 1(Compared with the function value obtained by inputting the new overall input parameter S 2 The predicted result obtained by this method will be closer to the target result. By repeating the above-mentioned steps of calculating the direction and adjusting the step size, the overall input parameters that can obtain the smallest function value by substituting them into the overall loss function L can finally be obtained. These overall input parameters can be the decision variables to be calculated using the decision variable calculation method.

[0039] In the specific embodiment described above, in the method for calculating decision variables, a member of the federated learning or a unit outside the federated learning can request inverse estimation, and all members of the federated learning are invited as collaborators. However, in practice, the federated learning does not necessarily have to be a member of the federated learning, and collaborators do not have to be members of the federated learning, as long as they can independently train the trained predictive model and use the trained predictive model to inversely estimate input parameters.

[0040] As described above, in step S12, the members of the federated learning first inversely estimate input parameters using a trained predictive model based on the target result provided by the inverse estimation requester. The inverse estimation method includes, but is not limited to, several aspects described below. Now, please refer to FIG. 3, which shows a flowchart of steps of a method for calculating decision variables according to another specific embodiment of the present invention. As shown in FIG. 3, the method for calculating decision variables in this specific embodiment further includes the following steps:

[0041] Step S120: The members of the federated learning compare all samples in the local dataset with the target result.

[0042] Step S122: The samples in the local dataset that match the target results are taken as reference samples for inversely estimating the input parameters.

[0043] It should be noted that in addition to the above steps, the method of this specific embodiment further includes step S10 and steps S14 to S18 in the specific embodiment described above, but since the contents of these are the same as the corresponding steps in the specific embodiment described above, they will not be described in detail again here.

[0044] In this specific example, a first member of the federated learning can use samples in the first local dataset used when training the trained predictive model as reference samples to inversely estimate input parameters. Specifically, if a confirmed decision variable (e.g., a parameter already implemented in a process) exists for the decision variable to be inversely estimated, the confirmed decision variables can be used as a vector. Similarly, corresponding sample parameters corresponding to the confirmed decision variables in all samples in the first local dataset can be used as another vector, and the two vectors can be compared to find samples that are similar or match. These samples have corresponding sample parameters similar to the confirmed decision variables. This means that these samples have high reference value. Therefore, other sample parameters that do not correspond to the confirmed decision variables in these samples can be input into the trained predictive model together with the confirmed decision variables, and the predicted results output by the trained predictive model can be confirmed to match the target result. If the predicted result matches the target result, the other sample parameters that do not correspond to the confirmed decision variables in this sample and the confirmed decision variables can be used as input parameters (e.g., the input parameter I1).

[0045] Please refer to Figure 4. Figure 4 shows a flowchart of the steps of a method for calculating decision variables according to another embodiment of the present invention. As shown in Figure 4, the method for calculating decision variables in this embodiment further includes the following steps:

[0046] Step S120': The members of the federated learning compare all samples in the local dataset with the target result to obtain multiple anchor samples, and form a multidimensional subspace using the anchor samples.

[0047] Step S122': Determine an initial sample in the multidimensional subspace.

[0048] Step S124': Obtain the direction of the initial sample in the multidimensional subspace, and form relay samples by increasing the step size along the direction of the initial sample, and input the relay samples into the trained prediction model to check whether the generated prediction result is close to the target result.

[0049] Step S126': The operation of inputting the relay samples whose direction has been determined and whose step size has been increased into the trained prediction model is continued until the prediction result generated by the trained prediction model matches the target result, and the last relay sample is used as the input parameter corresponding to the trained prediction model.

[0050] It should be noted that in addition to the above steps, the method of this specific embodiment further includes step S10 and steps S14 to S18 in the specific embodiment described above, but since the contents of these are the same as the corresponding steps in the specific embodiment described above, they will not be described in detail again here.

[0051] In step S120', the local dataset is formed from samples used to train the trained prediction model, so both the input and output results of the samples for the trained prediction model are known. Furthermore, samples whose output results closely match or are identical to the target result have high reference value and can be extracted as reference samples. Therefore, in this specific embodiment, these samples are used as anchor samples to form a multidimensional subspace, which then becomes the feasible solution space for the optimization problem. Steps S122', S124', and S126' are a method for finding the optimal feasible solution within the feasible solution space. Briefly, an initial point (initial sample) is first determined within the feasible solution space. Then, a numerical analysis method is used to find the direction of the initial point and adjust the step size, and the prediction result output from the trained prediction model is advanced to the next point (intermediate sample) that brings the prediction result closer to the target result. The above direction search and step size adjustment are repeated, and when the prediction result output from the trained prediction model most closely matches or is identical to the target result, that point is used as the input parameter. It should be noted that the method for determining the initial point or initial sample in the above-mentioned multi-dimensional subspace can be specified by the members of the federated learning, or by first finding a sample that is close to or coincides with the confirmed decision variable through similar steps in the specific embodiment of FIG.

[0052] Please refer to Figure 5. Figure 5 shows a flowchart of the steps of a method for calculating decision variables according to another embodiment of the present invention. As shown in Figure 5, the method for calculating decision variables in this embodiment further includes the following steps:

[0053] Step S120: The members of the federated learning configure a dummy layer to be connected to the input terminal of the trained prediction model, and form a parameter prediction model. The dummy layer becomes the input terminal of the parameter prediction model.

[0054] Step S122: Set the output of the parameter prediction model as the target result, input a training dataset containing at least one all-ones vector to the parameter prediction model to train the parameter prediction model, and then adjust multiple arc weights between the dummy layer and the trained prediction model using an optimizer in the machine learning method used to train the trained prediction model, and use these arc weights as input parameters of the trained prediction model.

[0055] It should be noted that in addition to the above steps, the method of this specific embodiment further includes step S10 and steps S14 to S18 in the specific embodiment described above, but since the contents of these are the same as the corresponding steps in the specific embodiment described above, they will not be described in detail again here.

[0056] The newly added dummy layer in step S120'' is used together with the original trained prediction model to form a parameter prediction model, which is an extended model. In practice, the dummy layer includes the same number of artificial neurons as the number of input points in the input layer of the trained prediction model. The artificial neurons can be connected to each of these input points. The bias value of the activation function of each artificial neuron is set to 0. As a result, when the input value of the activation function is 1, the output is also 1. It should be noted that although the trained prediction model forms a parameter prediction model together with the dummy layer, the model parameters of the trained prediction model are fixed in subsequent training. Furthermore, since an input of 1 to an artificial neuron also results in an output of 1, if the output of the parameter prediction model is a fixed result (e.g., set to the above-mentioned target result), the optimizer adjusts the input of the trained prediction model by adjusting the arc weights between each artificial neuron and each input point of the trained prediction model. Therefore, in step S122'', the output of the parameter prediction model can be set to the target result, and the arc weights obtained by training by inputting a training dataset including an all-ones vector can be used as input parameters of the trained prediction model. Similarly, in practice, a sample that approximates or matches the confirmed decision variables may first be found by following similar steps in the specific embodiment of FIG. 3, and the sample parameters may be used as the initial point for the optimizer to adjust the arc weights.

[0057] In practice, types of optimizers include Adaptive Moment Estimation (Adam), Stochastic Gradient Descent (SGD), Momentum, Nesterov Accelerated Gradient (NAG), Adaptive Gradient Algorithm (AdaGrad), Nadam (Nesterov-accelerated Adaptive Moment Estimation), Root Mean Square Propagation (RMSprop), Adaptive Delta (Adadelta), AdamW (Adam with Weight Decay), Adaptive Moment Estimation with Long-term Memory (AMSGrad), Adaptive Belief (AdaBelief), Layer-wise Adaptive Rate Scaling (LARS), Self-adaptive Hessian (AdaHessian), and Rectified Random Adaptation (RAdam). The optimizer may be Adam, Lookahead, MadGrad (Momentumized, Adaptive, and Decentralized Gradient Descent), Yogi optimizer, and AdamMax (Adaptive Moment Estimation with Maximum).

[0058] Please refer to Figure 6. Figure 6 shows a flowchart of the steps of a method for calculating decision variables according to another embodiment of the present invention. As shown in Figure 6, the method for calculating decision variables in this embodiment further includes the following steps:

[0059] Step S120': Each member of the federated learning compares all samples in the local dataset with the target result to obtain multiple anchor samples, and forms a multidimensional subspace using these anchor samples.

[0060] Step S122': Determine the initial sample in the multidimensional subspace.

[0061] Step S124': The optimizer that generated the trained prediction model performs a minimization operation on the objective function of the trained prediction model to obtain a gradient, and the direction opposite to the gradient is set as the direction of the initial sample.

[0062] Step S126': Generate relay samples by increasing the step size along the direction of the initial sample, and input the relay samples into the trained prediction model to check whether the generated prediction result is close to the target result.

[0063] Step S128': Continue inputting the relay samples whose direction has been determined and whose step size has been increased into the trained prediction model until the prediction result generated by the trained prediction model matches the target result, and use the last relay sample as an input parameter of the trained prediction model.

[0064] It should be noted that in addition to the above steps, the method of this specific embodiment further includes step S10 and steps S14 to S18 in the specific embodiment described above, but since the contents of these are the same as the corresponding steps in the specific embodiment described above, they will not be described in detail again here.

[0065] In this specific embodiment, the method of calculating the decision variables is similar to the above-described specific embodiment in that anchor samples are first found to form a feasible solution space (a multidimensional subspace), and an initial sample is predetermined within this feasible solution space. However, this specific embodiment differs from the above-described specific embodiment in the following respects. In this specific embodiment, the direction of the initial sample or subsequent relay samples is determined by calculation using an optimizer that trains the trained predictive model. Specifically, the optimizer can obtain a gradient by performing a minimization operation on an objective function representing the trained predictive model, and the direction opposite to the gradient can be used as the direction of the initial sample or subsequent relay samples. Next, using the direction calculated by the optimizer, the initial sample or relay samples are advanced by an appropriate step size to approach the target result. Then, when the trained predictive model's output matches the target result, the relay samples can be used as input parameters for the trained predictive model. Also, similar to the specific embodiment described above, the method for determining the initial point or initial sample in the multidimensional subspace in this specific embodiment may be to first find a sample that is close to or matches the confirmed decision variable and use it as the initial sample, using similar steps as in the specific embodiment of FIG.

[0066] According to the above-described specific embodiments, the members of the federated learning can calculate corresponding input parameters (e.g., the above-described input parameters I1 and I2) using various inverse estimation methods based on the target results provided by the inverse estimation requester. However, as described above, each member of the federated learning has different local data sets, machine learning algorithms used, model parameter adjustment capabilities, and inverse estimation methods and capabilities used. Therefore, the inverse estimation requester must first select a trained predictive model that meets its requirements in order to achieve efficient and accurate calculation of decision variables.

[0067] Please refer to Figure 7. Figure 7 shows a flowchart of the steps of a method for calculating decision variables according to another embodiment of the present invention. As shown in Figure 7, the method for calculating decision variables in this embodiment further includes the following steps:

[0068] Step S20: Provide a test sample, which includes confirmed test input parameters and test target results.

[0069] Step S22: Input the test input parameters into a trained prediction model candidate, and the trained prediction model candidate whose output result matches the test target result is set as the trained prediction model.

[0070] It should be noted that in the method for calculating the decision variables in this specific embodiment, after the above steps are completed, other steps (e.g., steps S10 to S18) in the specific embodiment described above are subsequently executed, and finally, the decision variables requested by the inverse estimation requester are calculated. Note that these steps have been described in detail in the specific embodiment described above, so they will not be described again here.

[0071] In step S20, the inverse estimation requester may provide a sample currently held by the inverse estimation requester, in which the decision variables and results have been completely confirmed, as a test sample to verify whether the trained predictive models of all members of the federated learning (defined as candidate trained predictive models in this specific embodiment) are what the inverse estimation requester requires. Both the test input parameters and the test target result in the test sample are specified. Therefore, in step S22, the candidate trained predictive model to which the test input parameters are input and which outputs a result that matches the test target result has prediction accuracy that meets the requirements of the inverse estimation requester, and can therefore be used as the trained predictive model for subsequent inverse estimation of decision variables.

[0072] Furthermore, the method for calculating decision variables in the present invention also requires that the members of the federated learning group involved in the calculation be required to perform inverse estimation, as in step S12 and its substeps in the specific embodiment described above. Therefore, the members of the federated learning group are also required by the inverse estimation requester to have the ability to perform inverse estimation. Now, please refer to FIG. 8, which shows a flowchart of the steps of the method for calculating decision variables according to another specific embodiment of the present invention. As shown in FIG. 8, the method for calculating decision variables in this specific embodiment further includes the following steps:

[0073] Step S20': Provide a first test sample, which includes a confirmed first test input parameter and a first test target result.

[0074] Step S22': The first test input parameters are input to the trained prediction model candidate, and the trained prediction model candidate whose output result matches the first test target result is designated as the first trained prediction model candidate.

[0075] Step S24: Provide a second test sample, which includes confirmed second test input parameters and second test target results.

[0076] Step S26: Provide the second test target results to the first trained prediction model candidate, respectively, to have the first trained prediction model candidate inversely estimate the first input parameter candidate, and then, the first trained prediction model candidate whose first input parameter candidate matches or is close to the second test input parameter candidate or whose first input parameter candidate passes the validity verification process is determined as the trained prediction model.

[0077] It should be noted that in the method for calculating the decision variables in this specific embodiment, after the above steps are completed, other steps (e.g., steps S10 to S18) in the specific embodiment described above are subsequently executed, and finally, the decision variables requested by the inverse estimation requester are calculated. Note that these steps have been described in detail in the specific embodiment described above, so they will not be described again here.

[0078] This specific example differs from the above-described specific example in the following respects. Specifically, as shown in steps S20′ to S22′, in this specific example, test input parameters of a first test sample are first provided to all members of the federated learning. All members then input the test input parameters into trained prediction models (in this specific example, all members' trained models are defined as trained prediction model candidates), and the output prediction results are returned. The inverse estimation requester selects a first trained prediction model candidate based on whether the prediction results match the first target test result of the first test sample. At this point, the inverse estimation requester can select a trained prediction model candidate that satisfies the required accuracy from all trained prediction model candidates participating in the federated learning. Next, the second target test result of the second test sample is provided to the trained prediction model with high accuracy (in this specific example, the first trained prediction model candidate), and inverse estimation is performed to obtain first input parameter candidates. Then, the inverse estimation requester compares the first input parameter candidate with the second test input parameters of the second test sample, and selects the first trained predictive model candidate that matches or approximates the second test input parameters as the trained predictive model to be used in the subsequent decision variable calculation step, since it has accurate inverse estimation capability.

[0079] In addition, the functions representing all trained predictive models may have many-to-one characteristics. That is, similar prediction results may be obtained for multiple different inputs to a trained predictive model. Therefore, even if the first input parameter candidates obtained by inverse estimation of the trained predictive model candidate based on the second test target result do not necessarily match or approximate the second test input parameters of the inverse estimation requester, this does not necessarily mean that the input parameters are infeasible. Therefore, the inverse estimation capability of the trained predictive model candidate may be verified through a validation process. In practice, this validation process can be performed by the inverse estimation requester. For example, if the inverse estimation requester is also a member of the federated learning, it may input the first input parameter candidates into its own trained predictive model and verify whether the prediction results match or approximate the second test target result. Alternatively, if the inverse estimation requester is not a member of the federated learning or wishes to perform multiple validations, the validation process may provide the first input parameter candidates to multiple members of the federated learning and input them into their trained predictive models to verify whether the prediction results match or approximate the second test target result. Therefore, if the first trained predictive model candidate passes the above-mentioned validity verification process, it also indicates that it has accurate inverse estimation capabilities, and is therefore selected as the trained predictive model to be used in the subsequent decision variable calculation step.

[0080] In brief, in this specific embodiment, first, by providing confirmed test input parameters, a trained predictive model and corresponding federated learning members whose output results match expectations are selected, and then, by providing confirmed target results, a trained predictive model and corresponding federated learning members whose inverse estimation ability matches expectations are selected.

[0081] In summary, the decision variable calculation method of the present invention uses trained predictive models provided by multiple members of the federated learning to inversely estimate decision variables that match a specific target result without performing federated learning. The inverse estimation requester can first inversely estimate input parameters from the target result using the trained predictive models of each member of the federated learning, provide a loss function, and sum the results to form overall input parameters and an overall loss function. Next, an optimization problem can be constructed using the overall input parameters and the overall loss function, and a solution can be found for the optimization problem. The overall input parameters calculated for the optimization problem can then be used as decision variables. The decision variable calculation method of the present invention allows a specific member of the federated learning or a unit outside the federated learning to request inverse estimation. Furthermore, since collaborators can be directly sought and selected without going through the federated model generated by federated learning, complex machine learning and inverse estimation processes can be avoided. Furthermore, the decision variable calculation method of the present invention eliminates the need for members of the federated learning to exchange highly sensitive and confidential data samples and information in the training dataset, nor the need to exchange model parameters of each member's trained predictive model. This not only reduces the complexity of the process but also further protects the confidentiality of the data.

[0082] The detailed description of the preferred specific embodiments above is intended to more clearly describe the features and spirit of the present invention, and is not intended to limit the scope of the present invention to the preferred specific embodiments disclosed above. Rather, it is intended that various modifications and equivalent structures be covered within the scope of the claims intended to be claimed by the present invention. Therefore, the scope of the claims intended to be claimed by the present invention should be interpreted in the broadest possible manner based on the above description so as to cover all possible modifications and equivalent structures. [Explanation of symbols]

[0083] S10~S18, S180~S184, S120~S122, S120'~S126', S120''~S122'', S120''~S128''', S20~S22, S24~S26, S20'~S22' Process steps

Claims

1. A method for calculating a decision variable, comprising: providing a plurality of trained predictive models, each of which is obtained by machine learning a plurality of local datasets using a machine learning method; providing a target outcome and inversely estimating a plurality of input parameters for the target outcome using the trained predictive model; a step of setting a plurality of loss functions corresponding to the trained prediction models, respectively, assigning a first weight value to each of the loss functions, and then summing the loss functions to generate a comprehensive loss function, wherein each of the loss functions is defined as the absolute value, square of the difference between the function value of the objective function representing each of the trained prediction models and the target result, or a function having a monotonically increasing characteristic with respect to the difference value; generating a comprehensive input parameter by adding second weight values ​​to the input parameters and then summing the input parameters, and constructing an optimization problem using the comprehensive input parameter and the comprehensive loss function; a step of obtaining the second weight value of each of the input parameters by solving the optimization problem, and calculating the overall input parameter as the decision variable.

2. The step of solving the optimization problem further comprises: calculating a derivative of the overall loss function for each of the second weight values; combining the derivatives to form a direction; 2. The method for calculating a decision variable according to claim 1, further comprising the step of inputting the comprehensive input parameters to the trained predictive model after increasing the step size along the direction, and determining whether the function value of the comprehensive loss function decreases.

3. The method of claim 1 , wherein the trained predictive models are each provided by multiple members of a federated learning model.

4. The step of inversely estimating each of the input parameters for the target outcome using the trained predictive model further includes: a first one of the members comparing the target result with all samples in a corresponding first one of the local data sets; 4. The method of claim 3, further comprising the step of selecting samples in the first local data set that match the target outcome as reference samples for inversely estimating the input parameters.

5. The step of inversely estimating each of the input parameters for the target outcome using the trained predictive model further includes: a second member of the members comparing the target result with all samples of a corresponding second local data set of the local data sets to obtain a plurality of anchor samples, and forming a multidimensional subspace with the anchor samples; determining an initial sample within the multidimensional subspace; obtaining a direction of the initial sample within the multidimensional subspace, forming relay samples by increasing step sizes along the direction of the initial sample, and inputting the relay samples into a second trained prediction model provided by the second member to determine whether the generated prediction result is close to the target result; 4. The method for calculating decision variables according to claim 3, further comprising: continuing to input the relay samples for which the direction has been determined and the step size has been increased into the second trained predictive model until the prediction result generated by the second trained predictive model matches the target result, and setting the last relay sample as the input parameter corresponding to the second trained predictive model.

6. The step of inversely estimating each of the input parameters for the target outcome using the trained predictive model further includes: a third member of the members setting a dummy layer connected to an input terminal of a corresponding third trained prediction model to form a parameter prediction model, the dummy layer serving as an input terminal of the parameter prediction model; 4. The method for calculating decision variables according to claim 3, further comprising the steps of: setting the output of the parameter prediction model to the target result; training the parameter prediction model by inputting a training dataset including at least one all-ones vector to the parameter prediction model; adjusting a plurality of arc weight values ​​between the dummy layer and the third trained prediction model by an optimizer in a machine learning method that trained the third trained prediction model; and setting the arc weight values ​​as the input parameters corresponding to the third trained prediction model.

7. The step of inversely estimating each of the input parameters for the target outcome using the trained predictive model further includes: a fourth member of the members comparing the target result with all samples of a corresponding fourth local data set of the local data sets to obtain a plurality of anchor samples, and forming a multidimensional subspace with the anchor samples; determining an initial sample within the multidimensional subspace; obtaining a gradient by performing a minimization operation on the objective function of the fourth trained predictive model using an optimizer used by the fourth member to generate a fourth trained predictive model, and setting the direction of the gradient opposite to that of the initial sample; forming relay samples by increasing the step size along the direction for the initial sample, and inputting the relay samples into the fourth trained prediction model to check whether the generated prediction result is close to the target result; 4. The method for calculating decision variables according to claim 3, further comprising: continuing to input the relay samples for which the direction has been determined and the step size has been increased into the fourth trained predictive model until the prediction result generated by the fourth trained predictive model matches the target result, and setting the last relay sample as the input parameter corresponding to the fourth trained predictive model.

8. The step of inversely estimating each of the input parameters for the target outcome using the trained predictive model further includes: providing a plurality of confirmed decision variables and calculating a first vector of the confirmed decision variables; obtaining corresponding sample parameters from sample parameters in all samples of the fourth local data set based on the confirmed decision variables, respectively, and calculating a second vector of the corresponding sample parameters; obtaining a reference sample by comparing the first vector with the second vector and comparing the predicted results generated by all samples of the fourth local dataset in the fourth trained predictive model with the target result, wherein the second vector of the reference sample is close to or coincides with the first vector, and the predicted results of the reference sample are close to or coincides with the target result; 8. The method of claim 7, further comprising the step of: selecting the reference sample as the initial sample.

9. Furthermore, providing a test sample, the test sample including a plurality of validated test input parameters and test target results; 2. The method for calculating a decision variable according to claim 1, further comprising the step of inputting the test input parameters to a plurality of candidate trained predictive models, and selecting the candidate trained predictive model whose output result matches the test target result as the trained predictive model.

10. Furthermore, providing a first test sample, the first test sample including a plurality of validated first test input parameters and a first test objective result; inputting the first test input parameters into a plurality of trained prediction model candidates, and determining the trained prediction model candidates whose output results match the first test target results as a plurality of first trained prediction model candidates; providing a second test sample, the second test sample including a verified plurality of second test input parameters and a second test objective result; 2. The method for calculating a decision variable according to claim 1, further comprising the step of: providing the second test target results to the first trained predictive model candidate, respectively, and having the first trained predictive model candidate inversely estimate a plurality of first input parameter candidates, and determining the first trained predictive model candidate whose first input parameter candidates match or are close to the second test input parameters or whose first input parameter candidates satisfy a validation process as the trained predictive model.

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