Small sample oriented meta-learning arx model multi-task parameter collaborative identification method

Abstract

This invention provides a multi-task parameter collaborative identification method for meta-learning ARX models with small sample sizes, relating to the fields of control science and engineering and machine learning. The method includes initializing system information vectors and parameter vectors for multiple tasks; defining task-specific context feature vectors for each task; establishing a mapping relationship between the context feature vectors and parameters of different tasks through a neural network; constructing a task-level loss function based on prediction error to update the context feature vectors; constructing a multi-task joint loss function to update the shared parameters of the neural network; and iteratively performing the collaborative update of the context feature vectors and shared parameters until convergence. This invention effectively solves the problems of poor adaptability and generalization ability, high sample size requirements, large computational overhead, and insufficient identification accuracy of traditional algorithms in multi-task scenarios, improving the efficiency, accuracy, and stability of multi-task parameter identification under small sample conditions.

Description

Technical Field

[0001] This invention relates to the fields of control science and engineering and machine learning technology, and in particular to a multi-task parameter collaborative identification method for meta-learning ARX models with small sample sizes. Background Technology

[0002] Autoregressive with exogenous input (ARX) models are a fundamental and important tool in engineering, science, and economics for modeling, predicting, and controlling linear dynamic systems with inputs. Optimization of their identification algorithms is of significant practical importance. However, existing technologies still have many shortcomings when facing complex scenarios such as multi-task switching and multimodal coordination.

[0003] On the one hand, traditional single linear system identification models struggle to meet the adaptability and generalization requirements of multi-task scenarios. In multi-task environments with similar contexts, these models cannot effectively extract features from different tasks, often requiring repeated training for each task, resulting in poor adaptability and weak generalization ability when switching tasks.

[0004] On the other hand, traditional identification algorithms have shortcomings in terms of computational efficiency and stability. For example, when faced with large amounts of data or ill-conditioned data, the least squares identification algorithm is prone to unstable results due to the direct inversion operation; while improved generalized least squares methods and other methods have improved stability to some extent, they have significantly increased computational complexity. Robust estimation methods also have the problem of large computational load, making it difficult to meet the requirements of real-time applications for low computational overhead.

[0005] Furthermore, there is a dynamic coupling between different tasks and contextual features, which further affects the parameter identification accuracy of traditional identification models, making it difficult to achieve accurate system parameter estimation in complex dynamic scenarios.

[0006] The aforementioned problems limit the effective application of ARX models in multi-task, small-sample, and dynamically coupled scenarios. Therefore, there is an urgent need for an ARX model parameter identification method that can improve multi-task adaptability, reduce computational overhead, and improve identification accuracy. Summary of the Invention

[0007] To address this, this invention provides a multi-task parameter collaborative identification method for meta-learning ARX models with small sample sizes. This method solves the problems in the prior art, such as the poor adaptability and generalization ability of traditional single linear system identification models in multi-task switching and multi-modal coordination scenarios, the large computational load of traditional algorithms, the high requirement for sample data, and the insufficient identification accuracy caused by the dynamic coupling characteristics of task and context features.

[0008] To address the aforementioned problems, embodiments of the present invention provide a multi-task parameter collaborative identification method for meta-learning ARX models with small sample sizes, the method comprising:

[0009] S1: Initialize the system information vectors and parameter vectors for multiple tasks;

[0010] S2: Define a context feature vector for each task;

[0011] S3: Establish a mapping relationship between context feature vectors and task parameters through a neural network;

[0012] S4: Construct a task-level loss function based on prediction error and update the context feature vector;

[0013] S5: Construct a multi-task joint loss function and update the shared parameters of the neural network;

[0014] S6: Iterate through the collaborative update of the context feature vector and shared parameters until convergence;

[0015] The shared parameters are transferred between multiple tasks through meta-learning, enabling rapid parameter identification of new tasks with small sample sizes.

[0016] Preferably, the neural network comprises an input layer, a hidden layer, and an output layer; wherein the input layer receives a context feature vector, the hidden layer performs a nonlinear transformation, and the output layer generates an ARX model parameter vector.

[0017] Preferably, updating the context feature vector in step S4 includes:

[0018] Calculate the gradient of the task-level loss function with respect to the context feature vector, and update the context feature vector using gradient descent:

[0019]

[0020] In the formula, This represents the update value of the q-th component of the context feature vector for the i-th task in the k-th iteration; Let be the update value of the q-th component of the context feature vector for the i-th task in the (k-1)-th iteration; η is the learning rate of the context parameters; The task-level loss function J(c) i For context component c q,i The partial derivatives of .

[0021] Preferably, updating the shared parameters in step S5 includes:

[0022] Calculate the gradient of the joint loss function for multiple tasks with respect to the weights and biases of the neural network, and update the shared parameters using gradient descent:

[0023]

[0024] In the formula, These are the weights from the j-th node in the hidden layer to the p-th node in the output layer after the k-th and k-1-th iterations, respectively. These are the biases of the p-th node in the output layer after the k-th and (k-1)-th iterations, respectively. These are the weights from the q-th node in the input layer to the j-th node in the hidden layer after the k-th and (k-1)-th iterations, respectively. λ represents the bias of the j-th node in the hidden layer after the k-th and (k-1)-th iterations, respectively; λ is the learning rate of the output layer; μ is the learning rate of the hidden layer. For multi-task joint loss function For weight v p,j The partial derivatives; For multi-task joint loss function For bias β p The partial derivatives; For multi-task joint loss function For weight w j,q The partial derivatives; For multi-task joint loss function For bias α j The partial derivatives of .

[0025] Preferably, the task-level loss function is defined as:

[0026]

[0027] In the formula, J(c i ) represents the task-level loss function; c i is the context feature vector; i is the task index; t is the time index; l is the amount of training data in a single task mini-batch; This represents the actual system output value for the i-th task at time t. Let θ be the information vector of the i-th task at time t; i Let be the parameter vector of the ARX model for the i-th task; This is the ARX model prediction output for the i-th task at time t.

[0028] Preferably, the multi-task joint loss function is defined as:

[0029]

[0030] In the formula, For multi-task joint loss function; For shared parameters; i is the task index; M is the number of tasks involved in the training phase; t is the time index; L is the length of the full dataset for a single task; y i(t) represents the actual system output value of the i-th task at time t; Let θ be the information vector of the i-th task at time t; i Let be the parameter vector of the ARX model for the i-th task; This is the ARX model prediction output for the i-th task at time t.

[0031] Preferably, the parameter identification of the new task is achieved through the following steps:

[0032] The shared parameters obtained from fixed training are updated with contextual feature vectors based on a small amount of data from a new task, and parameter estimates are obtained through neural network mapping.

[0033] This invention also provides a multi-task parameter collaborative identification system for few-shot meta-learning ARX models. This system is used to implement the aforementioned multi-task parameter collaborative identification method for few-shot meta-learning ARX models, specifically including:

[0034] The task initialization module is used to initialize the system information vectors and parameter vectors for multiple tasks.

[0035] The context definition module is used to define a context feature vector for each task.

[0036] The meta-learning mapping building block is used to establish a mapping relationship between context feature vectors and task parameters through neural networks;

[0037] The task-level optimization module is used to construct a task-level loss function based on the prediction error and update the context feature vector;

[0038] The shared knowledge transfer module is used to construct a multi-task joint loss function and update the shared parameters of the neural network.

[0039] The collaborative convergence module is used to iteratively update the context feature vector and shared parameters until convergence.

[0040] The shared parameters are transferred between multiple tasks through meta-learning, enabling rapid parameter identification of new tasks with small sample sizes.

[0041] This invention also provides an electronic device, which includes a processor, a memory, and a bus system. The processor and the memory are connected through the bus system. The memory is used to store instructions, and the processor is used to execute the instructions stored in the memory to implement the multi-task parameter collaborative identification method for small-sample meta-learning ARX models described above.

[0042] This invention also provides a computer storage medium storing a computer software product, the computer software product including several instructions to cause a computer device to execute the above-described method for multi-task parameter collaborative identification of a few-sample meta-learning ARX model.

[0043] As can be seen from the above technical solutions, this invention application has the following beneficial effects:

[0044] (1) This invention is based on a meta-learning framework. It constructs a mapping relationship between context feature vectors and task parameters through a neural network, enabling knowledge transfer of shared parameters across multiple tasks. For new tasks, there is no need for extensive repetitive training. Only a small amount of data is needed to update the context feature vectors, and parameter estimates can be quickly obtained through a pre-trained neural network. This effectively solves the problems of poor adaptability and weak generalization ability of traditional single models when switching between multiple tasks, and can dynamically adapt to the situational patterns that different tasks follow.

[0045] (2) Traditional identification algorithms require a large amount of sample data, while this invention significantly reduces the dependence on the number of samples through a collaborative optimization mechanism of context features and shared parameters. In small sample scenarios, by iteratively updating the task-level loss function and the multi-task joint loss function, and using gradient descent to accurately adjust the context feature vector and the shared parameters of the neural network, accurate parameter identification can still be achieved even if each task uses only a small amount of training data (such as 15 data points in the simulation experiment), thus meeting the modeling requirements in small sample scenarios.

[0046] (3) Compared to the instability of traditional least squares algorithms with large or ill-conditioned data, and the high computational complexity of improved algorithms such as generalized least squares, this invention avoids complex matrix inversion operations through a collaborative update strategy of neural network mapping and gradient descent, significantly reducing computational overhead and meeting the demand for low computational cost in real-time applications. Simultaneously, the algorithm effectively captures the dynamic coupling characteristics of task and context features. Through dual optimization of task-level and multi-task joint loss functions, it improves the accuracy and stability of parameter identification. The high degree of agreement between the predicted output and the actual output in simulation results verifies this advantage. Attached Figure Description

[0047] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly described below. Referring to the drawings will make the features and advantages of the present invention clearer. The drawings are illustrative and should not be construed as limiting the present invention in any way. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0048] Figure 1The flowchart of a multi-task parameter collaborative identification method for meta-learning ARX models with small sample sizes is provided by the present invention.

[0049] Figure 2 The flowchart of a multi-task parameter collaborative identification method for meta-learning ARX models with small sample sizes is provided by the present invention.

[0050] Figure 3 This is a schematic diagram of the neural network of the present invention;

[0051] Figure 4 This is a curve showing the relationship between the identification error δ and the number of iterations k for the training set of this invention under 20 different noise seeds and step sizes;

[0052] Figure 5 This is a box plot of the context feature vectors obtained during training under 20 different noise seeds and step sizes.

[0053] Figure 6 Box plots of the system parameters obtained during training under 20 different noise seeds and step sizes are shown below.

[0054] Figure 7 This is a comparison chart of the predicted output and the actual output of the four tasks in the test set of this invention;

[0055] Figure 8 This is the clustering result of the context feature vectors of the four tasks in the test set of this invention;

[0056] Figure 9 This invention provides a block diagram of a multi-task parameter collaborative identification system for a meta-learning ARX model oriented towards small sample sizes. Detailed Implementation

[0057] 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, 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.

[0058] Example 1: To address the problems of poor adaptability and generalization ability of traditional single linear system identification models in multi-task switching and multi-modal coordination scenarios, the high computational cost and large sample data requirements of traditional algorithms, and insufficient identification accuracy due to the dynamic coupling characteristics of task and context features, such as... Figure 1 or Figure 2 As shown, this invention proposes a multi-task parameter collaborative identification method for meta-learning ARX models with small sample sizes. This method includes:

[0059] S1: Initialize the system information vectors and parameter vectors for multiple tasks;

[0060] S2: Define a context feature vector for each task;

[0061] S3: Establish a mapping relationship between context feature vectors and task parameters through a neural network;

[0062] S4: Construct a task-level loss function based on prediction error and update the context feature vector;

[0063] S5: Construct a multi-task joint loss function and update the shared parameters of the neural network;

[0064] S6: Iterate through the collaborative update of the context feature vector and shared parameters until convergence;

[0065] Among them, shared parameters are transferred between multiple tasks through meta-learning, enabling rapid parameter identification of new tasks with small sample sizes.

[0066] As can be seen from the above technical solution, this invention proposes a multi-task parameter collaborative identification method for meta-learning ARX models oriented towards small samples. It initializes multi-task system information and parameter vectors, defines a context feature vector for each task, and utilizes a neural network to construct a mapping relationship between context features and task parameters. Subsequently, by constructing a task-level loss function based on prediction error and a multi-task joint loss function, gradient descent is used to alternately update the context feature vector and shared parameters of the neural network, achieving collaborative convergence. The shared parameters are transferred between multiple tasks through meta-learning. This scheme effectively solves the problems of poor adaptability and generalization ability of traditional algorithms in multi-task scenarios, high requirements for sample data volume, large computational overhead, and insufficient identification accuracy due to dynamic coupling. It not only enables rapid parameter identification of new tasks with small samples, reducing computational costs, but also improves multi-task adaptability and generalization ability, ensuring the accuracy and stability of parameter identification. Simulation results, such as high agreement between predicted and actual outputs, convergence of identification errors, and concentrated parameter distribution, verify its effectiveness.

[0067] This invention provides a multi-task parameter collaborative identification method for meta-learning ARX models with limited sample sizes. It achieves knowledge transfer between multiple tasks through meta-learning and combines neural networks with collaborative optimization strategies to achieve efficient parameter identification with limited sample sizes. The specific steps are as follows:

[0068] In this embodiment, in step S1, the system information vectors and parameter vectors of multiple tasks are initialized.

[0069] Task definition: Suppose that the training phase involves M tasks, and the i-th task is denoted as Γ. i Its ARX model is in the form of:

[0070] Γ i A i (z)y i (t)=B i (z)u i (t)+v i (t);

[0071] Among them, u i (t), y i (t) represent the system input and output of the i-th task, respectively, v i (t) is a function with zero mean and variance σ. i 2 Random noise; A i (z) and B i (z) is the unit shift operator in Z. -1 [Z -1 y i t =y i t Polynomials in ]

[0072]

[0073] In the formula, For output coefficients, n is the input coefficient. a Let n be the lag order (autoregressive term order) of the system output y(t). b The lag order (order of external input term) of the system input u(t).

[0074] Information vector and parameter vector initialization: Define the information vector of the i-th task at time t as:

[0075] The parameter vector is:

[0076]

[0077] During initialization, random values ​​or prior knowledge can be used to initialize the parameter vector θ. i Assign values. Based on the above formula, the final vector form of the regression model is obtained:

[0078]

[0079] Furthermore, the traditional least squares identification algorithm:

[0080] The objective function is defined by the vector form of the regression model as follows:

[0081]

[0082] Take the partial derivative with respect to θ and set it to zero:

[0083]

[0084] Therefore, the least squares estimate of θ is:

[0085]

[0086] definition

[0087]

[0088] v(t i )=[v(t1) T ,v(t2) T ,...,v(t n ) T ] T ∈R n It can be known that

[0089]

[0090] Therefore, the least squares estimate of θ can be written as:

[0091]

[0092] In this embodiment, in step S2, a context feature vector is defined for each task.

[0093] For the i-th task, define the context feature vector c. i ={c i1 ,c i2 ,...,c imi}∈R mi , where mi is the context feature dimension. Context feature vectors are used to characterize the unique properties of the task and serve as a bridge connecting the task and model parameters.

[0094] In this embodiment, in step S3, a mapping relationship between context feature vectors and task parameters is established through a neural network.

[0095] This invention uses a neural network comprising an input layer, a hidden layer, and an output layer to construct a mapping relationship, denoted as θ. i (c i ) = NN θ (c i ), where NN θ For a neural network, θ represents the network's shared parameters (including weights and biases). The input layer receives the context feature vector, the hidden layer performs nonlinear transformations, and the output layer generates the ARX model parameter vector.

[0096] like Figure 3The diagram shows the case of a BP neural network with s nodes. For task Γ... i The relationships between nodes at each level are as follows:

[0097]

[0098] Where h j It is the output of the hidden layer node, w jq Let α be the weight from the q-th node in the input layer to the j-th node in the hidden layer. j θ is the bias of the j-th node in the hidden layer. i,p It is θ i The p-th parameter in the equation, v pj Let β be the weight from the j-th node in the hidden layer to the p-th node in the output layer. p Let g(·) be the bias of the p-th node in the output layer, and g(·) and f(·) be the activation functions of the hidden layer and the output layer, respectively.

[0099] In this embodiment, in step S4, a task-level loss function based on the prediction error is constructed, and the context feature vector is updated.

[0100] Task-level loss function definition: For the i-th task, the loss function is the squared error between the predicted output and the actual output:

[0101]

[0102] In the formula, J(c i ) represents the task-level loss function; c i is the context feature vector; i is the task index; t is the time index; l is the amount of training data in a single task mini-batch; This represents the actual system output value for the i-th task at time t. Let θ be the information vector of the i-th task at time t; i Let be the parameter vector of the ARX model for the i-th task; This is the ARX model prediction output for the i-th task at time t.

[0103] Context feature vector update: c is updated using gradient descent. i The update formula for the q-th component in the k-th iteration is:

[0104]

[0105] In the formula, This represents the update value of the q-th component of the context feature vector for the i-th task in the k-th iteration; Let be the update value of the q-th component of the context feature vector for the i-th task in the (k-1)-th iteration; η is the learning rate of the context parameters; The task-level loss function J(c) i For context component c q,i The partial derivatives of .

[0106] Furthermore, the above calculation process needs to be combined with the chain rule of neural networks:

[0107]

[0108]

[0109] In this embodiment, in step S5, a multi-task joint loss function is constructed to update the shared parameters of the neural network.

[0110] Definition of Joint Loss Function for Multiple Tasks: The joint loss function is defined by combining the losses of all M tasks.

[0111]

[0112] In the formula, For multi-task joint loss function; For shared parameters; i is the task index; M is the number of tasks involved in the training phase; t is the time index; L is the length of the full dataset for a single task; y i (t) represents the actual system output value of the i-th task at time t; Let θ be the information vector of the i-th task at time t; i Let be the parameter vector of the ARX model for the i-th task; This is the ARX model prediction output for the i-th task at time t.

[0113] Shared parameter update: The shared parameters are updated using the gradient descent method, as shown in the following formula:

[0114] The weights from the j-th node in the hidden layer to the p-th node in the output layer:

[0115]

[0116] The bias of the p-th node in the output layer:

[0117]

[0118] in

[0119]

[0120] In the formula, These are the weights from the j-th node in the hidden layer to the p-th node in the output layer after the k-th and k-1-th iterations, respectively. λ represents the bias of the p-th node in the output layer after the k-th and (k-1)-th iterations, respectively; λ is the learning rate of the output layer. For multi-task joint loss function For weight v p,j The partial derivatives; For multi-task joint loss function For bias β p The partial derivatives of .

[0121] The weights from the q-th node in the input layer to the j-th node in the hidden layer:

[0122]

[0123] The bias of the j-th node in the hidden layer:

[0124]

[0125] in

[0126]

[0127] In the formula, These are the weights from the q-th node in the input layer to the j-th node in the hidden layer after the k-th and (k-1)-th iterations, respectively. , respectively, are the biases of the j-th node in the hidden layer after the k-th and (k-1)-th iterations; μ is the learning rate of the hidden layer; For multi-task joint loss function For weight w j,q The partial derivatives; For multi-task joint loss function For bias α j The partial derivatives of .

[0128] In this embodiment, in step S6, the collaborative update of the context feature vector and shared parameters is performed iteratively until convergence.

[0129] Repeat steps S4 and S5, alternatingly updating the context feature vector c. i and shared parameters Until the multi-task joint loss function Convergence (e.g., the change in loss during consecutive iterations is less than a preset threshold).

[0130] Furthermore, new task parameter identification: For new tasks with a small sample size, the shared parameters obtained during training are fixed. Based on a small amount of data (e.g., 15 data points) for the new task, the context feature vector c is updated using the gradient descent method in step S4. new Then, θ is mapped through a neural network. new =NN θ (c new ) Obtain parameter estimates to achieve rapid identification.

[0131] To further illustrate the advantages of the method of the present invention, the following explanation is based on specific simulation verification.

[0132] For n a The order is 3, n b Simulation experiments were conducted using a multi-task ARX model of order 2.

[0133] Γ i A i (z)y i (t)=B i (z)u i (t)+v i (t), i∈{1,2,3};

[0134] System input u i (t) is a zero-mean, unit-variance, uncorrelated random signal sequence, v i (t) has zero mean and variance. The white noise sequence. The training set is configured with three tasks to train the context parameters and shared parameters, with the parameters taking the following values:

[0135] θ1=[a 1,1 ,a 2,1 ,a 3,1 ,b 1,1 ,b 2,1 ,b 3,1 ] T =[0.525,0.117,0.080,0.142,1.350] T ∈R 5 ;

[0136] θ2=[a 1,2 ,a 2,2 ,a 3,2 ,b 1,2 ,b 2,2 ,b 3,2 ] T =[0.375,0.325,0.084,0.124,1.227] T ∈R 5 ;

[0137] θ3=[a 1,3 ,a 2,3 ,a 3,3 ,b 1,3 ,b 2,3 ,b 3,3 ] T =[0.175,0.637,0.088,0.071,1.181] T ∈R 5 ;

[0138] A fourth new task has been added to the test set, with parameters taking the following values:

[0139] θ4=[a 1,4 ,a 2,4 ,a 3,4 ,b 1,4 ,b 2,4 ,b 3,4 ] T =[0.150,0.460,0.080,0.054,1.377] T ∈R 5 ;

[0140] During the test set identification process, the shared parameters obtained during training are kept unchanged, while the context is continuously updated. Each of the four tasks uses only 15 data points for training and 50 data points for prediction validation. During validation, a task transition is performed every 50 data points. Experimental results verify the effectiveness of this invention, namely:

[0141] (1) The method of the present invention can accurately identify the parameters of different tasks and has good stability, such as Figure 4 , Figure 5 , Figure 6 As shown.

[0142] (2) After extracting the context and shared parameters, the method of this invention can effectively identify new tasks in the same context, such as... Figure 7 As shown.

[0143] (3) The method of this invention can effectively identify the dynamic differences in context parameters between different tasks in the same context, such as... Figure 8 As shown, once the context parameters of a task are obtained, the system parameters of that task can be accurately identified.

[0144] Example 2: Figure 9 As shown, this invention provides a multi-task parameter collaborative identification system for few-shot meta-learning ARX models. This system is used to implement the multi-task parameter collaborative identification method for few-shot meta-learning ARX models described in Embodiment 1 above, and specifically includes:

[0145] The task initialization module 100 is used to initialize the system information vectors and parameter vectors of multiple tasks.

[0146] Context definition module 200 is used to define a context feature vector for each task;

[0147] The meta-learning mapping building module 300 is used to establish a mapping relationship between context feature vectors and task parameters through a neural network;

[0148] The task-level optimization module 400 is used to construct a task-level loss function based on the prediction error and update the context feature vector.

[0149] The shared knowledge transfer module 500 is used to construct a multi-task joint loss function and update the shared parameters of the neural network.

[0150] The collaborative convergence module 600 is used to iteratively perform collaborative updates of the context feature vector and shared parameters until convergence.

[0151] Among them, shared parameters are transferred between multiple tasks through meta-learning, enabling rapid parameter identification of new tasks with small sample sizes.

[0152] This embodiment presents a multi-task parameter collaborative identification system for a few-shot meta-learning ARX model, used to implement the aforementioned multi-task parameter collaborative identification method for a few-shot meta-learning ARX model. Therefore, the specific implementation of the multi-task parameter collaborative identification system for a few-shot meta-learning ARX model can be found in the previous section on the embodiments of the multi-task parameter collaborative identification method for a few-shot meta-learning ARX model. For example, the task initialization module 100, context definition module 200, meta-learning mapping construction module 300, task-level optimization module 400, shared knowledge transfer module 500, and collaborative convergence module 600 are respectively used to implement steps S1, S2, S3, S4, S5, and S6 in the aforementioned multi-task parameter collaborative identification method for a few-shot meta-learning ARX model. Therefore, its specific implementation can be referred to the descriptions of the corresponding embodiments. To avoid redundancy, further details are omitted here.

[0153] Example 3: This embodiment of the invention provides an electronic device, which includes a processor, a memory, and a bus system. The processor and the memory are connected through the bus system. The memory is used to store instructions, and the processor is used to execute the instructions stored in the memory to implement the above-mentioned multi-task parameter collaborative identification method for small-sample meta-learning ARX models.

[0154] Example 4: This embodiment of the invention provides a computer storage medium storing a computer software product. The computer software product includes several instructions to cause a computer device to execute the above-described multi-task parameter collaborative identification method for small-sample meta-learning ARX models.

[0155] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0156] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0157] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0158] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A multi-task parameter collaborative identification method for meta-learning ARX models with small sample sizes, characterized in that, include: S1: Initialize the system information vectors and parameter vectors for multiple tasks; S2: Define a context feature vector for each task; S3: Establish a mapping relationship between context feature vectors and task parameters through a neural network. The neural network includes an input layer, a hidden layer, and an output layer. The mapping relationship is constructed using the input layer, hidden layer, and output layer. ,in For neural networks, For context feature vectors, The parameters are shared by the network, including weights and biases; the input layer receives the context feature vector, the hidden layer performs nonlinear transformations, and the output layer generates the ARX model parameter vector. S4: Construct a task-level loss function based on the prediction error to update the context feature vector. The task-level loss function is defined as follows: ； In the formula, The task-level loss function; For context feature vectors; For task indexing; For time indexing; For single-task, small-batch training data volume; For the first The task at time The actual output value of the system; For the first The task at time Information vector; For the first The parameter vector of the ARX model for each task; For the first The task at time The ARX model predicts the output; S5: Construct a multi-task joint loss function to update the shared parameters of the neural network. The multi-task joint loss function is defined as follows: ； In the formula, For multi-task joint loss function; For shared parameters; The number of tasks involved in the training phase; This refers to the total length of data for a single task. For the first The task at time The actual output value of the system; S6: Iterate through the collaborative update of the context feature vector and shared parameters until convergence; The shared parameters are transferred between multiple tasks through meta-learning, enabling rapid parameter identification of new tasks with limited samples.

2. The multi-task parameter collaborative identification method for meta-learning ARX models oriented towards small samples as described in claim 1, characterized in that, Step S4, updating the context feature vector, includes: Calculate the gradient of the task-level loss function with respect to the context feature vector, and update the context feature vector using gradient descent: ； In the formula, For the first The task in the first In the nth iteration, the context feature vector... Updated values ​​for each component; For the first The task in the first In the nth iteration, the context feature vector... Updated values ​​for each component; The learning rate is a context parameter; Task-level loss function For context components The partial derivatives of .

3. The multi-task parameter collaborative identification method for meta-learning ARX models oriented towards small samples as described in claim 1, characterized in that, Step S5 involves updating the shared parameters, including: Calculate the gradient of the joint loss function for multiple tasks with respect to the weights and biases of the neural network, and update the shared parameters using gradient descent: ； ； ； ； In the formula, , The first , After the nth iteration, the hidden layer... The node to the output layer The weight of each node; , The first , After the nth iteration, the output layer... The bias of each node; , The first , After the nth iteration, the input layer... The node is connected to the hidden layer. The weight of each node; , The first , After the nth iteration, the hidden layer... The bias of each node; The learning rate for the output layer; The learning rate for the hidden layer; For multi-task joint loss function Weights The partial derivatives; For multi-task joint loss function For bias The partial derivatives; For multi-task joint loss function Weights The partial derivatives; For multi-task joint loss function For bias The partial derivatives of .

4. The multi-task parameter collaborative identification method for meta-learning ARX models oriented towards small samples as described in claim 1, characterized in that, The parameter identification for the new task is achieved through the following steps: The shared parameters obtained from fixed training are updated with contextual feature vectors based on a small amount of data from a new task, and parameter estimates are obtained through neural network mapping.

5. A multi-task parameter collaborative identification system for meta-learning ARX models oriented towards small sample sizes, characterized in that, The system is used to implement the multi-task parameter collaborative identification method for small-sample meta-learning ARX models as described in any one of claims 1 to 4, specifically including: The task initialization module is used to initialize the system information vectors and parameter vectors for multiple tasks. The context definition module is used to define a context feature vector for each task. The meta-learning mapping building block is used to establish a mapping relationship between context feature vectors and task parameters through neural networks; The task-level optimization module is used to construct a task-level loss function based on the prediction error and update the context feature vector; The shared knowledge transfer module is used to construct a multi-task joint loss function and update the shared parameters of the neural network. The collaborative convergence module is used to iteratively update the context feature vector and shared parameters until convergence. The shared parameters are transferred between multiple tasks through meta-learning, enabling rapid parameter identification of new tasks with limited samples.

6. An electronic device, characterized in that, The electronic device includes a processor, a memory, and a bus system. The processor and the memory are connected through the bus system. The memory is used to store instructions, and the processor is used to execute the instructions stored in the memory to implement the multi-task parameter collaborative identification method for small-sample meta-learning ARX models as described in any one of claims 1 to 4.

7. A computer storage medium, characterized in that, The computer storage medium stores a computer software product, which includes several instructions to cause a computer device to execute the multi-task parameter collaborative identification method for small-sample meta-learning ARX models as described in any one of claims 1 to 4.

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