A Novel Online Sequential Learning Algorithm for ELM Based on Optimal Control

Aiming to address the deficiency in Extreme Learning Machine (ELM), particularly its ineffectiveness in handling data streaming scenarios and the necessity for retraining upon receiving new data after the model has been fitted, this paper introduces a novel algorithm designed to update ELM parameters online. The algorithm incorporates the concept of optimal control into the training of machine learning models, formulating the ELM output weights calculation problem as a series of state feedback control problems within a control system framework. This is addressed through the application of the Online Linear Quadratic Regulator (OLQR). The proposed algorithm demonstrates rapid and robust convergence, leveraging the advantages of optimal control technology. Moreover, the algorithm incorporates a regularization term into the quadratic objective function. This addition not only ensures high performance but also effectively mitigates overfitting. Extensive experimentation on UCI benchmark datasets substantiates that the proposed algorithm achieves faster convergence and superior generalization performance compared to the mainstream recursive least-squares-based online learning method. The code is available at https://www.gitlink.org.cn/BIT2024/OLQR-ELM/tree/master.