Online Multi-Task Learning with Recursive Least Squares and Recursive Kernel Methods

This paper introduces two novel approaches for Online Multi-Task Learning (MTL) Regression Problems. We employ a high performance graph-based MTL formulation and develop its recursive versions based on the Weighted Recursive Least Squares (WRLS) and the Online Sparse Least Squares Support Vector Regression (OSLSSVR). Adopting task-stacking transformations, we demonstrate the existence of a single matrix incorporating the relationship of multiple tasks and providing structural information to be embodied by the MT-WRLS method in its initialization procedure and by the MT-OSLSSVR in its multi-task kernel function. Contrasting the existing literature, which is mostly based on Online Gradient Descent (OGD) or cubic inexact approaches, we achieve exact and approximate recursions with quadratic per-instance cost on the dimension of the input space (MT-WRLS) or on the size of the dictionary of instances (MT-OSLSSVR). We compare our online MTL methods to other contenders in a real-world wind speed forecasting case study, evidencing the significant gain in performance of both proposed approaches.