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This paper introduces two novel approaches for Online Multi-Task Learning(MTL) Regression Problems. We employ a high performance graph-based MTLformulation and develop its recursive versions based on the Weighted RecursiveLeast Squares (WRLS) and the Online Sparse Least Squares Support VectorRegression (OSLSSVR). Adopting task-stacking transformations, we demonstratethe existence of a single matrix incorporating the relationship of multipletasks and providing structural information to be embodied by the MT-WRLS methodin its initialization procedure and by the MT-OSLSSVR in its multi-task kernelfunction. Contrasting the existing literature, which is mostly based on OnlineGradient Descent (OGD) or cubic inexact approaches, we achieve exact andapproximate recursions with quadratic per-instance cost on the dimension of theinput space (MT-WRLS) or on the size of the dictionary of instances(MT-OSLSSVR). We compare our online MTL methods to other contenders in areal-world wind speed forecasting case study, evidencing the significant gainin performance of both proposed approaches.

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