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 two alternative recursive versions based on the Weighted Recursive Least Squares (WRLS) and the Online Sparse Least Squares Support Vector Regression (OSLSSVR) strategies. 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.

翻译：本文提出了两种解决在线多任务学习回归问题的新方法。我们采用了一种基于图的高性能多任务学习框架，并基于加权递归最小二乘和在线稀疏最小二乘支持向量回归策略，分别开发了两种替代性的递归版本。通过采用任务堆叠变换，我们证明存在一个单一矩阵，该矩阵包含了多个任务之间的关系，并为MT-WRLS方法的初始化过程以及MT-OSLSSVR方法的多任务核函数提供了结构信息。与现有文献中大多基于在线梯度下降或三次非精确方法不同，我们实现了精确和近似的递归计算，其每次实例的计算代价在输入空间维度（MT-WRLS）或实例字典规模（MT-OSLSSVR）上呈二次增长。我们在一项实际的风速预测案例研究中，将所提出的在线多任务学习方法与其他竞争方法进行了比较，结果证明了这两种方法在性能上的显著提升。