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.

翻译：本文针对在线多任务学习回归问题提出了两种新型方法。我们采用一种基于图的高性能多任务学习框架，分别依据加权递推最小二乘法和在线稀疏最小二乘支持向量回归机，开发了其递推版本。通过采用任务堆叠变换，我们证明了存在单一矩阵能够整合多任务间的关联关系，为MT-WRLS方法在初始化过程中以及MT-OSLSSVR方法在多任务核函数中提供结构性信息。与现有主要基于在线梯度下降或三次非精确方法的文献不同，我们实现了输入空间维度（MT-WRLS）或实例字典规模（MT-OSLSSVR）上的二次单实例计算代价的精确与近似递推。通过真实风速预测案例研究，我们将所提出的在线多任务学习算法与其他竞品进行对比，证明了两种方法均能显著提升性能。