In this paper, we consider a deterministic online linear regression model where we allow the responses to be multivariate. To address this problem, we introduce MultiVAW, a method that extends the well-known Vovk-Azoury-Warmuth algorithm to the multivariate setting, and show that it also enjoys logarithmic regret in time. We apply our results to the online hierarchical forecasting problem and recover an algorithm from this literature as a special case, allowing us to relax the hypotheses usually made for its analysis.

翻译：本文考虑一种确定性在线线性回归模型，其中允许响应变量为多元。针对此问题，我们提出MultiVAW方法，将著名的Vovk-Azoury-Warmuth算法扩展至多元场景，并证明其同样具有时间对数遗憾。我们将研究成果应用于在线层级预测问题，并作为特例恢复出该领域文献中的某一算法，从而放宽了该算法分析中常用的假设条件。