Vector-valued learning, where the output space admits a vector-valued structure, is an important problem that covers a broad family of important domains, e.g. multi-task learning and transfer learning. Using local Rademacher complexity and unlabeled data, we derive novel semi-supervised excess risk bounds for general vector-valued learning from both kernel perspective and linear perspective. The derived bounds are much sharper than existing ones and the convergence rates are improved from the square root of labeled sample size to the square root of total sample size or directly dependent on labeled sample size. Motivated by our theoretical analysis, we propose a general semi-supervised algorithm for efficiently learning vector-valued functions, incorporating both local Rademacher complexity and Laplacian regularization. Extensive experimental results illustrate the proposed algorithm significantly outperforms the compared methods, which coincides with our theoretical findings.

翻译：向量值学习（输出空间具有向量值结构）是涵盖多任务学习、迁移学习等重要领域的关键问题。通过利用局部拉德马赫复杂度和无标签数据，我们从核方法和线性方法两个视角推导出针对一般向量值学习的新型半监督超额风险界。所推导的界显著优于现有结果，收敛速率从标记样本量的平方根提升至总样本量的平方根，或直接依赖于标记样本量。基于理论分析，我们提出一种结合局部拉德马赫复杂度和拉普拉斯正则化的通用半监督算法，用于高效学习向量值函数。大量实验结果表明，所提算法显著优于对比方法，这与我们的理论发现高度一致。