半监督多目标学习中，标签数据需求可因无标签数据大幅减少。
On the sample complexity of semi-supervised multi-objective learning
- 针对Bregman损失设计伪标签算法，利用无标签数据降低对标注数据依赖。
- 理论证明：在理想半监督条件下，无标签数据能显著减少标签样本需求。
- 适用于需要平衡多个任务且标注成本高的场景，如医疗图像分析。
在多目标学习（MOL）中，需用单一模型联合解决多个可能冲突的预测任务。获得良好权衡可能需要比单个任务更大容量的模型类\mathcal{G}，从而增加统计代价，这体现在已知的MOL界中与\mathcal{G}复杂度相关。我们证明，对于某些损失函数，这种代价在理想化的半监督设置下仍不可避免——即使学习者拥有各任务的贝叶斯最优解及协变量边缘分布。然而，对于采用Bregman损失的目标，我们证明模型类\mathcal{G}的复杂度仅影响无标签数据部分。具体地，我们建立了样本复杂度上界，精确揭示了无标签数据如何显著缓解对标注数据的需求。这些率由一种简单的半监督算法通过伪标签实现。
原文摘要 · Abstract (English)
In multi-objective learning (MOL), several possibly competing prediction tasks must be solved jointly by a single model. Achieving good trade-offs may require a model class $\mathcal{G}$ with larger capacity than what is necessary for solving the individual tasks. This, in turn, increases the statistical cost, as reflected in known MOL bounds that depend on the complexity of $\mathcal{G}$. We show that this cost is unavoidable for some losses, even in an idealized semi-supervised setting, where the learner has access to the Bayes-optimal solutions for the individual tasks as well as the marginal distributions over the covariates. On the other hand, for objectives defined with Bregman losses, we prove that the complexity of $\mathcal{G}$ may come into play only in terms of unlabeled data. Concretely, we establish sample complexity upper bounds, showing precisely when and how unlabeled data can significantly alleviate the need for labeled data. These rates are achieved by a simple, semi-supervised algorithm via pseudo-labeling.
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