Partial-label (PL) learning is a typical weakly supervised classification problem, where a PL of an instance is a set of candidate labels such that a fixed but unknown candidate is the true label. For PL learning, there are two lines of research: (a) the identification-based strategy (IBS) purifies each label set and extracts the true label; (b) the average-based strategy (ABS) treats all candidates equally for training. In the past two decades, IBS was a much hotter topic than ABS, since it was believed that IBS is more promising. In this paper, we theoretically analyze ABS and find it also promising in the sense of the robustness of its loss functions. Specifically, we consider five problem settings for the generation of clean or noisy PLs, and we prove that average PL losses with bounded multi-class losses are always robust under mild assumptions on the domination of true labels, while average PL losses with unbounded multi-class losses (e.g., the cross-entropy loss) may not be robust. We also conduct experiments to validate our theoretical findings. Note that IBS is heuristic, and we cannot prove its robustness by a similar proof technique; hence, ABS is more advantageous from a theoretical point of view, and it is worth paying attention to the design of more advanced PL learning methods following ABS.

本研究分析了偏标记学习的策略（IBS）和平均策略（ABS），发现使用平均PL损失（APLL）可以在多类损失有限的情况下始终保持鲁棒性，而使用无界损失的APLL可能是非鲁棒的。研究还发现，使用有限损失的ABS可以与使用无界损失的IBS（目前性能最好的策略）相匹配或超越其性能。

偏标记学习中平均损失的鲁棒性