Traditional supervised learning aims to train a classifier in the closed-set world, where training and test samples share the same label space. In this paper, we target a more challenging and realistic setting: open-set learning (OSL), where there exist test samples from the classes that are unseen during training. Although researchers have designed many methods from the algorithmic perspectives, there are few methods that provide generalization guarantees on their ability to achieve consistent performance on different training samples drawn from the same distribution. Motivated by the transfer learning and probably approximate correct (PAC) theory, we make a bold attempt to study OSL by proving its generalization error-given training samples with size n, the estimation error will get close to order O_p(1/\sqrt{n}). This is the first study to provide a generalization bound for OSL, which we do by theoretically investigating the risk of the target classifier on unknown classes. According to our theory, a novel algorithm, called auxiliary open-set risk (AOSR) is proposed to address the OSL problem. Experiments verify the efficacy of AOSR. The code is available at github.com/Anjin-Liu/Openset_Learning_AOSR.

翻译：传统监督的学习目标是在封闭的世界中培训一个分类者,培训和测试样品都具有相同的标签空间。在本文中,我们的目标是一个更具挑战性和更现实的环境:开放的学习(OSL),在培训期间看不到的班级中存在测试样品。虽然研究人员从算法角度设计了许多方法,但很少有方法能够保证他们能够在同一分布的不同培训样品上取得一致的性能。根据我们的理论,我们提议采用一种新颖的算法,即所谓的辅助开放风险(AOSR)来解决OSL问题。实验将核查AOSR的功效。这个代码可在Github-Star.com/Anjin-Lset.