Conventional supervised learning typically assumes that the learning task can be solved by learning a single function since the data is sampled from a fixed distribution. However, this assumption is invalid in open-ended environments where no task-level data partitioning is available. In this paper, we present a novel supervised learning framework of learning from open-ended data, which is modeled as data implicitly sampled from multiple domains with the data in each domain obeying a domain-specific target function. Since different domains may possess distinct target functions, open-ended data inherently requires multiple functions to capture all its input-output relations, rendering training a single global model problematic. To address this issue, we devise an Open-ended Supervised Learning (OSL) framework, of which the key component is a subjective function that allocates the data among multiple candidate models to resolve the "conflict" between the data from different domains, exhibiting a natural hierarchy. We theoretically analyze the learnability and the generalization error of OSL, and empirically validate its efficacy in both open-ended regression and classification tasks.

翻译：受常规监督的学习通常假定学习任务可以通过学习一个单一功能来解决,因为数据是从固定分布中抽样的。然而,这一假设在没有任务级别数据分割的开放环境中是无效的。在本文中,我们提出了一个从开放式数据学习的新的受监督学习框架,这个框架的模型是来自多个领域的隐含抽样数据,每个领域的数据都符合一个特定领域的目标功能。由于不同领域可能具有不同的目标功能,因此,开放数据本身需要多个功能来捕捉其所有输入输出关系,使培训成为一个单一的全球模型有问题。为了解决这个问题,我们设计了一个不限成员名额的超视域学习框架,其中关键部分是主观功能,将多种候选模型中的数据用于解决不同领域数据之间的“冲突”问题,展示自然等级。我们从理论上分析了OSL的可学习性和一般化错误,并从经验上验证它在开放回归和分类任务中的功效。