In this paper, we generalize the problem of single index model to the context of continual learning in which a learner is challenged with a sequence of tasks one by one and the dataset of each task is revealed in an online fashion. We propose a strategy that is able to learn a common single index for all tasks and a specific link function for each task. The common single index allows to transfer the informaton gained from the previous tasks to a new one. We provide a theoretical analysis of our proposed strategy by proving some regret bounds. Moreover, as a by-product from our work to provide an example of a within-task algorithm, we develop a novel online algorithm for learning single index model in an online setting and provide its regret bound.
翻译:在本文中,我们将单一指数模式的问题概括到持续学习的背景下,即学习者面临逐项任务顺序的挑战,每项任务的数据集以在线方式披露。我们提出了一个能够学习所有任务的共同单一指数和每项任务的具体链接功能的战略。共同单一指数允许将从以往任务中获得的Informon转换为新任务。我们通过证明某些遗憾来提供对我们拟议战略的理论分析。此外,作为我们工作的一个副产品,我们开发了一种新的在线算法,用于在网上环境中学习单一指数模型,并提供遗憾约束。