We consider a statistical version of curriculum learning (CL) in a parametric prediction setting. The learner is required to estimate a target parameter vector, and can adaptively collect samples from either the target model, or other source models that are similar to the target model, but less noisy. We consider three types of learners, depending on the level of side-information they receive. The first two, referred to as strong/weak-oracle learners, receive high/low degrees of information about the models, and use these to learn. The third, a fully adaptive learner, estimates the target parameter vector without any prior information. In the single source case, we propose an elimination learning method, whose risk matches that of a strong-oracle learner. In the multiple source case, we advocate that the risk of the weak-oracle learner is a realistic benchmark for the risk of adaptive learners. We develop an adaptive multiple elimination-rounds CL algorithm, and characterize instance-dependent conditions for its risk to match that of the weak-oracle learner. We consider instance-dependent minimax lower bounds, and discuss the challenges associated with defining the class of instances for the bound. We derive two minimax lower bounds, and determine the conditions under which the performance weak-oracle learner is minimax optimal.

翻译：我们考虑参数预测设置中课程学习（CL）的统计版本。学习器需要估计目标参数向量，并能够自适应地从目标模型或其他与目标模型相似但噪声较小的源模型中收集样本。根据接收的辅助信息水平，我们考虑三类学习器。前两类分别称为强/弱oracle学习器，它们接收关于模型的高/低程度信息并利用这些信息进行学习。第三类是完全自适应学习器，它在没有任何先验信息的情况下估计目标参数向量。在单源情况下，我们提出一种消除学习方法，其风险与强oracle学习器相匹配。在多源情况下，我们主张弱oracle学习器的风险是自适应学习器风险的现实基准。我们开发了一种自适应多轮消除CL算法，并刻画了其风险与弱oracle学习器相匹配的实例依赖条件。我们考虑实例依赖的极小化最优下界，并讨论了为界定该下界而定义实例类别所面临的挑战。我们推导了两个极小化最优下界，并确定了弱oracle学习器达到极小化最优性能的条件。