We study the problem of meta-learning through the lens of online convex
optimization, developing a meta-algorithm bridging the gap between popular
gradient-based meta-learning and classical regularization-based multi-task
transfer methods. Our method is the first to simultaneously satisfy good sample
efficiency guarantees in the convex setting, with generalization bounds that
improve with task-similarity, while also being computationally scalable to
modern deep learning architectures and the many-task setting. Despite its
simplicity, the algorithm matches, up to a constant factor, a lower bound on
the performance of any such parameter-transfer method under natural task
similarity assumptions. We use experiments in both convex and deep learning
settings to verify and demonstrate the applicability of our theory.

本文介绍了基于在线凸优化的元学习问题，并提出了一种元算法，使得流行的基于梯度的元学习和传统的基于正则化的多任务转移方法之间的差距得以弥合。我们的方法是第一个在凸设置下同时满足良好的样本效率保证，并且具有随着任务相似度提高而改善的泛化界限，同时在现代深度学习体系结构和多任务环境下具有可伸缩性的方法。尽管算法很简单，但它匹配了下限，是任何此类参数传输方法在自然任务相似度假设下的性能的常数因子。我们在凸和深度学习设置下的实验验证和演示了我们理论的适用性。