We build a theoretical framework for designing and understanding practical
meta-learning methods that integrates sophisticated formalizations of
task-similarity with the extensive literature on online convex optimization and
sequential prediction algorithms. Our approach enables the task-similarity to
be learned adaptively, provides sharper transfer-risk bounds in the setting of
statistical learning-to-learn, and leads to straightforward derivations of
average-case regret bounds for efficient algorithms in settings where the
task-environment changes dynamically or the tasks share a certain geometric
structure. We use our theory to modify several popular meta-learning algorithms
and improve their meta-test-time performance on standard problems in few-shot
learning and federated learning.

本文提出了一种理论框架来设计和理解实用的元学习方法，该方法将任务相似性的复杂形式化与在线凸优化和序列预测算法的广泛文献融合。该方法使任务相似性能够自适应地学习，为统计学习 - to-learn 的转移风险提供更加精确的界限，并在任务环境动态变化或任务共享一定几何结构的情况下，导出高效算法的平均情况后悔界限。我们使用该理论修改了几种流行的元学习算法，并在少样本学习和联邦学习的标准问题上改善了它们在元测试时的性能。