In this note, we present a novel measure of similarity between two functions. It quantifies how the sub-optimality gaps of two functions convert to each other, and unifies several existing notions of functional similarity. We show that it has convenient operation rules, and illustrate its use in empirical risk minimization and non-stationary online optimization.

翻译：本文提出了一种衡量两个函数间相似性的新度量方法。该度量量化了两个函数的次优性差距如何相互转化，并统一了现有的几种函数相似性概念。我们证明了该度量具有便捷的运算规则，并通过经验风险最小化和非平稳在线优化问题展示了其应用价值。