提出一种新函数相似性度量，用于优化与学习任务。

A Similarity Measure Between Functions with Applications to Statistical Learning and Optimization

• 基于次优性差距转换定义函数相似性
• 统一了多种现有函数相似性概念
• 适用于经验风险最小化与非平稳在线优化

本文提出一种全新的函数相似性度量，通过量化两个函数的次优性差距如何相互转化来衡量其相似性，并统一了若干现有的函数相似性概念。该度量具备便利的运算规则，可有效应用于经验风险最小化和非平稳在线优化问题，为分析函数间关系提供了新的工具。

原文摘要 · Abstract (English)

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.

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