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

2025/01/14 by Chengpiao Huang, Kaizheng Wang, Huang, Chengpiao +1
Computer Science · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Neural Networks and Applications #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2501.08317

openalex publication_date 2025/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Bounded Statistics
• Comparing Apples to Oranges: Learning Similarity Functions for Data Produced by Different Distributions
• Algorithmic Robustness for Learning via (ε, γ, τ)-Good Similarity Functions
• Understanding (dis)similarity measures
• On Similarity