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

arXiv: https://arxiv.org/abs/2501.08317 · HTML: https://mlsanity.com/paper/2501.08317/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 14 Jan 2025.

## Abstract (arXiv)

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.