A Similarity Measure Between Functions with Applications to Statistical Learning and Optimization
This work provides a theoretical tool for statistical learning and optimization, but it appears incremental as it builds on existing similarity notions.
The authors introduced a novel similarity measure between functions that quantifies how sub-optimality gaps convert between them, unifying existing notions, and demonstrated its application in empirical risk minimization and non-stationary online optimization.
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.