# Optimality Implies Kernel Sum Classifiers are Statistically Efficient

## TL;DR

This paper introduces a new theoretical framework combining optimization and learning theory to analyze the sample complexity of optimal kernel sum classifiers, providing insights into their efficiency and justifying prior assumptions.

## Contribution

It presents a novel analysis method for optimal classifiers using learning theory bounds, and introduces a new Rademacher complexity for such classes.

## Key findings

- Optimal classifiers have favorable sample complexity.
- The analysis justifies assumptions in multiple kernel learning.
- New Rademacher complexity bounds for optimal classifiers.

## Abstract

We propose a novel combination of optimization tools with learning theory bounds in order to analyze the sample complexity of optimal kernel sum classifiers. This contrasts the typical learning theoretic results which hold for all (potentially suboptimal) classifiers. Our work also justifies assumptions made in prior work on multiple kernel learning. As a byproduct of our analysis, we also provide a new form of Rademacher complexity for hypothesis classes containing only optimal classifiers.