Asymptotic sequential Rademacher complexity of a finite function class

TL;DR

This paper characterizes the large-sample limit of the sequential Rademacher complexity for finite function classes using viscosity solutions of a G-heat equation and G-normal variables, providing bounds for this complexity.

Contribution

It introduces a novel connection between sequential Rademacher complexity and G-heat equations, expanding understanding of complexity limits in learning theory.

Findings

Derived the asymptotic form of sequential Rademacher complexity

Connected complexity to viscosity solutions of G-heat equations

Provided bounds for the asymptotic complexity

Abstract

For a finite function class we describe the large sample limit of the sequential Rademacher complexity in terms of the viscosity solution of a $G$-heat equation. In the language of Peng's sublinear expectation theory, the same quantity equals to the expected value of the largest order statistics of a multidimensional $G$-normal random variable. We illustrate this result by deriving upper and lower bounds for the asymptotic sequential Rademacher complexity.