An Improved Uniform Convergence Bound with Fat-Shattering Dimension

TL;DR

This paper presents an improved uniform convergence bound for real-valued functions using fat-shattering dimension, reducing the gap between upper and lower bounds on sample complexity.

Contribution

It introduces a tighter uniform convergence bound that eliminates the squared logarithmic factor present in previous bounds.

Findings

New bound closes the gap with lower bounds

Reduces sample complexity estimates

Advances theoretical understanding of real-valued function classes

Abstract

The fat-shattering dimension characterizes the uniform convergence property of real-valued functions. The state-of-the-art upper bounds feature a multiplicative squared logarithmic factor on the sample complexity, leaving an open gap with the existing lower bound. We provide an improved uniform convergence bound that closes this gap.