`local' vs. `global' parameters -- breaking the gaussian complexity barrier

TL;DR

This paper demonstrates that for convex, subgaussian function classes, the learning error rate is governed by local covering estimates instead of traditional gaussian averages, providing sharper bounds.

Contribution

It introduces a novel approach linking error rates to local covering estimates, breaking the previous gaussian complexity barrier in learning theory.

Findings

Error rate determined by local covering estimates

Established sharp upper and lower bounds

Breaks the gaussian complexity barrier

Abstract

We show that if $F$ is a convex class of functions that is $L$-subgaussian, the error rate of learning problems generated by independent noise is equivalent to a fixed point determined by `local' covering estimates of the class, rather than by the gaussian averages. To that end, we establish new sharp upper and lower estimates on the error rate for such problems.