Adversarial Smoothed Analysis

TL;DR

This paper extends smoothed analysis of condition numbers to adversarial, radially symmetric distributions, showing that previous bounds remain valid even with singularities at the perturbation center.

Contribution

It generalizes existing smoothed analysis results to include adversarial distributions with singularities, broadening the applicability of the bounds.

Findings

Bounds on condition numbers hold for adversarial distributions

Results extend previous smoothed analysis to new distribution classes

Singularities at the perturbation center do not invalidate bounds

Abstract

The purpose of this note is to extend the results on uniform smoothed analysis of condition numbers from \cite{BuCuLo:07} to the case where the perturbation follows a radially symmetric probability distribution. In particular, we will show that the bounds derived in \cite{BuCuLo:07} still hold in the case of distributions whose density has a singularity at the center of the perturbation, which we call {\em adversarial}.