Online nearest neighbor classification

TL;DR

This paper demonstrates that the classical 1-nearest neighbor algorithm achieves sublinear regret, meaning it makes fewer mistakes over time, in online non-parametric classification against certain adversaries in the realizable setting.

Contribution

It provides a theoretical analysis showing the effectiveness of 1-nearest neighbor in online classification with adversarial conditions.

Findings

Achieves sublinear regret in online classification

Works against dominated or smoothed adversaries

Validates classical algorithm in online setting

Abstract

We study an instance of online non-parametric classification in the realizable setting. In particular, we consider the classical 1-nearest neighbor algorithm, and show that it achieves sublinear regret - that is, a vanishing mistake rate - against dominated or smoothed adversaries in the realizable setting.