Margin-Independent Online Multiclass Learning via Convex Geometry

TL;DR

This paper introduces a novel online multiclass learning method that minimizes total distance to correct label regions, achieving loss bounds independent of query count under certain conditions, and presents a reduction from multiclass to binary classification.

Contribution

It proposes a margin-independent online multiclass learning algorithm for nearest neighbor labelings and introduces a new reduction technique from multiclass to binary classification.

Findings

Achieves query-independent loss bounds for nearest neighbor labelings.

Shows that learning general convex sets incurs near-linear loss per query.

Develops a novel reduction from multiclass to binary classification.

Abstract

We consider the problem of multi-class classification, where a stream of adversarially chosen queries arrive and must be assigned a label online. Unlike traditional bounds which seek to minimize the misclassification rate, we minimize the total distance from each query to the region corresponding to its correct label. When the true labels are determined via a nearest neighbor partition -- i.e. the label of a point is given by which of $k$ centers it is closest to in Euclidean distance -- we show that one can achieve a loss that is independent of the total number of queries. We complement this result by showing that learning general convex sets requires an almost linear loss per query. Our results build off of regret guarantees for the geometric problem of contextual search. In addition, we develop a novel reduction technique from multiclass classification to binary classification which may be of independent interest.