Margin-Independent Online Multiclass Learning via Convex Geometry
This work addresses online learning efficiency for multiclass classification, offering a novel approach with theoretical guarantees, though it is incremental in building on contextual search and reduction techniques.
The paper tackles online multiclass classification by minimizing the total distance from queries to correct label regions instead of misclassification rate, achieving a loss independent of the number of queries for nearest neighbor partitions, while showing that learning general convex sets incurs almost linear loss per query.
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.