Active Learning via Regression Beyond Realizability

TL;DR

This paper introduces a new active learning framework for multiclass classification that works effectively even when the standard realizability assumption is violated, broadening practical applicability.

Contribution

It proposes an epoch-based active learning algorithm that operates under weaker conditions than realizability, using convex model classes and improper aggregation.

Findings

Achieves label and sample complexity comparable to prior work in non-realizable settings.

Demonstrates failure of previous algorithms under non-realizable conditions.

Provides an epoch-based method that fits models from the full class to queried data.

Abstract

We present a new active learning framework for multiclass classification based on surrogate risk minimization that operates beyond the standard realizability assumption. Existing surrogate-based active learning algorithms crucially rely on realizability$\unicode{x2014}$the assumption that the optimal surrogate predictor lies within the model class$\unicode{x2014}$limiting their applicability in practical, misspecified settings. In this work we show that under conditions significantly weaker than realizability, as long as the class of models considered is convex, one can still obtain a label and sample complexity comparable to prior work. Despite achieving similar rates, the algorithmic approaches from prior works can be shown to fail in non-realizable settings where our assumption is satisfied. Our epoch-based active learning algorithm departs from prior methods by fitting a model from the full class to the queried data in each epoch and returning an improper classifier obtained by aggregating these models.