Online Importance Weight Aware Updates

TL;DR

This paper introduces a novel importance weight-aware update method for online learning that improves robustness and efficiency, especially in active learning scenarios with large importance weights and adversarial noise.

Contribution

It develops an invariance-preserving update approach for importance weights, providing theoretical guarantees and practical improvements over standard gradient multiplication methods.

Findings

Superior prediction accuracy with similar computational cost

Reduced sensitivity to learning rate settings

Effective online active learning in noisy, adversarial environments

Abstract

An importance weight quantifies the relative importance of one example over another, coming up in applications of boosting, asymmetric classification costs, reductions, and active learning. The standard approach for dealing with importance weights in gradient descent is via multiplication of the gradient. We first demonstrate the problems of this approach when importance weights are large, and argue in favor of more sophisticated ways for dealing with them. We then develop an approach which enjoys an invariance property: that updating twice with importance weight $h$ is equivalent to updating once with importance weight $2h$. For many important losses this has a closed form update which satisfies standard regret guarantees when all examples have $h=1$. We also briefly discuss two other reasonable approaches for handling large importance weights. Empirically, these approaches yield substantially superior prediction with similar computational performance while reducing the sensitivity of the algorithm to the exact setting of the learning rate. We apply these to online active learning yielding an extraordinarily fast active learning algorithm that works even in the presence of adversarial noise.