Characterizing and Correcting Effective Target Shift in Online Learning

TL;DR

This paper analyzes how online kernel regression is affected by effective target shifts under distributional changes and proposes a target correction method to improve online learning performance.

Contribution

It derives a closed-form expression linking online and offline kernel regression and introduces a target correction technique to match offline performance in online settings.

Findings

Target correction improves online learning in non-stationary environments.

Online kernel regression is equivalent to offline regression with shifted targets.

Iterative target correction enhances performance on CIFAR-10 and CORe50.

Abstract

Online learning from a stream of data is a defining feature of intelligence, yet modern machine learning systems often struggle in this setting, especially under distributional shift. To understand its basic properties, we study the relationship between online and offline learning in the context of kernel regression. We derive a closed-form expression for the function learned by online kernel regression, revealing that online kernel regression is equivalent to offline regression with shifted, inaccurate target outputs. Conversely, we show that by compensating for this effective shift in the teaching signal through target correction, online kernel-based learning can provably learn the same predictor as its offline counterpart. We derive both a closed-form expression for this target correction and an iterative form that can be applied sequentially. Applying this framework to image classification tasks on CIFAR-10 and CORe50, we show that online stochastic gradient descent with iteratively corrected targets outperforms learning with the true targets in continual learning settings. This work therefore provides a basic framework for analyzing and improving online learning in non-stationary environments.