Characterizing and Correcting Effective Target Shift in Online Learning
For researchers studying online learning under distributional shift, this work provides a theoretical framework and practical correction method to improve performance, though it is limited to kernel regression and specific settings.
The paper derives a closed-form expression for online kernel regression, showing it is equivalent to offline regression with shifted targets, and proposes a target correction method that enables online learning to match offline performance. On CIFAR-10 and CORe50, online SGD with corrected targets outperforms standard online learning in continual learning settings.
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.