Adapting to Online Label Shift with Provable Guarantees

TL;DR

This paper addresses online label shift in machine learning, proposing a new risk estimator and ensemble algorithms with provable guarantees, achieving optimal dynamic regret under changing label distributions.

Contribution

It introduces an unbiased risk estimator and novel online ensemble methods for online label shift, with theoretical guarantees and adaptive performance bounds.

Findings

Achieves optimal dynamic regret in online label shift scenarios.

Effectively adapts to label distribution changes over time.

Validated through extensive experiments supporting theoretical results.

Abstract

The standard supervised learning paradigm works effectively when training data shares the same distribution as the upcoming testing samples. However, this stationary assumption is often violated in real-world applications, especially when testing data appear in an online fashion. In this paper, we formulate and investigate the problem of \emph{online label shift} (OLaS): the learner trains an initial model from the labeled offline data and then deploys it to an unlabeled online environment where the underlying label distribution changes over time but the label-conditional density does not. The non-stationarity nature and the lack of supervision make the problem challenging to be tackled. To address the difficulty, we construct a new unbiased risk estimator that utilizes the unlabeled data, which exhibits many benign properties albeit with potential non-convexity. Building upon that, we propose novel online ensemble algorithms to deal with the non-stationarity of the environments. Our approach enjoys optimal \emph{dynamic regret}, indicating that the performance is competitive with a clairvoyant who knows the online environments in hindsight and then chooses the best decision for each round. The obtained dynamic regret bound scales with the intensity and pattern of label distribution shift, hence exhibiting the adaptivity in the OLaS problem. Extensive experiments are conducted to validate the effectiveness and support our theoretical findings.