This paper focuses on supervised and unsupervised online label shift, where the class marginals $Q(y)$ varies but the class-conditionals $Q(x|y)$ remain invariant. In the unsupervised setting, our goal is to adapt a learner, trained on some offline labeled data, to changing label distributions given unlabeled online data. In the supervised setting, we must both learn a classifier and adapt to the dynamically evolving class marginals given only labeled online data. We develop novel algorithms that reduce the adaptation problem to online regression and guarantee optimal dynamic regret without any prior knowledge of the extent of drift in the label distribution. Our solution is based on bootstrapping the estimates of \emph{online regression oracles} that track the drifting proportions. Experiments across numerous simulated and real-world online label shift scenarios demonstrate the superior performance of our proposed approaches, often achieving 1-3\% improvement in accuracy while being sample and computationally efficient. Code is publicly available at https://github.com/acmi-lab/OnlineLabelShift.

翻译：本文聚焦于监督和无监督在线标签偏移问题，其中类别边际分布 $Q(y)$ 变化，但类别条件分布 $Q(x|y)$ 保持不变。在无监督设置中，我们的目标是使基于离线标注数据训练的学习器能够适应带有未标注在线数据的动态标签分布。在有监督设置中，我们需在仅依赖在线标注数据的同时，既完成分类器学习，又适应动态演变的类别边际分布。我们提出了新颖算法，将自适应问题简化为在线回归，并在无需预知标签分布漂移程度的情况下，保证最优动态遗憾。本方法的核心理念在于通过引导在线回归预言机（oracle）的估计来追踪不断漂移的比例。在多种模拟和真实在线标签偏移场景下的实验表明，所提方法性能优异，通常可实现1-3%的准确率提升，同时保持样本与计算效率。代码已开源：https://github.com/acmi-lab/OnlineLabelShift。