Learning-to-Defer (L2D) methods route each query either to a predictive model or to external experts. While existing work studies this problem in batch settings, real-world deployments require handling streaming data, changing expert availability, and shifting expert distribution. We introduce the first online L2D algorithm for multiclass classification with bandit feedback and a dynamically varying pool of experts. Our method achieves regret guarantees of $O((n+n_e)T^{2/3})$ in general and $O((n+n_e)\sqrt{T})$ under a low-noise condition, where $T$ is the time horizon, $n$ is the number of labels, and $n_e$ is the number of distinct experts observed across rounds. The analysis builds on novel $\mathcal{H}$-consistency bounds for the online framework, combined with first-order methods for online convex optimization. Experiments on synthetic and real-world datasets demonstrate that our approach effectively extends standard Learning-to-Defer to settings with varying expert availability and reliability.

翻译：延迟学习方法（Learning-to-Defer, L2D）将每条查询路由至预测模型或外部专家。现有研究在批量设置下探讨该问题，但实际部署需要处理流式数据、专家可用性变化及专家分布迁移。我们提出首个面向多类分类的在线L2D算法，适用于带强盗反馈和动态变化专家池的场景。该算法在一般条件下实现$O((n+n_e)T^{2/3})$的遗憾界，在低噪声条件下达到$O((n+n_e)\sqrt{T})$，其中$T$为时间范围，$n$为标签数量，$n_e$为跨轮次观测到的不同专家数。理论分析基于在线框架下新型$\mathcal{H}$一致性界，并结合在线凸优化的一阶方法。合成数据集与真实数据集的实验表明，该方法能有效将标准延迟学习拓展至专家可用性与可靠性动态变化的场景。