Online Learning-to-Defer with Varying Experts

Yannis Montreuil, Hoang Duy Dang, Maxime Meyer, Lai Xing Ng, Axel Carlier, Wei Tsang Ooi

TL;DR: We introduce a Learning-to-Defer approach in the online learning setting that allows deferral to a varying number of experts.

Abstract: 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, $n$ the number of labels, and $n_e$ 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.

Submission Number: 1204