Online Learning-to-Defer with Varying Experts
Abstract
Learning-to-Defer (L2D) methods route each query either to a predictive model or to external experts. Real-world deployments require handling streaming data, changing expert availability, shifting expert reliability, and feedback observed only for the selected action. We introduce an online multiclass L2D algorithm that combines queried-action bandit feedback with a dynamically varying pool of experts. Let N=n+ne, let B bound the Frobenius norm of the linear score matrix, and let ρ bound the augmented input norm. Assuming linear calibration and zero surrogate minimizability gap for the projected comparator class, our method achieves expected true-deferral regret O((BN3/2ρ+1)T2/3), improving to O(BN3/2ρ√T+B2N3ρ2) under a concentrated-score condition. The analysis combines an online ℋ-consistency transfer bound with projected online convex optimization. Experiments on synthetic and real-world datasets demonstrate selective routing under varying expert availability and reliability.
Related
- Online Learning with LLM Experts from Limited Feedback
- Strongly Adaptive Online Learning with Time-Varying Movement Costs
- Private Online Prediction from Experts with Small Losses
- Tracking a Small Set of Experts in Online Convex Optimization
- Minimax Alternating Regret for the Experts Problem and Online Convex Optimization
BibTeX
@misc{duy2026online,
title = {{Online Learning-to-Defer with Varying Experts}},
author = {Dang Hoang Duy and Yannis Montreuil and Maxime Meyer and Axel Carlier and Lai Xing Ng and Wei Tsang Ooi},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2605.12340},
eprint = {2605.12340},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.12340},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Online Learning-to-Defer with Varying Experts
AU - Dang Hoang Duy
AU - Yannis Montreuil
AU - Maxime Meyer
AU - Axel Carlier
AU - Lai Xing Ng
AU - Wei Tsang Ooi
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2605.12340
UR - https://arxiv.org/abs/2605.12340
AB - Learning-to-Defer (L2D) methods route each query either to a predictive model or to external experts. Real-world deployments require handling streaming data, changing expert availability, shifting expert reliability, and feedback observed only for the selected action. We introduce an online multiclass L2D algorithm that combines queried-action bandit feedback with a dynamically varying pool of experts. Let N=n+n_e, let B bound the Frobenius norm of the linear score matrix, and let ρ bound the augmented input norm. Assuming linear calibration and zero surrogate minimizability gap for the projected comparator class, our method achieves expected true-deferral regret O((BN^3/2ρ+1)T^2/3), improving to O(BN^3/2ρ√T+B^2N^3ρ^2) under a concentrated-score condition. The analysis combines an online ℋ-consistency transfer bound with projected online convex optimization. Experiments on synthetic and real-world datasets demonstrate selective routing under varying expert availability and reliability.
ER -