A Query Is Not a Commitment: Learning to Correct Expert Answers in Online Deferral
Abstract
An inaccurate expert can still provide useful information after correction. We study online learning to defer in which the learner chooses an expert and fixes a correction function before purchasing its answer, then applies that function to the answer received. The difficulty is that observed losses reflect both expert quality and an unfinished correction: early errors can discourage queries that would be valuable after learning. We propose ORUCB, which pools shared and expert-specific polynomial responses. A bound on cumulative response-learning error calibrates confidence-weighted risk regression and exploration, allowing the router to account for this error when deciding which answers to buy. Under bounded residuals and disagreements, a fixed feasible model of optimal responses, and linear models of free and optimal queried risk, the calibrated algorithm achieves high-probability pseudo-regret O(√Tlog(T+1)) over T rounds for fixed problem parameters. The guarantee permits singular answer distributions and misspecified shared responses; optimality is relative to the bounded response class. On four test streams, the selected cubic policy has lower fee-inclusive cost than seven baselines that deploy answers unchanged. Comparisons with a common correction learner examine routing, while six-price comparisons measure cost and query rates.
Related
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- Learning to Solve Two-Stage Stochastic Unit Commitment Problems with Quality Guarantees
- CARE-MoE: Conflict-Aware Routing-Guided Expert Mixture-of-Experts for Continual Learning
- Think Short, Defer Smart, Act, and Repeat: Calibrated Reasoning and Uncertainty-Aware Deferral for Edge LLM Agents
- Spectral geometry: old questions and new answers
BibTeX
@misc{montreuil2026query,
title = {{A Query Is Not a Commitment: Learning to Correct Expert Answers in Online Deferral}},
author = {Yannis Montreuil and Axel Carlier and Lai Xing Ng and Wei Tsang Ooi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07084},
eprint = {2610.07084},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07084},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Query Is Not a Commitment: Learning to Correct Expert Answers in Online Deferral
AU - Yannis Montreuil
AU - Axel Carlier
AU - Lai Xing Ng
AU - Wei Tsang Ooi
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.07084
UR - https://arxiv.org/abs/2610.07084
AB - An inaccurate expert can still provide useful information after correction. We study online learning to defer in which the learner chooses an expert and fixes a correction function before purchasing its answer, then applies that function to the answer received. The difficulty is that observed losses reflect both expert quality and an unfinished correction: early errors can discourage queries that would be valuable after learning. We propose ORUCB, which pools shared and expert-specific polynomial responses. A bound on cumulative response-learning error calibrates confidence-weighted risk regression and exploration, allowing the router to account for this error when deciding which answers to buy. Under bounded residuals and disagreements, a fixed feasible model of optimal responses, and linear models of free and optimal queried risk, the calibrated algorithm achieves high-probability pseudo-regret O(√Tlog(T+1)) over T rounds for fixed problem parameters. The guarantee permits singular answer distributions and misspecified shared responses; optimality is relative to the bounded response class. On four test streams, the selected cubic policy has lower fee-inclusive cost than seven baselines that deploy answers unchanged. Comparisons with a common correction learner examine routing, while six-price comparisons measure cost and query rates.
ER -