PreprintCC BY 4.0arXiv
Online Learning with LLM Experts from Limited Feedback
Abstract
We study adaptive routing of prompts to large language model (LLM) experts to maximize response quality in an online setting with limited feedback. We formulate it as a bandit problem with K actions that represent experts and d features that encode prompts, over a horizon of T rounds. We propose algorithms that strategically select and observe rewards to minimize regret. In the full-information setting, we achieve a regret of Õ(d T / √m), while in the bandit setting we achieve Õ(d T √(K / m)), where m ≪ T is a budget on feedback. Our experiments show that we efficiently learn high-quality routing strategies across diverse LLMs from limited feedback.
Related
- Online Learning-to-Defer with Varying Experts
- 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
- Online Feedback Optimization for Constrained Stochastic Problems with Decision-Dependent Distributions
BibTeX
@misc{wei2026online,
title = {{Online Learning with LLM Experts from Limited Feedback}},
author = {Wang Wei and Soumyabrata Pal and Koyel Mukherjee and Franck Dernoncourt and Ryan A. Rossi and Branislav Kveton and Hoda Eldardiry},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05820},
eprint = {2609.05820},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05820},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Online Learning with LLM Experts from Limited Feedback
AU - Wang Wei
AU - Soumyabrata Pal
AU - Koyel Mukherjee
AU - Franck Dernoncourt
AU - Ryan A. Rossi
AU - Branislav Kveton
AU - Hoda Eldardiry
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2609.05820
UR - https://arxiv.org/abs/2609.05820
AB - We study adaptive routing of prompts to large language model (LLM) experts to maximize response quality in an online setting with limited feedback. We formulate it as a bandit problem with K actions that represent experts and d features that encode prompts, over a horizon of T rounds. We propose algorithms that strategically select and observe rewards to minimize regret. In the full-information setting, we achieve a regret of Õ(d T / √m), while in the bandit setting we achieve Õ(d T √(K / m)), where m ≪ T is a budget on feedback. Our experiments show that we efficiently learn high-quality routing strategies across diverse LLMs from limited feedback.
ER -