Online Learning with LLM Experts from Limited Feedback

📅 2026-09-05
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📝 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 $\tilde{O}(d T / \sqrt{m})$, while in the bandit setting we achieve $\tilde{O}(d T \sqrt{K / m})$, where $m \ll T$ is a budget on feedback. Our experiments show that we efficiently learn high-quality routing strategies across diverse LLMs from limited feedback.
Problem

Research questions and friction points this paper is trying to address.

online learning
large language model
limited feedback
adaptive routing
Innovation

Methods, ideas, or system contributions that make the work stand out.

Online Learning
Large Language Model (LLM) Experts
Limited Feedback
Bandit Problem
Adaptive Routing
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