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arXiv · 2602.02061

Learning to Route and Schedule LLMs from User Retrials via Contextual Queueing Bandits

Seoungbin Bae·Junyoung Son·Dabeen Lee
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Abstract

Explosive demands for LLMs often cause user queries to accumulate in server queues, requiring efficient routing (query-LLM matching) and scheduling (query prioritization) mechanisms. Several online algorithms are being deployed, but they overlook the following two key challenges inherent to conversational LLM services: (1) unsatisfied users may retry queries, increasing the server backlog, and (2) requests for ``explicit" feedback, such as ratings, degrade user experiences. In this paper, we develop a joint routing and scheduling algorithm that leverages ``implicit" feedback inferred from user retrial behaviors. The key idea is to propose and study the framework of contextual queueing bandits with multinomial logit feedback (CQB-MNL). CQB-MNL models query retrials, as well as context-based learning for user preferences over LLMs. Our algorithm, anytime CQB (ACQB), achieves efficient learning while maintaining queue stability by combining Thompson sampling with forced exploration at a decaying rate. We show that ACQB simultaneously achieves a cumulative regret of $\widetilde{\mathcal{O}}(\sqrt{t})$ for routing and a queue length regret of $\widetilde{\mathcal{O}}(t^{-1/4})$ for any large $t$. For experiments, we refine query embeddings via contrastive learning while adopting a disjoint parameter model to learn LLM-specific parameters. Experiments on synthetic data, offline routing datasets (SPROUT, EmbedLLM, and RouterBench), and real user conversation logs (WildChat-1M) confirm that our methods improve routing, scheduling, and queue stability against strong online and offline-trained baselines.

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BibTeXRIS

Seoungbin Bae, Junyoung Son, Dabeen Lee. 2026-06-27. Learning to Route and Schedule LLMs from User Retrials via Contextual Queueing Bandits. https://arxiv.org/abs/2602.02061

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