MTRouter: Cost-Aware Multi-Turn LLM Routing with History-Model Joint Embeddings

No single large language model (LLM) is optimal across all queries and budget constraints, making model routing essential for cost-effective deployment. Existing routers adopt diverse formulations and implementations, making fair comparison and extension difficult. We present a unified formulation of LLM routing as a sequential decision process characterized by five components: context encoders, model encoders, scoring functions, decision rules, and learning signals, covering single-turn, multi-turn, and personalized routing. Based on this formulation, we develop an automated pipeline for constructing routing supervision and evaluating routers jointly on response quality and inference cost. The resulting benchmark, xRouteBench, spans generic LLM, memory-augmented, vision, time-series, and personalized routing tasks. We further introduce LLMRouter, an open-source modular infrastructure with more than 16 representative routers. Our empirical study shows that learned routers outperform the strongest fixed-model baseline by 14.6% relatively, lightweight routers become more competitive under tight cost constraints, and user-conditioned routing consistently improves personalization.

Large language models (LLMs) achieve impressive performance across multiple domains, but using the most capable model for every query is prohibitive at scale. LLM routing exploits diversity in model capability and cost by assigning each query to a suitable model to balance utility and budget. Current methods have two limitations: (i) they either use heuristics that do not always enforce the budget constraint or impose a fixed per-query budget that cannot adapt across the workload and leads to suboptimal performance; (ii) they require supervised learning on a dense dataset with statistics for every query-model pair, which is expensive to collect. To address these challenges, we formulate LLM routing as a constrained contextual multi-armed bandit problem and introduce WISERouter (WR for short), a framework that supports offline learning from historical interactions as well as online learning with exploration. We further prove that WR-Online achieves a sublinear regret bound of $O(\sqrt{T})$ over a time horizon $T$. Empirical results on RouterBench and SWE-Bench demonstrate that (i) WR-Offline surpasses existing baselines in performance under a fixed budget and adheres more closely to budget constraints, and (ii) WR-Online achieves comparable performance to the baselines, while using substantially less exploration data.

The rapid development of large language models, each with distinct capabilities and inference costs, raises a practical deployment question: given an incoming request, which model should handle it? We present OrcaRouter, a production-oriented LLM router that combines a LinUCB-based contextual bandit over lexical and sentence-embedding features with a hybrid offline-online learning protocol. Offline, OrcaRouter obtains full-information feedback by evaluating each candidate model on a curated set of routing prompts, yielding a reward matrix used to fit one ridge regressor per arm. At deployment time, it initializes from these parameters and can optionally continue learning from bandit feedback, updating only the selected model's arm after observing its reward. At the time of our RouterArena submission (May 20, 2026), OrcaRouter-Adaptive ranked second on the public RouterArena leaderboard with an arena score of 72.08, achieving 75.54% accuracy at a cost of USD 1.00 per 1,000 queries.