@inproceedings{zhang-etal-2026-mtrouter,
    title = "{MTR}outer: Cost-Aware Multi-Turn {LLM} Routing with History{--}Model Joint Embeddings",
    author = "Zhang, Yiqun  and
      Li, Hao  and
      Wang, Zihan  and
      Feng, Shi  and
      Yang, Xiaocui  and
      Wang, Daling  and
      Zhang, Bo  and
      Bai, Lei  and
      Hu, Shuyue",
    editor = "Liakata, Maria  and
      Moreira, Viviane P.  and
      Zhang, Jiajun  and
      Jurgens, David",
    booktitle = "Proceedings of the 64th Annual Meeting of the {A}ssociation for {C}omputational {L}inguistics (Volume 1: Long Papers)",
    month = jul,
    year = "2026",
    address = "San Diego, California, United States",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingest-acl/2026.acl-long.2045/",
    pages = "44206--44226",
    ISBN = "979-8-89176-390-6",
    abstract = "Multi-turn, long-horizon tasks are increasingly common for large language models (LLMs), but solving them typically requires many sequential model invocations, accumulating substantial inference costs. Here, we study cost-aware multi-turn LLM routing: selecting which model to invoke at each turn from a model pool, given a fixed cost budget. We propose MTRouter, which encodes the interaction history and candidate models into joint history{--}model embeddings, and learns an outcome estimator from logged trajectories to predict turn-level model utility. Experiments show that MTRouter improves the performance{--}cost trade-off: on ScienceWorld, it surpasses GPT-5 while reducing total cost by 58.7{\%}; on Humanity{'}s Last Exam (HLE), it achieves competitive accuracy while reducing total cost by 43.4{\%} relative to GPT-5, and these gains even carry over to held-out tasks. Further analyses reveal several mechanisms underlying its effectiveness: relative to prior multi-turn routers, MTRouter makes fewer model switches, is more tolerant to transient errors, and exhibits emergent specialization across models.Code: https://github.com/ZhangYiqun018/MTRouter"
}