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

• URL: http://arxiv.org/abs/2604.23530v1
• Date: Sun, 26 Apr 2026 04:42:21 GMT
• Title: MTRouter: Cost-Aware Multi-Turn LLM Routing with History-Model Joint Embeddings
• Abstract summary: We study cost-aware multi-turn routing for large language models.<n>We propose MT, which encodes the interaction history and candidate models into joint history-model embeddings.<n>Experiments show that MT improves the performance-cost trade-off.
• Score: 47.963523156965174
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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

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