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

arXiv: https://arxiv.org/abs/2604.23530 · HTML: https://mlsanity.com/paper/2604.23530/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 19 references that are in the map.
- First posted on arXiv 26 Apr 2026.

## Builds on (most cited first, 10 of 10)

- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [ToolLLM: Facilitating Large Language Models to Master 16000+ Real-world APIs](https://mlsanity.com/paper/2307.16789/) (2023)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [OSWorld: Benchmarking Multimodal Agents for Open-Ended Tasks in Real Computer Environments](https://mlsanity.com/paper/2404.07972/) (2024)
- [GAIA: a benchmark for General AI Assistants](https://mlsanity.com/paper/2311.12983/) (2023)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)

## Built on by (most cited first, 10 of 10)

- [The Handoff Tax: Continuing Non-Native Trajectories in LLM Agents](https://mlsanity.com/paper/2608.24358/) (2026)
- [Error-Aware Reverse Auction Mechanism for Large Language Model Routing](https://mlsanity.com/paper/2608.12719/) (2026)
- [RSI-Router: Evolving Subtask-Level LLM Routing and Skills for Cost-Efficient Agents](https://mlsanity.com/paper/2609.34712/) (2026)
- [Do Not Restart: Residual Completion for Stateful Agent Handoffs](https://mlsanity.com/paper/2609.13800/) (2026)
- [Learning What to Activate: Combinatorial Capability Allocation for Long-Horizon Multimodal Agents](https://mlsanity.com/paper/2609.27869/) (2026)
- [Trust the Brand, Lose Control: How Identity Hijacks LLM Agent Orchestration](https://mlsanity.com/paper/2609.32635/) (2026)
- [You Cannot Pick a Provider From the Price List: Market-Aware Routing for Open-Weight LLM Inference](https://mlsanity.com/paper/2609.37902/) (2026)
- [TurnCost: Turns, Not Observations: Cache-Aware Loop Engineering for Coding Agents](https://mlsanity.com/paper/2610.15093/) (2026)
- [Whose turn is it? Context-guided model routing for stateful agents](https://mlsanity.com/paper/2610.19292/) (2026)
- [New Model, Old Habits: Behavior Transfer under Model Swapping in Multi-Session LLM Agents](https://mlsanity.com/paper/2610.19712/) (2026)

## Abstract (arXiv)

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