# Handoff Curves: Initial Selection, Later Handoff, and Supervision Targets in Multi-turn LLM Routing

arXiv: https://arxiv.org/abs/2610.15993 · HTML: https://mlsanity.com/paper/2610.15993/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 46 references that are in the map.
- First posted on arXiv 11 Oct 2026.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [MiniLM: Deep Self-Attention Distillation for Task-Agnostic Compression of Pre-Trained Transformers](https://mlsanity.com/paper/2002.10957/) (2020)
- [τ-bench: A Benchmark for Tool-Agent-User Interaction in Real-World Domains](https://mlsanity.com/paper/2406.12045/) (2024)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [MultiWOZ -- A Large-Scale Multi-Domain Wizard-of-Oz Dataset for Task-Oriented Dialogue Modelling](https://mlsanity.com/paper/1810.00278/) (2018)
- [Hybrid LLM: Cost-Efficient and Quality-Aware Query Routing](https://mlsanity.com/paper/2404.14618/) (2024)
- [Large Language Model Routing with Benchmark Datasets](https://mlsanity.com/paper/2309.15789/) (2023)
- [MultiWOZ 2.4: A Multi-Domain Task-Oriented Dialogue Dataset with Essential Annotation Corrections to Improve State Tracking Evaluation](https://mlsanity.com/paper/2104.00773/) (2021)
- [When Does Combining Language Models Help? A Co-Failure Ceiling on Routing, Voting, and Mixture-of-Agents Across 67 Frontier Models](https://mlsanity.com/paper/2606.27288/) (2026)
- [SWE-Router: Routing in Multi-turn Agentic Software Engineering Tasks](https://mlsanity.com/paper/2607.00053/) (2026)
- [TRIM: Hybrid Inference via Targeted Stepwise Routing in Multi-Step Reasoning Tasks](https://mlsanity.com/paper/2601.10245/) (2026)
- [The Replay Gap: Static Evaluation of Model Switching in LLM Agents Scores the Wrong World](https://mlsanity.com/paper/2608.08239/) (2026)
- [ReDAct: Uncertainty-Aware Deferral for LLM Agents](https://mlsanity.com/paper/2604.07036/) (2026)
- [Evaluating Performance Drift from Model Switching in Multi-Turn LLM Systems](https://mlsanity.com/paper/2603.03111/) (2026)
- [vLLM Semantic Router: Signal Driven Decision Routing for Mixture-of-Modality Models](https://mlsanity.com/paper/2603.04444/) (2026)
- [TwinRouterBench: Fast Static and Live Dynamic Evaluation for Realistic Agentic LLM Routing](https://mlsanity.com/paper/2605.18859/) (2026)
- [The Handoff Tax: Continuing Non-Native Trajectories in LLM Agents](https://mlsanity.com/paper/2608.24358/) (2026)
- [What Does a Routing Oracle Measure Under Stochastic Decoding? Coupling, Scorer Choice, and Single-Commit Ceilings](https://mlsanity.com/paper/2607.03436/) (2026)
- [From Myopic Selection to Long-Horizon Awareness: Sequential LLM Routing for Multi-Turn Dialogue](https://mlsanity.com/paper/2604.12385/) (2026)
- [Opportunity Is Not Realizability: Selection-Valid Diagnostics for Multi-LLM Routing](https://mlsanity.com/paper/2608.08265/) (2026)
- [Most of the LLM Routing Gap Is Task Type](https://mlsanity.com/paper/2608.23023/) (2026)
- [Dynamic Mixed-Precision Routing for Efficient Multi-step LLM Interaction](https://mlsanity.com/paper/2602.02711/) (2026)
- [TACIT-Switch: Cost-Aware Model Escalation for LLM Agents from Censored Supervision](https://mlsanity.com/paper/2608.27911/) (2026)

## Abstract (arXiv)

We study how initial model selection, later handoff, and training targets affect success and cost in LLM tasks that span multiple turns. We compare several router architectures using handoff curves, which record task success and cost as the handoff step changes. Our dataset contains 34,204 complete executions of three Qwen models across BFCL, MultiWOZ, and τ-retail, providing offline supervision for routing decisions. In our primary comparison, with Qwen3.5 35B-A3B as the starting model, allowing a later handoff does not establish an improvement in utility over initial selection on BFCL or MultiWOZ, and increases cost on BFCL across a range of cost weights. Changing the supervision targets improves router performance on both our dataset and TwinRouterBench. On our dataset, replacing noisy training success curves with monotone fits raises success by 0.2 to 4.1 percentage points at the same cost across the reported operating points. On TwinRouterBench, we construct targets that describe the model capability needed for the remaining work and difficult steps ahead. Compared with training on the benchmark's per-step labels, these targets raise trajectory pass scores by 7.8 percentage points and cost savings by 6.3 percentage points on the full static bank. A live deployment of the router trained with these targets resolves 79 of 100 instances at a router cost of 0.59 US dollars per instance.