# LLM Routing with Dueling Feedback

arXiv: https://arxiv.org/abs/2510.00841 · HTML: https://mlsanity.com/paper/2510.00841/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 55 references that are in the map.
- First posted on arXiv 1 Oct 2025.

## Builds on (most cited first, 30 of 38)

- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Text Embeddings by Weakly-Supervised Contrastive Pre-training](https://mlsanity.com/paper/2212.03533/) (2022)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [RouteLLM: Learning to Route LLMs with Preference Data](https://mlsanity.com/paper/2406.18665/) (2024)
- [LLM-Blender: Ensembling Large Language Models with Pairwise Ranking and Generative Fusion](https://mlsanity.com/paper/2306.02561/) (2023)
- [Hybrid LLM: Cost-Efficient and Quality-Aware Query Routing](https://mlsanity.com/paper/2404.14618/) (2024)
- [RouterBench: A Benchmark for Multi-LLM Routing System](https://mlsanity.com/paper/2403.12031/) (2024)
- [GraphRouter: A Graph-based Router for LLM Selections](https://mlsanity.com/paper/2410.03834/) (2024)
- [Routing to the Expert: Efficient Reward-guided Ensemble of Large Language Models](https://mlsanity.com/paper/2311.08692/) (2023)
- [AutoMix: Automatically Mixing Language Models](https://mlsanity.com/paper/2310.12963/) (2023)
- [Why is Posterior Sampling Better than Optimism for Reinforcement Learning?](https://mlsanity.com/paper/1607.00215/) (2016)
- [Fly-Swat or Cannon? Cost-Effective Language Model Choice via Meta-Modeling](https://mlsanity.com/paper/2308.06077/) (2023)
- [Universal Model Routing for Efficient LLM Inference](https://mlsanity.com/paper/2502.08773/) (2025)
- [Learning to Route LLMs with Confidence Tokens](https://mlsanity.com/paper/2410.13284/) (2024)
- [Feel-Good Thompson Sampling for Contextual Bandits and Reinforcement Learning](https://mlsanity.com/paper/2110.00871/) (2021)
- [MixLLM: Dynamic Routing in Mixed Large Language Models](https://mlsanity.com/paper/2502.18482/) (2025)
- [EmbedLLM: Learning Compact Representations of Large Language Models](https://mlsanity.com/paper/2410.02223/) (2024)
- [Harnessing the Power of Multiple Minds: Lessons Learned from LLM Routing](https://mlsanity.com/paper/2405.00467/) (2024)
- [MetaLLM: A High-performant and Cost-efficient Dynamic Framework for Wrapping LLMs](https://mlsanity.com/paper/2407.10834/) (2024)
- [Cost-Effective Online Multi-LLM Selection with Versatile Reward Models](https://mlsanity.com/paper/2405.16587/) (2024)
- [Faster Cascades via Speculative Decoding](https://mlsanity.com/paper/2405.19261/) (2024)
- [The Avengers: A Simple Recipe for Uniting Smaller Language Models to Challenge Proprietary Giants](https://mlsanity.com/paper/2505.19797/) (2025)
- [Stochastic Contextual Dueling Bandits under Linear Stochastic Transitivity Models](https://mlsanity.com/paper/2202.04593/) (2022)
- [Eagle: Efficient Training-Free Router for Multi-LLM Inference](https://mlsanity.com/paper/2409.15518/) (2024)
- [LLM Bandit: Cost-Efficient LLM Generation via Preference-Conditioned Dynamic Routing](https://mlsanity.com/paper/2502.02743/) (2025)
- [Beyond GPT-5: Making LLMs Cheaper and Better via Performance-Efficiency Optimized Routing](https://mlsanity.com/paper/2508.12631/) (2025)
- [Model-based RL with Optimistic Posterior Sampling: Structural Conditions and Sample Complexity](https://mlsanity.com/paper/2206.07659/) (2022)
- [Feel-Good Thompson Sampling for Contextual Dueling Bandits](https://mlsanity.com/paper/2404.06013/) (2024)

## Built on by (most cited first, 7 of 7)

- [Dynamic Model Routing and Cascading for Efficient LLM Inference: A Survey](https://mlsanity.com/paper/2603.04445/) (2026)
- [Correlation-Aware Contextual Bandits with Surrogate Rewards for LLM Routing](https://mlsanity.com/paper/2607.09015/) (2026)
- [Algorithm for Contextual Queueing Bandits with Rate-Optimal Queue Length Regret](https://mlsanity.com/paper/2606.09668/) (2026)
- [Zero-Shot Confidence Estimation for Small LLMs: When Supervised Baselines Aren't Worth Training](https://mlsanity.com/paper/2605.02241/) (2026)
- [Steering Frozen LLMs: Adaptive Social Alignment via Online Prompt Routing](https://mlsanity.com/paper/2603.15647/) (2026)
- [CUPID in the Model Zoo: Online Matchmaking for Selecting Your Dream LLM](https://mlsanity.com/paper/2606.00846/) (2026)
- [Context-dependent agent evaluation with orthogonal equilibrium learning](https://mlsanity.com/paper/2609.31897/) (2026)

## Abstract (arXiv)

We study LLM routing, the problem of selecting the best model for each query while balancing user satisfaction, model expertise, and inference cost. We formulate routing as contextual dueling bandits, learning from pairwise preference feedback rather than absolute scores, thereby yielding label-efficient and dynamic adaptation. Building on this formulation, we introduce Category-Calibrated Fine-Tuning (CCFT), a representation-learning method that derives model embeddings from offline data using contrastive fine-tuning with categorical weighting. These embeddings enable the practical instantiation of Feel-Good Thompson Sampling for Contextual Dueling Bandits (FGTS.CDB), a theoretically grounded posterior-sampling algorithm. We propose four variants of the categorical weighting that explicitly integrate model quality and cost, and we empirically evaluate the proposed methods on the RouterBench and MixInstruct datasets. Across both benchmarks, our methods achieve lower cumulative regret and faster convergence, with better robustness and performance-cost balance than strong baselines built with a general-purpose OpenAI embedding model.