RACER: Risk-Aware Calibrated Efficient Routing for Large Language Models

Sai Hao, Hao Zeng, Hongxin Wei, Bingyi Jing
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:40499-40524, 2026.

Abstract

Efficiently routing queries to the optimal large language model (LLM) is crucial for optimizing the cost-performance trade-off in multi-model systems. However, most existing routers rely on single-model selection, making them susceptible to misrouting. In this work, we formulate LLM routing as the $\alpha$-VOR problem to minimize expected set size while controlling the misrouting risk, and propose a novel method – RACER, extending base routers to output model sets that can be subsequently aggregated for improved output. In particular, RACER constructs nested model sets via augmented scoring and utilizes finite-sample concentration bounds to calibrate a threshold that allows for both variable set sizes and abstention. We theoretically prove that RACER achieves rigorous distribution-free risk control on unseen test data in a post-hoc and model-agnostic manner. Extensive experiments verify our theoretical guarantees and demonstrate that RACER consistently enhances downstream accuracy across a wide range of benchmarks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-hao26c, title = {{RACER}: Risk-Aware Calibrated Efficient Routing for Large Language Models}, author = {Hao, Sai and Zeng, Hao and Wei, Hongxin and Jing, Bingyi}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {40499--40524}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/hao26c/hao26c.pdf}, url = {https://proceedings.mlr.press/v306/hao26c.html}, abstract = {Efficiently routing queries to the optimal large language model (LLM) is crucial for optimizing the cost-performance trade-off in multi-model systems. However, most existing routers rely on single-model selection, making them susceptible to misrouting. In this work, we formulate LLM routing as the $\alpha$-VOR problem to minimize expected set size while controlling the misrouting risk, and propose a novel method – RACER, extending base routers to output model sets that can be subsequently aggregated for improved output. In particular, RACER constructs nested model sets via augmented scoring and utilizes finite-sample concentration bounds to calibrate a threshold that allows for both variable set sizes and abstention. We theoretically prove that RACER achieves rigorous distribution-free risk control on unseen test data in a post-hoc and model-agnostic manner. Extensive experiments verify our theoretical guarantees and demonstrate that RACER consistently enhances downstream accuracy across a wide range of benchmarks.} }
Endnote
%0 Conference Paper %T RACER: Risk-Aware Calibrated Efficient Routing for Large Language Models %A Sai Hao %A Hao Zeng %A Hongxin Wei %A Bingyi Jing %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-hao26c %I PMLR %P 40499--40524 %U https://proceedings.mlr.press/v306/hao26c.html %V 306 %X Efficiently routing queries to the optimal large language model (LLM) is crucial for optimizing the cost-performance trade-off in multi-model systems. However, most existing routers rely on single-model selection, making them susceptible to misrouting. In this work, we formulate LLM routing as the $\alpha$-VOR problem to minimize expected set size while controlling the misrouting risk, and propose a novel method – RACER, extending base routers to output model sets that can be subsequently aggregated for improved output. In particular, RACER constructs nested model sets via augmented scoring and utilizes finite-sample concentration bounds to calibrate a threshold that allows for both variable set sizes and abstention. We theoretically prove that RACER achieves rigorous distribution-free risk control on unseen test data in a post-hoc and model-agnostic manner. Extensive experiments verify our theoretical guarantees and demonstrate that RACER consistently enhances downstream accuracy across a wide range of benchmarks.
APA
Hao, S., Zeng, H., Wei, H. & Jing, B.. (2026). RACER: Risk-Aware Calibrated Efficient Routing for Large Language Models. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:40499-40524 Available from https://proceedings.mlr.press/v306/hao26c.html.

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