# Expected Reward Prediction, with Applications to Model Routing

arXiv: https://arxiv.org/abs/2603.20217 · HTML: https://mlsanity.com/paper/2603.20217/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reward modeling and RLHF, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 21 of its 23 references that are in the map.
- First posted on arXiv 3 Mar 2026.

## Placed in

- LLM alignment / RLHF / preference optimisation / [Reward modeling and RLHF](https://mlsanity.com/alignment/reward-modeling-and-rlhf/)

## Builds on (most cited first, 21 of 21)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Gemma: Open Models Based on Gemini Research and Technology](https://mlsanity.com/paper/2403.08295/) (2024)
- [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)
- [MTEB: Massive Text Embedding Benchmark](https://mlsanity.com/paper/2210.07316/) (2022)
- [RewardBench: Evaluating Reward Models for Language Modeling](https://mlsanity.com/paper/2403.13787/) (2024)
- [Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMs](https://mlsanity.com/paper/2406.15927/) (2024)
- [Secrets of RLHF in Large Language Models Part II: Reward Modeling](https://mlsanity.com/paper/2401.06080/) (2024)
- [Routing to the Expert: Efficient Reward-guided Ensemble of Large Language Models](https://mlsanity.com/paper/2311.08692/) (2023)
- [Regularizing Hidden States Enables Learning Generalizable Reward Model for LLMs](https://mlsanity.com/paper/2406.10216/) (2024)
- [AutoMix: Automatically Mixing Language Models](https://mlsanity.com/paper/2310.12963/) (2023)
- [The Perfect Blend: Redefining RLHF with Mixture of Judges](https://mlsanity.com/paper/2409.20370/) (2024)
- [MetaLLM: A High-performant and Cost-efficient Dynamic Framework for Wrapping LLMs](https://mlsanity.com/paper/2407.10834/) (2024)
- [Transforming and Combining Rewards for Aligning Large Language Models](https://mlsanity.com/paper/2402.00742/) (2024)
- [OptLLM: Optimal Assignment of Queries to Large Language Models](https://mlsanity.com/paper/2405.15130/) (2024)

## Abstract (arXiv)

Reward models are a standard tool to score responses from LLMs. Reward models are built to rank responses to a fixed prompt sampled from a single model, for example to choose the best of n sampled responses. In this paper, we study whether scores from response-level reward models lifted to score a model's suitability for a prompt, prior to seeing responses from that model. Specifically, we show that it is straightforward to predict the expected reward that an LLM would earn from the reward model under repeated sampling. Further, we show that these expected reward predictions are precise and discriminative enough to support an application to a model routing protocol that routes prompts to models at inference time to maximize reward while controlling computational cost. We demonstrate the performance of this routing procedure on the open-perfectblend dataset, using a model pool composed of Llama3.1-Instruct 8B/70B, Gemma2-IT 9B/27B, and Gemma1-IT 7B models. Our simple expected reward prediction--based routing (ERP) outperforms baselines that route prompts to models with the best average performance within each prompt's category, and explains the success of more complex routing protocols that implicitly estimate an expected reward. Our approach has the added advantage of being trivially extensible as new models are added to the pool.