# PoEM: Predicting RL Outcomes from Existing Policies

arXiv: https://arxiv.org/abs/2609.30226 · HTML: https://mlsanity.com/paper/2609.30226/

## 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 52 of its 57 references that are in the map.
- First posted on arXiv 24 Sep 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, 30 of 52)

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- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
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- [Pick-a-Pic: An Open Dataset of User Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2305.01569/) (2023)
- [Enhancing Chat Language Models by Scaling High-quality Instructional Conversations](https://mlsanity.com/paper/2305.14233/) (2023)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1910.00177/) (2019)
- [OpenAssistant Conversations -- Democratizing Large Language Model Alignment](https://mlsanity.com/paper/2304.07327/) (2023)
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- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [RewardBench: Evaluating Reward Models for Language Modeling](https://mlsanity.com/paper/2403.13787/) (2024)
- [DExperts: Decoding-Time Controlled Text Generation with Experts and Anti-Experts](https://mlsanity.com/paper/2105.03023/) (2021)
- [InternLM2 Technical Report](https://mlsanity.com/paper/2403.17297/) (2024)
- [Interpretable Preferences via Multi-Objective Reward Modeling and Mixture-of-Experts](https://mlsanity.com/paper/2406.12845/) (2024)
- [Successor Features for Transfer in Reinforcement Learning](https://mlsanity.com/paper/1606.05312/) (2016)
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- [Personalized Soups: Personalized Large Language Model Alignment via Post-hoc Parameter Merging](https://mlsanity.com/paper/2310.11564/) (2023)

## Abstract (arXiv)

Foundation models are post-trained with reinforcement learning (RL) to maximize specific rewards, such as human alignment, correctness, or instruction following. This post-training process is computationally intensive, sometimes unstable, and has to be run from scratch every time the reward model changes or when we want to combine multiple rewards. We hence ask: given a new reward function, is it possible to predict the RL outcomes without actually running RL on it? We answer this in the affirmative by introducing PoEM, a framework to predict the outputs of RL on a new reward function using a set of models already post-trained on other rewards. First, we show that if the new reward function can be written as a linear combination of existing ones, then the new policy in log-space can be written as a linear combination of the existing log-policies. Surprisingly, even in cases where the rewards are not linearly connected, we observe that often log-policies from RL training span an approximately low-rank subspace across rewards. To our benefit, the weighting coefficients for this combination can be estimated using only the reward or basis policy outputs on the samples. We turn these observations into an algorithm that takes post-trained models and a new reward function, and approximates the target RL policy without actually running any additional RL training. We experimentally validate our approach across synthetic and real rewards, spanning both text and image modalities.