چکیده
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.
متن کامل
Computer Science > Machine Learning arXiv:2609.30226v1 (cs) [Submitted on 24 Sep 2026] Title:PoEM: Predicting RL Outcomes from Existing Policies Authors:Kimia Hamidieh, Giannis Daras, Antonio Torralba View a PDF of the paper titled PoEM: Predicting RL Outcomes from Existing Policies, by Kimia Hamidieh and 2 other authors View PDF HTML (experimental) Abstract: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. Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computation and Language (cs.CL); Computer Vision and Pattern Recognition (cs.CV) Cite as: arXiv:2609.30226 [cs.LG] (or arXiv:2609.30226v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2609.30226 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Kimia Hamidieh [view email] [v1] Thu, 24 Sep 2026 17:50:25 UTC (1,918 KB) Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) IArxiv recommender toggle IArxiv Recommender (What is IArxiv?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)