The Best Optimizer Depends on Batch Size

A paper submitted to arXiv on 6 Oct 2026 (arXiv:2610.08975) finds that the best optimizer for language model pretraining changes with batch size even after extensive hyperparameter tuning, and that no principled scaling rule for Muon works consistently across training settings. The authors challenge the common practice of benchmarking adaptive optimizers at a single batch size, arguing that hyperparameter scaling rules do not preserve optimizer rankings as batch size and gradient noise change.

Computer Science Machine Learning Submitted on 6 Oct 2026 Title:The Best Optimizer Depends on Batch Size View PDF https://arxiv.org/pdf/2610.08975 HTML experimental https://arxiv.org/html/2610.08975v1 Abstract:A plethora of new adaptive optimizers are designed to efficiently estimate and use minibatch gradient statistics to shape parameter updates, but they are typically benchmarked at a single batch size. Hyperparameter scaling rules promise to preserve performance as batch size and gradient noise change, suggesting that the best optimizer at one batch size should remain the best at another. We challenge this approach to developing and evaluating optimizers by showing: 1 no principled scaling rule for Muon works consistently across training settings, and 2 the best optimizer for language model pretraining changes with batch size even after extensive hyperparameter tuning. Additional Features Current browse context: cs.LG References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer What is the Explorer? https://info.arxiv.org/labs/showcase.html arxiv-bibliographic-explorer Connected Papers What is Connected Papers? https://www.connectedpapers.com/about Litmaps What is Litmaps? https://www.litmaps.co/ scite Smart Citations What are Smart Citations? https://www.scite.ai/ Code, Data and Media Associated with this Article alphaXiv What is alphaXiv? https://alphaxiv.org/ CatalyzeX Code Finder for Papers What is CatalyzeX? https://www.catalyzex.com DagsHub What is DagsHub? https://dagshub.com/ Gotit.pub What is GotitPub? http://gotit.pub/faq Hugging Face What is Huggingface? https://huggingface.co/huggingface ScienceCast What is ScienceCast? https://sciencecast.org/welcome Demos Recommenders and Search Tools Influence Flower What are Influence Flowers? https://influencemap.cmlab.dev/ CORE Recommender What is CORE? https://core.ac.uk/services/recommender IArxiv Recommender What is IArxiv? https://iarxiv.org/about 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 https://info.arxiv.org/labs/index.html .