Optimistic Dual Averaging Unifies Modern Optimizers
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910209867251712 |
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| author | Pethick, Thomas Xie, Wanyun Machacek, Roman Cevher, Volkan |
| author_facet | Pethick, Thomas Xie, Wanyun Machacek, Roman Cevher, Volkan |
| contents | We introduce SODA, a generalization of Optimistic Dual Averaging, which provides a common perspective on state-of-the-art optimizers like Muon, Lion, AdEMAMix and NAdam, showing that they can all be viewed as optimistic instances of this framework. Based on this framing, we propose a practical SODA wrapper for any base optimizer that eliminates weight decay tuning through a theoretically-grounded $1/k$ decay schedule. Empirical results across various scales and training horizons show that SODA consistently improves performance without any additional hyperparameter tuning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11172 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimistic Dual Averaging Unifies Modern Optimizers Pethick, Thomas Xie, Wanyun Machacek, Roman Cevher, Volkan Machine Learning We introduce SODA, a generalization of Optimistic Dual Averaging, which provides a common perspective on state-of-the-art optimizers like Muon, Lion, AdEMAMix and NAdam, showing that they can all be viewed as optimistic instances of this framework. Based on this framing, we propose a practical SODA wrapper for any base optimizer that eliminates weight decay tuning through a theoretically-grounded $1/k$ decay schedule. Empirical results across various scales and training horizons show that SODA consistently improves performance without any additional hyperparameter tuning. |
| title | Optimistic Dual Averaging Unifies Modern Optimizers |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.11172 |