Optimistic Dual Averaging Unifies Modern Optimizers
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.
| Authors | Thomas Pethick, Wanyun Xie, Roman Machacek et al. |
|---|---|
| Primary category | cs.LG |
| Published | 11 May 2026 |
| Last updated at source | 11 May 2026 |
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