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arXiv · 2605.11172

Optimistic Dual Averaging Unifies Modern Optimizers

Thomas Pethick·Wanyun Xie·Roman Machacek·Volkan Cevher
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Abstract

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.

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Thomas Pethick, Wanyun Xie, Roman Machacek, Volkan Cevher. 2026-05-11. Optimistic Dual Averaging Unifies Modern Optimizers. https://arxiv.org/abs/2605.11172

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