Optimistic Dual Averaging Unifies Modern Optimizers
SODA unifies modern optimizers via optimistic dual averaging and improves them with a theoretical 1/k weight decay schedule requiring no tuning.
Published 2026Sydney Poster Session 3 · Wed, Dec 9, 10:00 AM–1:00 PM local time · Hall 1-4arXiv ↗OpenReview ↗
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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.