# Omega: Optimistic EMA Gradients

arXiv: https://arxiv.org/abs/2306.07905 · HTML: https://mlsanity.com/paper/2306.07905/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 18 references that are in the map.
- First posted on arXiv 13 Jun 2023.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [A Variational Inequality Perspective on Generative Adversarial Networks](https://mlsanity.com/paper/1802.10551/) (2018)
- [Reducing Noise in GAN Training with Variance Reduced Extragradient](https://mlsanity.com/paper/1904.08598/) (2019)
- [Connecting Generative Adversarial Networks and Actor-Critic Methods](https://mlsanity.com/paper/1610.01945/) (2016)
- [Stochastic Variance Reduction for Variational Inequality Methods](https://mlsanity.com/paper/2102.08352/) (2021)
- [Stochastic Gradient Descent-Ascent and Consensus Optimization for Smooth Games: Convergence Analysis under Expected Co-coercivity](https://mlsanity.com/paper/2107.00052/) (2021)
- [Stochastic Gradient Descent-Ascent: Unified Theory and New Efficient Methods](https://mlsanity.com/paper/2202.07262/) (2022)
- [Revisiting Stochastic Extragradient](https://mlsanity.com/paper/1905.11373/) (2019)
- [Last-Iterate Convergence of Optimistic Gradient Method for Monotone Variational Inequalities](https://mlsanity.com/paper/2205.08446/) (2022)
- [Stochastic Extragradient: General Analysis and Improved Rates](https://mlsanity.com/paper/2111.08611/) (2021)
- [A Lagrangian Duality Approach to Active Learning](https://mlsanity.com/paper/2202.04108/) (2022)
- [Smooth Monotone Stochastic Variational Inequalities and Saddle Point Problems: A Survey](https://mlsanity.com/paper/2208.13592/) (2022)

## Abstract (arXiv)

Stochastic min-max optimization has gained interest in the machine learning community with the advancements in GANs and adversarial training. Although game optimization is fairly well understood in the deterministic setting, some issues persist in the stochastic regime. Recent work has shown that stochastic gradient descent-ascent methods such as the optimistic gradient are highly sensitive to noise or can fail to converge. Although alternative strategies exist, they can be prohibitively expensive. We introduce Omega, a method with optimistic-like updates that mitigates the impact of noise by incorporating an EMA of historic gradients in its update rule. We also explore a variation of this algorithm that incorporates momentum. Although we do not provide convergence guarantees, our experiments on stochastic games show that Omega outperforms the optimistic gradient method when applied to linear players.