Smooth minimax games often proceed by simultaneous or alternating gradient updates. Although algorithms with alternating updates are commonly used in practice, the majority of existing theoretical analyses focus on simultaneous algorithms for convenience of analysis. In this paper, we study alternating gradient descent-ascent (Alt-GDA) in minimax games and show that Alt-GDA is superior to its simultaneous counterpart (Sim-GDA) in many settings. We prove that Alt-GDA achieves a near-optimal local convergence rate for strongly convex-strongly concave (SCSC) problems while Sim-GDA converges at a much slower rate. To our knowledge, this is the first result of any setting showing that Alt-GDA converges faster than Sim-GDA by more than a constant. We further adapt the theory of integral quadratic constraints (IQC) and show that Alt-GDA attains the same rate globally for a subclass of SCSC minimax problems. Empirically, we demonstrate that alternating updates speed up GAN training significantly and the use of optimism only helps for simultaneous algorithms.
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This content will become publicly available on July 19, 2025
Stochastic Smoothed Gradient Descent Ascent for Federated Minimax Optimization
In recent years, federated minimax optimization has attracted growing interest due to its extensive applications in various machine learning tasks. While Smoothed Alternative Gradient Descent Ascent (Smoothed-AGDA) has proved successful in centralized nonconvex minimax optimization, how and whether smoothing techniques could be helpful in a federated setting remains unexplored. In this paper, we propose a new algorithm termed Federated Stochastic Smoothed Gradient Descent Ascent (FESS-GDA), which utilizes the smoothing technique for federated minimax optimization. We prove that FESS-GDA can be uniformly applied to solve several classes of federated minimax problems and prove new or better analytical convergence results for these settings. We showcase the practical efficiency of FESS-GDA in practical federated learning tasks of training generative adversarial networks (GANs) and fair classification.
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- NSF-PAR ID:
- 10538566
- Publisher / Repository:
- Proceedings of The 27th International Conference on Artificial Intelligence and Statistics
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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