arXiv:2505.01423v2 Announce Type: replace-cross Abstract: Efficient computation of min-max problems is a central question in optimization, learning, games, and control. Arguably the most natural algorithm is gradient-descent-ascent (GDA). However, since the 1970s, conventional wisdom has argued that GDA fails to converge even on simple problems. This failure spurred an extensive literature on modifying GDA with additional building blocks such as extragradients, optimism, momentum, anchoring, etc. In contrast, we show that GDA converges in its original form by simply using a judicious choice of
This research provides a fundamental re-evaluation of a long-standing assumption in optimization theory, potentially unlocking new efficiencies for foundational AI algorithms.
Improved convergence for gradient-descent-ascent (GDA) could significantly enhance the training and stability of AI models, particularly in adversarial settings and multi-agent systems.
The conventional wisdom regarding GDA's failure to converge is challenged, suggesting that simpler, more efficient optimization methods might be viable without complex modifications.
- · AI researchers
- · Machine learning practitioners
- · Developers of multi-agent systems
- · Optimization software providers
- · Researchers focused on complex GDA modifications
This could lead to simpler, more robust, and potentially faster training for various AI and optimization problems.
The re-validation of GDA might simplify the theoretical and practical landscape for designing and implementing competitive learning and game theory algorithms.
More stable and efficient optimization could accelerate the development and deployment of complex AI agents and autonomous systems across various industries.
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Read at arXiv cs.LG